a) The sinusoidal function is y = 7·sin(π/15(t - 2.5)) + 9
b) The height of the shorts at t = 10 minute is approximately 6 meters
The above answers were arrived at as follows
a) The general form of a sinusoidal equation is presented as follows;
y = A·sin(B(t - h)) + k
Where;
A = The amplitude of the graph of the function
The period, T = 2·π/B
h = The horizontal shift
k = The vertical shift
The maximum height of the blade = 16 meters
The minimum height of the blade = 2 meters
The time the blade moves from maximum height to minimum height = 25 s - 10 s = 15 s
Therefore, the time it takes the blade to move from maximum height to minimum height, the period, T= 2 × 15 s = 30 s
Therefore;
B = 2·π/30 = π/15
B = π/15
When B·(t - h) = π/2, t = 10
Therefore;
(π/15)·(10 - h) = π/2
10 - h = 15/2
h = 10 - 15/2 = 2.5
The horizontal shift, h = 2.5
The amplitude, A = (Max - Min)/2
∴ A = (16 - 2)/2 = 7
A = 7
The vertical shift, k = Min - (-Amplitude)
∴ k = 2 - (-7) = 9
The vertical shift, k = 9 Up
Therefore, the equation of the sinusoidal equation that describes the height of shorts in terms of time is given by plugging in the values of the variables, A, B, h, and k to get the following equation;
y = 7·sin(π/15·(t - 2.5)) + 9
b) The height of the shorts at exactly, t = 10 minutes = 600 seconds, is given as follows;
y = 7·sin(π/15·(t - 2.5)) + 9
10 minutes = 600 seconds
When t = 10 minutes = 600 seconds
∴ y = 7·sin(π/15(600 - 2.5)) + 9 = 5.5 ≈ 6
The height of the shorts at exactly t = 10 minutes ≈ 6 meters.
Get more information on sinusoidal functions here;
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what is the area of the figure below?
Answer:
15x^9
Step-by-step explanation:
A=l x w
5x^4 times 3x^5 is basically 3*5*x^4*x^5
when you multiply exponents with the same base, you add the exponents, so it becomes 15x^9
Match the two numbers with their least common multiple (LCM).
Answer:
Step-by-step explanation:
6 and 4 : LCM is 12
6 and 8: LCM is 24
6 and 10 LCM is 30.
Which represents a unit rate?
Answer:
A unit rate is a rate with 1 in the denominator. If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.
Example 2 Determine the sum of the first 100 terms for the series 2+5+ 8 + ...
Answer:
15050
Step-by-step explanation:
Hello!
So basically, this arithmetic sequence follows the rule (3n-1). What you are looking for is the summation of (3n-1) with a lower limit of 1 and an upper limit of 100. This, plugging it into a calculator (etc. symbolab) or even calculating it manually, we get ∑↑100↓n=1⇒3n-1=15050.
Answer:
S₁₀₀ = 15050
Step-by-step explanation:
There is a common difference between consecutive terms
5 - 2 = 8 - 5 = 3
This indicates the sequence is arithmetic with sum to n terms
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = 2 and d = 3 , then
S₁₀₀ = [tex]\frac{100}{2}[/tex] [ (2 × 2) + (99 × 3) ]
= 50 (4 + 297)
= 50 × 301
= 15050
The value of w???????
Answer:
Step-by-step explanation:
The angle bisector of a triangle divides the opposite side in 2 segments that are proportional to the other 2 sides of the triangle. Namely:
[tex]\frac{15}{18}=\frac{w}{30}[/tex] and cross multiply.
18w = 450 so
w = 25
Mark made a sandwich that was 5 inches long and 7 inches high. If he cuts
the sandwich in half, what would be the diagonal length of the sandwich?
Explanation
a sanwich which is most commonly a square, has the side lengths of 5 and 5.
cuting this in half will give you a 45-45-90 triangle
the legs will be measure of x, and the hypotonuse will be x[tex]\sqrt{2}[/tex]
so the hypotonuse is 5[tex]\sqrt{2}[/tex]
The diagonal length of the sandwich after it is cut in half is approximately 6.106 inches.
