Answers
According to the Pythagorean Theorem 1. b = 122. a = 1/4 for more detail scroll down.
What is the Pythagorean Theorem?The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. The theorem can be written as an equation: c^2 = a^2 + b^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
1. To use the Pythagorean theorem to find the length of side b, you can use the equation: c^2 = a^2 + b^2. In this case, c = 15 and a = 9, so you can substitute those values into the equation and solve for b:
15^2 = 9^2 + b^2
225 = 81 + b^2
b^2 = 225 - 81
b^2 = 144
b = sqrt(144)
b = 12
2. In the second case a is unknown and the other two sides are in fraction form, so we can use Pythagorean theorem to find the value of a.
The equation is c^2 = a^2 + b^2
(5/12)^2 = a^2 + (4/12)^2
25/144 = a^2 + 16/144
a^2 = 9/144
a = sqrt(9/144)
a = sqrt(1/16)
a = 1/4
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Related Questions
Use a graphing utility to graph the function to approximate (to two decimal places) any relative minima or maxima of the function. (If an answer does not exist, enter DNE.)
h(x) = x3 − 6x2 + 16
Answers
Answer:Use a graphing utility to graph the function and approximate (to two decimal places) any relative minima or maxima. (If an answer does not exist, enter DNE.)
f
(
x
)
=
x
3
−
3
x
2
−
x
+
3
relative minimum
(
x
,
y
)
=
c
Step-by-step explanation:
a subscript n baseline equals area of the shaded region in term n. a subscript 1 baseline equals 4 drag the numbers and symbols to the line to create an expression that represents the recursive definition of a subscript n baseline.
Answers
The value of a sub n, we must start with the previous value of a sub n minus 1, and then add four to it.
a_n = a_n-1 + 4
This formula is used to represent the recursive definition of a subscript n baseline. The formula is read as "a sub n is equal to a sub n minus 1 plus 4". This means that in order to find the value of a sub n, we must start with the previous value of a sub n minus 1, and then add four to it.
For example, let's say we want to find the value of a sub 5. We can start by looking at the previous value of a sub 4, which is 12. We then add four to 12, giving us 16. Therefore, a sub 5 is equal to 16.
To calculate this in a more general way, we can say that a sub n is equal to 4 times n minus 1, plus the initial value of a sub 1. That is, a sub n is equal to 4 (n-1) + 4. For example, a sub 5 is equal to 4 (5-1) + 4, which is equal to 16.
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there's a simple rule that allows us to convert a number from the binary system to the decimal. for example, 42
Answers
The rule for converting a binary number to Decimal point is to multiply each binary digit by two to the power of its position from the right, and add all the resulting values together. For example, 42 in binary is 101010, so the conversion is 1*2^5 + 0*2^4 + 1*2^3 + 0*2^2 + 1*2^1 + 0*2^0 = 32 + 8 + 2 = 42.
1. Start with the rightmost binary digit (the ones place) and multiply it by 2^0.
2. Move to the next digit to the left (the twos place) and multiply it by 2^1.
3. Continue this process until you reach the leftmost binary digit.
4. Add all the products together to get the decimal equivalent.
For example, 42 in binary is 101010, so the calculations are: 0*2^0 + 1*2^1 + 0*2^2 + 1*2^3 + 0*2^4 + 1*2^5 = 0 + 2 + 0 + 8 + 0 + 32 = 42.
The rule for converting a binary number to decimal is to multiply each binary digit by two to the power of its position from the right, and add all the resulting values together. To do this, start with the rightmost binary digit (the ones place) and multiply it by 2^0. Then move to the next digit to the left (the twos place) and multiply it by 2^1. Continue this process until you reach the leftmost binary digit. Add all the products together to get the decimal equivalent. For example, 42 in binary is 101010, so the calculations are:
0*2^0 + 1*2^1 + 0*2^2 + 1*2^3 + 0*2^4 + 1*2^5 = 0 + 2 + 0 + 8 + 0 + 32 = 42.
