Liam has 5 quarters, 10 dimes and and 7 nickels.
What is quarter and dime?1 dollar is 100 cents - a full dollar, so 100 cents.
One dollar is written on one side of the coin, sometimes as "$1".
1 quarter dollar equals 25 cents - 1/4 of a dollar equals 25%, so 25 cents
On one side of the coin, a quarter dollar is written.
1 dime is 10 cents - 1/10th of a dollar, so 10%, so 10 cents, dime begins with d, decimal begins with, and decimal is base-10. One dime is written on one side of the coin.
1 nickel is 5 cents - made of nickel alloy, 1 cent/penny is possibly not made of nickel because it costs more than 1 cent, so it begins with 5 cents.
On one side of the coin, five cents are written.
Let d be the no. of dimes, n be the no. of nickels and q be the no. of quarters.
Given that
2q = d
n + 3 = d
money in dimes = money in quarters
10d = 25q
d can be written as
d = q/2
So
10(2q) = 25q
2q/q = 25/10
q = 2.5
as 2.5 cant be a number for quarter, lets double it
q = 5
d = 2q
d = 2(5)
d = 10
n = d - 3
n = 10 - 3
n = 7
Thus, Liam has 5 quarters, 10 dimes and and 7 nickels.
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Find the minimum value of the function z = 4x+3y subject to the following constraints.
x≤ 15
y≤ 13
3x+y≥ 16
2x+11y252
Note that the ALEKS graphing calculator can be used to make computations easier.
Z=
The minimum value for given linear equation 4x+3y will be 24.
What are linear equations?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.
Now,
The minimum value for z=4x+3y will be at (6,0) i.e. 24
because this point follows the given linear inequalities too
as given in the graph provided in image.
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Is parallelogram TUVW a rectangle?
It is a rectangle, TUVW. A parallelogram has diagonals that are perpendicular and angles that are all 90 degrees.
Is a parallelogram ever a rectangle?No, a parallelogram is not always a rectangle. In a rectangle, all angles must be equal to 90°. But for a parallelogram, no angles need to be equal to 90°. In a rectangle the diagonals are equal but in a parallelogram, diagonals are not equal.
Parallelogram has opposite sides equal and parallel. Rectangle also has opposite sides equal and parallel. The difference between the two is that sides of rectangles form 90 degree while that of parallelogram don't.
A square is a parallelogram. This is always true. Squares are quadrilaterals with 4 congruent sides and 4 right angles, and they also have two sets of parallel sides. Parallelograms are quadrilaterals with two sets of parallel sides.
It is a rectangle, TUVW. A parallelogram has diagonals that are perpendicular and angles that are all 90 degrees.
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What is the relative minimum of the function?
Enter your answer in the box.
Answer: -5
Step-by-step explanation:
The minimum value is -5 at x = 1. Coordinate (1,-5)
what is the slope through the line of (4, 7) and (6, 2)
The slope through the line of (4, 7) and (6, 2) can be found by using the slope formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.
Substituting the values for (4, 7) and (6, 2) into the formula:
m = (2 - 7) / (6 - 4)
m = -5 / 2
m = -2.5
So, the slope of the line through (4, 7) and (6, 2) is -2.5.
Hello:
--> find the slope between the points (4, 7) and (6, 2)
Let's consider our point given:
--> (x1, y1): (4, 7)
--> (x2, y2): (6, 2)
Let's consider what formula we need:
[tex]\text{Slope}=\dfrac{y2-y1}{x2-x1}=\dfrac{2-7}{6-4}=\dfrac{-5}{2}=-\dfrac{5}{2}[/tex]
Thus our slope is -5/2
Answer: -5/2
cindy has $26 that she has to spend. She can buy a box of cookies for $3 each or a box of brownies for $2 each. Complete this table showing some possible combinations of the number of each type of treat she can buy.
The possible combinations of the number of each type of treat that Cindy can buy include:
6 box of cookies and 4 box of brownies8 box of cookies and 1 box of brownies4 box of cookies and 6 box of brownies.How to calculate the word problem?A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
In this case, 6 box of cookies and 4 box of brownies will be:
= 6($3) + 4($2)
= $26
8 box of cookies and 1 box of brownies also give $26.