How to calculate the lengthUsing the Pythagorean theorem, we can calculate the diagonal length as follows:
diagonal² = length² + height²
diagonal² = (5 inches)² + (3.5 inches)²
diagonal² = 37.25 inches²
Taking the square root of both sides, we find:
diagonal = √37.25 inches
Calculating the square root of 37.25, we get:
diagonal ≈ 6.106 inches
Therefore, the diagonal length of the sandwich after it is cut in half is approximately 6.106 inches.
Learn more about length
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how do i know when an equation has 1 solution
Answer:
you can plug it back into the original equation to see if it fits the solution. if not then you have another solution you need to solve for.
Answer:
if we're talking on linear equations, then the two equations would intersect at one point. or when you solve it, it'll be only 1 number that can fit that equation.
p.s.: sub to #gauthmath# sub reddit if ya can ^^
The perimeter of a rectangle is 74 inches. If the length is five more than the width, what are the rectangle's measurements?
Answer:
P=2(74)+2(5)
148+10=158
BRAINLEST IF CORRECT!!!!
x + 133 = 180
x = 180 - 133 (Linear Pair)
x = 47
Therefore x° = 47°
Answered by Gauthmath must click thanks and mark brainliest
Answer:
47
Step-by-step explanation:
reason: Being sum of supplement angle
The Chesapeake Bay holds about 18 trillion gallons of water. The bay covers 4,480 square miles or 2,867,200 acres. Each acre can hold 750,000 oysters. Each oyster can filter 50 gallons of water each day. Can there be enough oysters to filter the whole Chesapeake Bay in one day
Answer:
There are enough oysters
Step-by-step explanation:
Given
[tex]Volume = 18\ trillion\ gallon[/tex]
[tex]Area = 2867200\ acre[/tex]
[tex]1\ acre = 750000\ oysters[/tex]
[tex]1\ oyster = 50\ gallons[/tex]
Required
Determine if there is enough water for a day
We have:
[tex]1\ oyster = 50\ gallons[/tex]
Convert to oysters: multiply both sides by 750000
[tex]750000 * 1\ oyster = 50\ gallon *750000[/tex]
[tex]750000\ oysters = 37500000\ gallons[/tex]
Given that:
[tex]1\ acre = 750000\ oysters[/tex]
So, we have:
[tex]1\ acre= 37500000\ gallons[/tex]
Convert to acre: Multiply by 2867200
[tex]2867200 * 1\ acre= 37500000\ gallons * 2867200[/tex]
[tex]2867200\ acres= 107520000000000\ gallons[/tex]
By comparison:
[tex]18000000000000\ gallons < 107520000000000\ gallons[/tex]
i.e. the volume of water in the bay is less than the capacity of the oysters. Hence, there are enough oysters.
find a volume of a cube whose base radius is 5 cm and height 28 cm
Answer:
The volume of the cube is 21952.
Step-by-step explanation:
V = L x W x H
because a cube's sides are all the same, the length, width, and height are also the same. So we use the formula:
V= S^3
(S standing for side)
we know the height is 28 and as all sides measure the same we use the equation:
V= 28^3
28^3 = 21952
So, V= 21952
Latoya's annual salary is $26,000. A total of $7352.24 will be deducted for taxes and health insurance. She will receive her paycheck monthly in 12 equal installments. How much will she get paid with each paycheck?
Step-by-step explanation:
Lets translate this word problem into math.
"Latoya's annual salary is $26,000" = We start with the number 26,000
"A total of $7352.24 will be deducted for taxes and health insurance" = It's the number we started with "deducted" (minus) 7352.24
"She will receive her paycheck monthly in 12 equal installments" = Our number will be divided by 12
"How much will she get paid with each paycheck?" = "Find answer pls thx"
To put it all together...
[tex]\frac{26,000-7,352.24}{12}[/tex]
Now all we have to do is solve!
[tex]\frac{26,000-7,352.24}{12}[/tex]
Subtract.[tex]\frac{18,647.76}{12}[/tex]
Divide.[tex]1,553.98[/tex]
Answer:
Latoya will get paid $1,553.98 with each paycheck.