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A principal of $5000 is invested in an account paying an annual rate of 7%. Find the amount in the account after 6 years if the account is compounded semiannually,quarterly, and monthly
Answers
The amount in the account after 6 years if the account is compounded semiannually, quarterly, or monthly is 6724.4, 6736.7, and 6664.9.
What is compound interest?
Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
Here, we have
Given: A principal of $5000 is invested in an account paying an annual rate of 7%.
We have to find the amount in the account after 6 years if the account is compounded semiannually, quarterly, or monthly.
A) Compounded semi-annually:
= 5000*(1 + 0.05/2)^(2*6) = 6724.4
B) Compounded quarterly:
= 5000*(1 + 0.05/4)^(4*6) = 6736.7
C) Compounded monthly:
= 5000*(1 + 0.05/12)^(12*6) = 6664.9
Hence, the amount in the account after 6 years if the account is compounded semiannually, quarterly, or monthly is 6724.4, 6736.7, and 6664.9.
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−4≤−2(y−1)<2
Step 2 of 2 : Graph the solution set.
Answers
The solution set for the inequality -4≤-2(y-1)<2 is the set of all y-values that make the inequality true.
To graph the solution set, we can begin by plotting the inequality as an inequality on the y-axis, and then identifying the solutions that make the inequality true:
First, we can simplify the left side of the inequality: -4≤-2(y-1)
Next, we can solve for y by isolating y: -4/2≤y-1
Then we can add 1 to both sides of the inequality: -2≤y
Now, we can graph the inequality y ≥ -2, which is a line that is equal to or greater than -2.
On the right side, we have -2(y-1)<2
2(y-1)>-2
y-1>-1
y>-1
So we can graph the inequality y>-1, which is a line that is greater than -1.
So the solution set is the region above the line y=-2 and below the line y=-1. The region is a strip between two lines.
It is important to note that the solution set doesn't include the values of the lines, as the inequality is strict, not inclusive.
Jenna earned $125 of interest by leaving her money in the bank for 4 years at a 5% interest rate. What was the principle amount that Jenna put in the bank
Answers
The principal amount that Jenna put in the bank is $625.
What is simple interest?Borrowers must pay lenders simple interest as a fee in exchange for a loan. Compound interest is excluded from the calculation and just the original principal is used. Simple interest applies to all loans, not just specific ones. Additionally, it refers to the kind of interest that banks give their customers on their savings accounts.
Given interest earned = $125
time = 4 years
rate = 5%
let the principal be p
this is the case of simple interest,
SI = (p*r*t)/100
substitute the values
125 (p* 5 * 4)/100
125 x 100 = p x 20
p = 12500/20
p = $625
Hence principal amount is $625.
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Return to the calculator tab, and click the clear button to begin A new calculation. this time, you'll check for valid triangles given two angles and the side between themUnder sides, enter 5 for a. under angles, enter 30 for b and 50 for c. then click calculate. how many triangles can be created from the given conditions?
Answers
There can be one valid triangle created from the given conditions of side a being 5 and angles b and c being 30 and 50 degrees respectively.
To calculate how many triangles can be created from two angles and a side, the user must click the “calculator” tab. Once this is done, it is important to click the “clear” button to begin a new calculation. After this, the user must enter the side (a) under the “sides” section, and the angles (b and c) under the “angles” section. This example used 5 for the side, 30 for angle b, and 50 for angle c. Once the information is entered, the user must click “calculate”. This will result in a valid triangle being created from the given conditions. It is important to note that if the user entered different values, a different result may be obtained. Therefore it is important to ensure that the values entered are the desired ones. Additionally, if the sum of the angles entered are not equal to 180 degrees, then no valid triangle can be created.
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you have found the following ages( in years)of 5 porcupines?
what is the standard deviation? round your answers to the nearest tenth
Answers
The standard deviation is 4.0, while mean is 10.2.
What is standard deviation?Data dispersion in regard to the mean is quantified by a standard deviation, or. Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
Mean = 10.2
The standard deviation is 4.0.
Age in the mean is the average age.
Mean = (16 + 10 + 5 + 7 + 13)/5
Mean = 51/5 = 10.2
The variance's square root will reveal the standard deviation.
(16 - 10.2) + (10 -10.2) + (5-10.2) + (7-10.2)+( 13-10.2) ( 13-10.2)
5.8 + 0.2 -5.2 - 3.2 + 2.8
each number into squares
33.64 + 0.04 + 27.04 + 10.24 + 7.84
Variation: 78.8/5 = 15.76
Standard deviation = 3.969 = 4.0.
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The complete question is,
16, 10, 5, 7, 13
What is the porcupines' typical age based on your sample? Where can I find the standard deviation? in a circle tenths of a percent, closest.
Morgan and her children went into a grocery store and she bought $10 worth of peaches and mangos. Each peach costs $1 and each mango costs $2. She bought a total of 8 peaches and mangos altogether. Graphically solve a system of equations in order to determine the number of peaches, 2, and the number of mangos, y, that Morgan bought.Morgan and her children went into a grocery store and she bought $10 worth of peaches and mangos. Each peach costs $1 and each mango costs $2. She bought a total of 8 peaches and mangos altogether. Graphically solve a system of equations in order to determine the number of peaches, ~, and the number of mangos, y, that Morgan bought.
pls show the asnwer with a graph clear pleaseee
Answers
On solving the linear equations x + y = 8 and x + 2y = 10, the value for peaches and mangoes is 6 and 2 respectively.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
Let the number of peaches be = x
Let the number of mangoes be = y
Total number of peaches and mangoes Morgan bought = 8
The linear equation for Morgan if she has bought 8 fruits -
x + y = 8 ....(1)
The cost of one peach is = $1
The cost of one mango is = $2
Total amount for Morgan to spend is = $ 10
The linear equation for Morgan if she has $10 to spend -
x + 2y = 10 ....(2)
Subtracting equation (1) from (2) -
x + 2y - (x + y) = 10 - 8
x + 2y - x - y = 2
y = 2
Substituting the value of y in equation (1) -
x + y = 8
x + 2 = 8
x = 8 - 2
x = 6
Now, to check equate the values of x and y in equation (2) -
x + 2y = 10
6 + 2(2) = 10
6 + 4 = 10
10 = 10
The graph is also plotted and it can be seen that the equations intersect at point (6,2).
Therefore, Morgan bought x = 6 peaches and y = 2 mangoes.
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Showing the amount of each monthly payment that goes toward principal and interest for the first three months of the loan.
A home mortgage of $140,000 with a fixed APR of 6% for 30 years.
Answers
For each month, you will pay $700 in interest.
What is simple interest?
Simple interest is a method of calculating the interest on a loan or investment where the interest is determined based on the initial principal (the original amount of the loan or investment) and a fixed interest rate. The interest is calculated based on the amount of time the principal is invested or borrowed.
The formula for simple interest is:
I = Prt
Where:
I is the interest
P is the principal
r is the annual interest rate (expressed as a decimal)
t is the time (in years)
For example, if you have a home mortgage of $140,000 with a fixed APR of 6% for 30 years, the simple interest calculation for each month will be:
I = (140,000 x 0.06) / 12 = $700
Hence, for each month, you will pay $700 in interest.
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x f(x)=2x−1 g(x)=12x −2 −34 −1 −1 −12 −12 0 0 0 1 1 12 2 3 1
Answers
The value of the composite function (f + g)(x) = 14x - 3
How to determine the composite functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = 2x - 1
g(x) = 12x - 2
The composite function (f + g)(x) is calculated as
(f + g)(x) = f(x) + g(x)
Substitute the known values in the above equation, so, we have the following representation
(f + g)(x) = 2x - 1 + 12x - 2
Evaluate the like terms
(f + g)(x) = 14x - 3
Hence, the composite function is (f + g)(x) = 14x - 3
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Complete question
Consider the functions f(x)=2x−1 g(x)=12x −2
Calculate (f + g)(x)
refer to exhibit 26-5. the data illustrate that the firm in question is a group of answer choices price taker (perfectly competitive firm). factor price taker. price searcher (monopolist, oligopolist, etc.). factor price searcher.