Sue wants to put rectangular garden on her property using 90 meters of fencing. There is a ns through her property, so she decides to increase the size of the garden by ne side of the rectangle. (Fencing is then needed only on the other three river that runs through her property, so she using the river as one side of the rectangle. (ren sides). Let x represent the length of the side of the rectangle parallel
a. Express the garden's area as a function of x.
b. Using your graphing calculator, determine the maximum area that Sue will be able to enclose for her garden and the dimensions of that area. (Hint: A good viewing window might be (-40, 100; 0, 1100])
Answer:
a) A(x) = 90*x/2 - x²/2
b) A(max) = 1012.5 m²
Step-by-step explanation:
L = 90 meters of fencing
Rectangular area is
A(r) = x*y . where x and y are the sides of the rectangle
the perimeter is ( we are going to fence only 3 sides, then)
x + 2*y = 90 or . y = ( 90 - x ) /2
Area as a function of x is:
A(x) = x * ( 90 - x)/2
A(x) = 90*x/2 - x²/2
Tacking derivatives on both sides of the equation:
A´(x) =45 - 2*x/2 A´(x) =45 - x
A´(x) = 0 . 45 - x = 0 . x = 45 . meters
and . y = ( 90 - x ) 2
y = ( 90- 45 )/2
y = 22.5 meters
A(max) = 45*22.5 m²
A(max) = 1012.5 m²
If we get the second derivative of A(x) . A"(x) = - 1 A"(x) < 0
Then A(x) has a maximum for x = 45
A giant and a dragon live next door to each other. The giant's house is 23 meters tall. His house is 35 meters shorter than the dragon's house.
Is the answer option c?
Answer:
No it isnt corret answer.
Answer: Choice D
Explanation:
Recall that the quadrants are labeled such that Q1 (shorthand for quadrant 1) is in the upper right corner. Then we have Q2 in the upper left corner. We work counterclockwise around as shown in the diagram below.
Therefore, the curve is found in Q1 and Q3
help asap------------
Answer:
the real is -19
the imaginary is -24 (or -24i depending on what the computer is looking for as an answer)
Step-by-step explanation:
help please for functions
Answer:
A
Step-by-step explanation:
The domain of a graph is the set of number you can input for x that will give you a y value. From the looks of it, this graph has all x-values larger than zero.
We know it is not b since we see x-values of the graph go past x=10.
We know it is not c because there are no negative x-values.
We know it is not D because there are no negative x-values. Real number include negative numbers.
Help please please help me please
Answer:
[tex]\sqrt[2]{8}[/tex]
Step-by-step explanation:
Remember the basic format of a fraction raised to a fractional exponent:
[tex]a^\frac{b}{c}=\sqrt[b]{a^c}[/tex]
Some terms to keep in mind are the following:
(a) is the base
(c) is the exponent
(b) is the index
Apply this information to the given problem:
[tex]2^\frac{3}{2}[/tex]
In this case, (2) is the base, and the index; (3) is the exponent. Apply the general format of the fraction exponent to change the expression from an exponent to a radical.
[tex]2^\frac{3}{2}=\sqrt[2]{2^3}[/tex]
Simplify the term under the radical:
[tex]\sqrt[2]{2^3}=\sqrt[2]{8}[/tex]
the area of a square table is 225/81 square meters. find the length of a side of the table
9514 1404 393
Answer:
5/3 meters
Step-by-step explanation:
The area is the square of the side length, so the side length is the square root of the area.
s = √(225/81) = 15/9 = 5/3 . . . meters
The length of a side of the table is 5/3 meters.
Last year 160 new candidates submitted applications to work for an agency. This year, that number is on target to increase by 25%. There are 6 months left in the year. How many new applications has the agency received so far this year?
Answer:100
Step-by-step explanation:
Given
Last year 160 new candidates submitted to work for agency
It is expected to increase by 25% that is , increase in one year should be
[tex]\Rightarrow 160+160\times 25\%\\\Rightarrow 160(1+0.25)\\\Rightarrow 160\times 1.25\\\Rightarrow 200[/tex]
200 application in the upcoming year. So, in 6 months, agency must have accepted 100 applications.
What are the steps involved in multiplying/ dividing rational expressions??
Answer:
Multiplication:
Step 1: Factor both the numerator and the denominator.
Step 2: Write as one fraction. Write it as a product of the factors of the numerators over the product of the factors of the denominators. DO NOT multiply anything out at this point.