Answers
According to the given data, the firm in question must be a price-taker, which is a perfectly competitive firm.
A price-taker is basically an individual or a particular company that must accept prices that are prevailing in a market and lacks the market share to be able to influence the market price on its own. All the economic participants can be considered to be price-takers in a market consisting of perfect competition.
In the given data set, the marginal revenue is constant which is very typical for competitive firms. This happens because the market decides the optimal price level and companies do not have much say over the price. This is a way by which they can maximize profits.
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The picture shows two ladders propped against
facing walls. The end of the first ladder is 5m
above the base of the second wall. The second
ladder is 5m above the base of the first wall.
5m
Can you work out at what height the
ladders cross?
Are you surprised that we don't need to know
the distance between the two walls?
5m
5m
10m
Answers
This means E is the same fraction of the b metres above the floor, so is ab/a+b metres above the floor.
What is equal angles ?
Equal angles can be defined as the angles which are equal .
Given ,
The picture shows two ladders propped against facing walls. The end of the first ladder is 5m above the base of the second wall. The second
ladder is 5m above the base of the first wall.
the angles ∠BAD and ∠ADC are alternate angles, and therefore equal. Likewise, angles ∠ABC and BCD are also alternate and therefore equal.
∠BEA and ∠CED are opposite, which means that they are equal. You can see these equal angles in the diagram on the right.
This means that the triangles ABE and DCE have the same angles as each other, and are therefore similar.
so,
This means:
AE/ED=AB/DC=5m/10m=1/2
Therefore AE=1/3 AD.
This means E is 1/3 of the way up from the floor to D, so is at a height of
This means E is 13 of the way up from the floor to D, so is at a height of 10m/ 3=3 1/3m
If instead B is a metres above the floor, then:
AE/ED=AB/DC=a/10
Therefore AE=a/10+a AD.
This means E is the same fraction of the 10m above the floor, so is 10a/10+a metres above the floor.
If instead D is b metres above the floor, then:
AE/ED=AB/DC=a/b
Therefore AE=a/a+b AD.
This means E is the same fraction of the b metres above the floor, so is ab/a+b metres above the floor.
Therefore, This means E is the same fraction of the b metres above the floor, so is ab/a+b metres above the floor.
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In 2007, there were 120 houses in a subdivision. The number of houses in the subdivision increased by approximately 8% per year from 2007-2017. Enter the BEST estimate of the number of houses in the subdivision in 2017.
Answers
Answer:
216
Step-by-step explanation:
2017-2007=10
8*10=80
80% of 120= 96
120+96=216
•25 POINTS•
Guessers will be reported.
Answers
Answer:
Step-by-step explanation:
If its going by 4 each time then it should be 21 but for n its 6
A pyramid is composed of six isosceles triangles and a hexagonal base. Each isosceles triangle has a height of 6 in. and a base of 10 in. The area of the hexagonal base is 259.8 in².
What is the surface area of the pyramid?
Answers
The surface area of the hexagonal pyramid is S = 575.9 inches²
What is the surface area of the pyramid?The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid
Surface Area of Pyramid = B + ( 1/2 ) ( P x h )
Given data ,
Let the surface area of the hexagonal pyramid be S
Now , the equation will be
The base of the hexagonal pyramid a = 10 inches
The height of the lateral face h = 6 inches
The base area of the pyramid = ( 3√3 / 2 )a²
The lateral surface area of the pyramid = 3a √ ( ( 3a²/4 ) + h² )
So , The total surface area of hexagonal pyramid is S
S = ( 3√3 / 2 )a² + 3a √ ( ( 3a²/4 ) + h² )
Substituting the values in the equation , we get
The base area of the pyramid = 259.8 inches²
The lateral surface area of the pyramid = 3 ( 10 ) √ ( 3 ( 100/4 ) + 36 )
On simplifying the equation , we get
The lateral surface area of the pyramid = 316.1 inches²
Total surface area of hexagonal pyramid S = 259.8 inches² + 316.1 inches²
The total surface area of hexagonal pyramid S = 575.9 inches²
Hence , the surface area of the pyramid is 575.9 inches²
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Kristin is the manager of a local bank where there are currently 6,700 checking accounts. She wants to collect a sample of checking accounts in order to compile information about customer behavior at the bank. Several different sampling scenarios are described below. Identify the type of sample used in each scenario. Choose from:A. Simple random sample (SRS)B. Stratified sampleC. Cluster sampleD. Systematic sampleE. Convenience sample
Answers
Selecting elements from an ordered sampling frame is a statistical approach used in survey methodology known as systematic sampling and in the given situation (D) systematic sampling would be the best.
What is a Systematic sample?Systematic sampling is a statistical technique used in survey methodology that involves choosing components from an ordered sampling frame.
An equiprobability approach is the most typical type of systematic sampling.
This method treats the list's evolution in a cyclical manner, returning to the top after it has been completed.
The sampling process begins with the random selection of one element from the list, followed by the selection of every kth element in the frame, where k is the sampling interval, also known as the skip, and is equal to:
k = N/n.
Therefore, in the given situation (D) systematic sampling would be the best.
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Charisse is adding a weather protective stain to the exterior of her shed. She measures the walls to be 8 feet long and 6 feet high. There are no windows on the shed, and the roof and the bottom do not need the protective stain. Additionally, the front door, which is 3 feet wide and 6 feet high, does not need to be stained. What is the total surface area Charisse needs to stain? Multiple choice question. cross out A) 66 ft2 cross out B) 144 ft2 cross out C) 174 ft2 cross out D) 192 ft2
Answers
Charisse needs to stain an area of 174 square feet.
How to calculate the total surface area Charisse needs to stain?
The total surface area of the shed's walls that needs to be stained is the sum of the areas of the four walls, minus the area of the front door.
The area of one wall is 8 feet × 6 feet = 48 square feet.
Since there are 4 walls, the total area of all walls is 48 square feet × 4 = 192 square feet.
The area of the front door is 3 feet × 6 feet = 18 square feet
Now we can subtract the area of the door from the total area of all walls:
192 square feet - 18 square feet = 174 square feet
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Explain how the commutative property is applied when finding GCF using factor trees
Answers
Answer: The commutative property is applied when finding the GCF by taking the factor that has more than 1 factor other than itself(composite) and multiply them until you can no longer multiply. You then take the factors that are in common and multiply them.
Step-by-step explanation: my teacher made me use this way.
Luke stacked seven pieces of wood on top of each other. IF each piece was ten over 12 of a foot tall, how tall was his pile?
Answers
The length of the pile of the piece of woods put together by Luke would be = 5.8ft
What is a pile?A pile of objects such as wood is defined as the combination of two or more different parts of the object in an orderly form.
The number of woods stacked by Like = 7
The length of each wood = 10/12ft
Therefore the length of the whole pile of wood ;
= 7×10/12
= 70/12
= 5.8ft
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V-7>24 inequality simplify your answer as much as possible
Answers
To simplify the inequality, we need to perform the same mathematical operation on both sides of the inequality.
V-7 > 24
Add 7 to both sides of the inequality:
V > 31
So, the simplified inequality is V > 31.
Your bag of rice says to mix 1 cup of rice to 2 cups of water. How many cups of water would be needed to mix with 1/3 cup of rice?
Answers
1/3 cup of rice would be 1/3 rice ratio, we need to find the ratio of water for 1/3 rice.
x will stand for water.