Step 3: Simplify the rational expression.
Step 4: Multiply any remaining factors in the numerator and/or denominator.
Division:
Step 1: Completely factor both the numerators and denominators of all fractions.
Step 2: Change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal.
Step 3: Cancel or reduce the fractions. Remember that to reduce fractions; you can cancel something in the numerator with something in the denominator, but in order to cancel something in the numerator and denominator the two factors must be EXACTLY the same.
Step 4: Rewrite the remaining factor. Notice that you do NOT need to actually multiply anything in the numerator or denominator.
Someone please help
Convert the credit card rate to the APR. Ohio, 0.02192% daily rate. Please round your answer to the nearest percent. (zero decimal place.) Enter only the number without $ sign.
Answer:
8%
Step-by-step explanation:
APR means annual percentage rate.
To convert the daily rate to an APR, multiply the daily rate by the number of days in a year
365 days = 1 year
0.02192% x 365 = 8.0008%
To round off to the nearest percent, look at the first number after the decimal, if it is less than 5, add zero to the units term, If it is equal or greater than 5, add 1 to the units term.
The tenth digit is 0, so the number would be rounded off to 8%
B
C
5
C
A
12
Find the length of “c” using
the Pythagorean Theorem.
Enter
Answer:
13
Step-by-step explanation:
We know that a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
5^2 + 12^2 = c^2
25+144 = c^2
169 = c^2
Taking the square root of each side
sqrt(169) = sqrt(c^2)
13 =c
Jackie is 8 years younger than her neighbor, Paula. The sum of their ages is 30. How old are Jackie and Paula?
Answer:
Jackie: 11
Paula: 19
Step-by-step explanation:
11+19 = 30
i’m using this app so much but i really do appreciate the help pleasee no wrong answers
Answer:
C is correct
Step-by-step explanation:
a is wrong because: 1*-1*-1*-1 =1
b) 1*1*1*1 =1
d) 1*-1*1*1 =1
only c 1*-1*-1*1 =-1 at the end of polynomial
SEE QUESTION IN IMAGE
Answer:
Step-by-step explanation:
15) should be b) 6.7, 6 as the median is the average of the 25th and 26th result, these both occur in the 6 group and is the only option with a whole number for median
To check the mean
(2(4) + 7(5) + 17(6) + 10(7) + 8(8) + 6(9)) / 50 = 6.66 ≈ 6.7
16) mode is 1 child as the single largest grouping is 11 families
there were 46 families polled so the median occurs between 23 and 24
7 + 11 + 6 is 24 therefore median falls under 2 children.
a) 1, 2
17. Find an equation of the straight line that is perpendicular to x - y = 5 and passes through the point (8, -1).
18. Find the equation of the line in slope-intercept form that passes through the points (12, 4) and (4, 6)
Answer:
17.y=-x+12
18.y=-1/4x+7
Step-by-step explanation:
17.a Solve for y (y=-5+x)
17. b Reciprocal (y=-1x-5)
17. c Subsitute equation into (8,-1) (-1=-13=y=x+12)
18.a Subtract y values and x values= (6-4)/(4-12)=2/-8=-1/4, this will be your slope
18. b Plug in -1/4 into either of the two ordered pairs to find y value=(12,4)=(4=-3)=y value=7.
18. c=y=-1/4x+7
Can someone explain this I don't understand
Answer:
16°
Step-by-step explanation:
For this problem, it's helpful to know SOH-CAH-TOA. When you see which sides are given, you can use that acronym to figure out which trigonometric function you need to use. In this case, the side adjacent to the angle in question (53) and the hypothenuse (55) are given. So we would look at CAH, and know we need to use cosine. However, since we are finding an angle, we need to use [tex]cos^{-1}[/tex] (inverse cosine). Now we just solve:
? = [tex]cos^{-1} (adjacent / hypotenuse)[/tex]
? = [tex]cos^{-1} (53/55)[/tex]
? = 15.5° -> 16°
Explain the relationship between an inda vidual and a society
Answer:
The relation between individual and society is very close. Essentially, “society” is the regularities, customs and ground rules of antihuman behavior. ... Man is biologically and psychologically equipped to live in groups, in society. Society has become an essential condition for human life to arise and to continue.