1/(3*x) equals 1/2
Multiply by 2x
The answer is 2/3
What proportion of the variation iny can be explained by the variation in the values of x? Report answer as percentage accurate to one decimal place: (If the answer is 0.84471 _ then it would be 84. 5%6 .. syou would enter 84.5 without the percent symbol:) r^2 =
Answers
A. To find the correlation coefficient, we can use the formula:
r = (n * Σxy - Σx * Σy) / √ ((n * Σx² - (Σx)²) * (n * Σy² - (Σy)²))
Where n is the number of data points.
Plugging in the values for the given data set:
r = (12 * 712.94 - 1451.9 * 511.6) / √ ((12 * 1297.14 - 1451.9²) * (12 * 636.35 - 511.6²))
r = -0.636
So, the correlation coefficient is -0.636.
B. To find the proportion of the variation in y that can be explained by the variation in x, we can use the formula:
r² = r²
r² = (-0.636) ²
r² = 0.40496
So, 40.5% of the variation in y can be explained by the variation in the values of x.
C. To find the regression line,we can use the formula:
y = a + bx
Where a is the y-intercept and b is the slope of the line.
To find b, we can use the formula:
b = (n * Σxy - Σx * Σy) / (n * Σx² - (Σx)²)
Plugging in the values for the given data set:
b = (12 * 712.94 - 1451.9 * 511.6) / (12 * 1297.14 - 1451.9²)
b = -0.856
To find a, we can use the formula:
a = (Σy - b * Σx) / n
Plugging in the values for the given data set:
a = (511.6 - -0.856 * 1451.9) / 12
a = 55.54
So, the regression line is:
y = 55.54 - 0.856x
The negative slope of -0.856 means that as x increases, y decreases, which is consistent with the negative correlation coefficient of -0.636. The y-intercept of 55.54 means that when x is 0, y is predicted to be 55.54.
Complete question:
Run a regression analysis on the following bivariate set of data with y as the response variable.
x y
43.8 54.1
41.3 51.2
35.3 60.1
48.1 44.9
42.8 51.8
44.7 50.8
39.4 56.6
38.2 56.6
40.7 53.5
45.3 51.1
45 46.7
41.1 52.2
A. Find the correlation coefficient and report it accurate to three decimal places.
r = ________________
B. What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place. (If the answer is 0.84471, then it would be 84.5%...you would enter 84.5 without the percent symbol.)
r² =_______________ %
C. Based on the data, calculate the regression line (each value to three decimal places)
y =___________ x + _______________
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a father is now four times as old as his son. five years ago, he was exactly one and a half times as old as his son ten years from now. find the sum of their present ages
Answers
Answer:
sum of their present ages is 5 + 20 = 25 years.
Step-by-step explanation:
The father's current age is 4x (because he is four times as old as his son)
Five years ago, the father's age was (4x - 5) and the son's age was (x - 5)
Ten years from now, the father's age will be (4x + 10) and the son's age will be (x + 10)
From the second statement, we know that:
(4x - 5) = 1.5(x - 5)
And from the third statement, we know that:
(4x + 10) = 1.5(x + 10)
We can solve these equations simultaneously to find the present ages of the father and the son.
Solving the first equation:
4x - 5 = 1.5x - 7.5
2.5x = 12.5
x = 5
So the son's current age is 5 years old.
The father's current age is 4x = 4(5) = 20 years old.
So, the sum of their present ages is 5 + 20 = 25 years.
Suppose you are working with a data set that is normally distributed, with a mean of 300 and a standard deviation of 41. Determine the value of X from the following information
Answers
The value of X that is less than 17% of the values is given as follows:
X = 339.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 300, \sigma = 41[/tex]
The value of X that is less than 17% of the measures is X when Z has a p-value of 0.83, so X when Z = 0.955, hence:
0.955 = (X - 300)/41
X - 300 = 0.955 x 41
X = 339.
Missing InformationThe problem asks for the value of X that is less than 17% of the values.
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On a 800km trip, Ryan's family travelled at 90km/h for the first 600km and 100km/h for
the remainder of the journey. If they had travelled 90km/h for the entire journey, how
much longer would the trip have taken?
Answers
The trip would have taken 8.89 hours instead of 8 hours.
How to calculate distance traveled?Distance traveled can be calculated by multiplying the speed at which the object is traveling by the amount of time the object has been in motion.
For example, if a car is traveling at 60 miles per hour for two hours, the distance traveled would be 120 miles.
To calculate distance more accurately, you can use the formula d = rt, where d is the distance, r is the rate of speed, and t is the time in which the object has been in motion.
It is important to note that this formula assumes a constant speed throughout the duration of the journey.
It is also important to remember that the unit of measurement used for both the speed and the time must be the same. Therefore, if the speed is in miles per hour, the time must also be in hours.
In order to calculate this, we need to first calculate the time it took for the family to travel the first 600km at 90km/h. This can be calculated using the formula:
Time = Distance / Speed
So, the time it took for the family to travel the first 600km is:
Time = 600km / 90km/h = 6.67 hours
Then, we can calculate the time it would have taken for the family to travel 800km at 90km/h using the same formula:
Time = 800km / 90km/h = 8.89 hours
Therefore, the trip would have taken 8.89 hours, which is 0.89 hours longer than the original trip which took 8 hours.
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Using separation of variables, solve the differential equation,
(3+x^10)(????y/????x) = x^9/y
Use C to represent the arbitrary constant.
y^2=_____________
Answers
The value of y² is 1/5 ln(3+x¹⁰) + C
What is the separation of variables?
Separation of variables, in mathematics, is any of several strategies for rewriting equations so that each of two variables appears on a different side of the problem. These strategies are used to solve ordinary and partial differential equations.
Here, we have
Given: (3+^10)(/) = ^9/
We have to solve the differential equation by using the separation of variables.
Rewrite as y dy = x⁹/3+x¹⁰ dx
As (3+x¹⁰)' = 10x⁹, we solve
y²/2 = 1/10 ln(3+x¹⁰) + C
y² = 1/5 ln(3+x¹⁰) + 2C
Since C is any constant, y² = 1/5 ln(3+x¹⁰) + C
Hence, the value of y² is 1/5 ln(3+x¹⁰) + C
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please help due tn!!
Answers
Answer:
Step-by-step explanation:
Answer:
244.5
Step-by-step explanation:
Use A Budgeting Calc This Anwser Is Correct
HELP ME OUT PLEASE!!!!!!
What is the range of h?
All real numbers greater than or equal to -5
All real numbers greater than or equal to 0
All real numbers
All real numbers greater than or equal to -2
Answers
The range of the function h(x) is -
"all real numbers greater than or equal to -2"
What are functions?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.Any subset of the Cartesian product of two sets X and Y defines a binary relation R ⊆ X × Y between these two sets.A binary relation is univalent (also called right-unique) if -[tex]${\displaystyle \forall x\in X,\forall y\in Y,\forall z\in Y,\quad ((x,y)\in R\land (x,z)\in R)\implies y=z.}[/tex]
A binary relation is total if -[tex]${\displaystyle \forall x\in X,\exists y\in Y,\quad (x,y)\in R.}[/tex]
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is a table representing a function.
Range is defined as the set of all possible values of f(x). Therefore, all real numbers greater than or equal to -2, will belong to the range of the function h(x).
Therefore, the range of the function h(x) is -
"all real numbers greater than or equal to -2"
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5 in thick slice is cut off the top of a cube resulting in a rectangular box that has volume 135in^3. find the side length of the original cube
Answers
The side length of the original cube is 8.90 inches
How to find the side length of the original cube?Let x be the side length of the original cube. After cutting off the top, the remaining rectangular box has dimensions of x-5, x-5, and x.
The volume of this rectangular box is:
(x-5)(x-5)(x) = x³ - 10x² + 25x
x³ - 10x² + 25x = 135
x³ - 10x² + 25x -135 = 0
Use cubic formula.
x =8.90
Therefore, the side length of the original cube is 8.90 inches
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