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Obtain an estimate for the computation shown below by rounding the numbers so that the resulting arithmetic can easily be performed by hand or in your head.
0.87 x 310
The estimation of the numbers given as 0.87 × 310 will give 270.
Howw to calculate the estimation?You must approximate (eliminate or round off) the decimals to obtain whole numbers before you can use the whole numbers to find the product of two decimals using estimation. A figure is discovered through estimation.
A value, amount, or size that rounds off to the nearest whole number is said to be approximating.
The estimation of the numbers given as 0.87 × 310 will give:
= 0.9 × 300
= 270.
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A stack of four cards contains two red cards and two black cards. I select two cards, one at a time with replacement. Consider the events A = the first card selected is red. B = the second card selected is red. The events A and B are O not independent O mutually exclusive O mutually exclusive and not independent. O independent
P(A) and P(B) are independent events.
Option (D) is correct.
What are events in probability?
In probability, an event is a set of outcomes of an experiment. For example, if you flip a coin, the possible outcomes are "heads" or "tails", and the event "getting heads" is the set of all outcomes where the coin lands on heads. Events can be mutually exclusive, meaning that they cannot happen at the same time, or they can be non-exclusive, meaning that they can happen at the same time.
The events A and B are independent. This means that the probability of event B happening (the second card selected is red) is not affected by whether or not event A has already happened (the first card selected is red).
In other words, the probability of selecting a red card on the second draw is still 1/2, regardless of whether a red card or a black card was selected on the first draw. This is because the cards are being drawn with replacement, meaning that the first card selected is returned to the stack before the second card is drawn, so the second draw is not affected by the first draw.
To calculate the probability of both events A and B happening, we can use the formula P(A and B) = P(A) x P(B|A) where P(B|A) is the conditional probability of event B given that event A has already happened. Since we know that the probability of event A is 1/2, and the probability of event B is also 1/2, we can calculate P(A and B) as: P(A and B) = (1/2) x (1/2) = 1/4
Therefore, P(A) and P(B) are independent events.
Option (D) is correct.
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6x + 4y = 7Kx + 8y = 7What is the value of K?
The value of K in the given equations 6x+4y=7 and Kx+8y=7 is k=(-4y/x)+6.
What are equations?Two things are equal, according to an equation.
It will be written with the equals sign "=" as in x+2=6.
What is on the left (x + 2) is equal to what is on the right ((6)), according to that equation.
A remark like "this equals that" can be compared to an equation.
So, we have the equations:
6x + 4y = 7
Kx + 8y = 7
Now, we know that both equations are equal to 7. so, we can write it as:
6x + 4y = Kx + 8y
Solve with subject K as follows:
6x + 4y = Kx + 8y
Kx - 6x = 4y - 8y
(K-6)x = -4y
k-6 = -4y/x
k = (-4y/x) + 6
Therefore, the value of K in the given equations 6x+4y=7 and Kx+8y=7 is k=(-4y/x)+6.
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In addition to therapy, anti-depressant drugs are used in the treatment of depression. The data Type numbers in
below are from a study comparing two anti-depressant drugs. A baseline measurement for symptomatic behavior for depression is taken. After treatment with medication, another measurement taken. The data given in the table is for improvement which is for the reduction
in symptomatic behavior.
Drug A 2.30 2.39 4.03 2.90 3.45 3.29 3.82 3.27 4.08 1.83 4.07 5.06
Drug B 9.31 7.37 4.50 6.00 7.22 4.21 5.25 5.99 8.37 3.82 3.69 3.40
The primitive data type number has the entry 1, or 1, in the database dictionary.
What is a number data type?The database dictionary's entry for the number data type, which is a primitive data type, is 1, or 1. It is possible for a number to be a whole number, a positive or negative number, or a floating point number, and it can also denote an amount.
Numbers are stored as numeric data types in database columns. Exact numeric kinds, values where the precision and scale need to be retained, are normally the categories into which these data types are grouped. There are six distinct sorts of numbers: INTEGER, BIGINT, DECIMAL, NUMERIC, NUMBER, and MONEY.
Integral, Floating Point, Character, Character String, and Composite types are the five fundamental categories of data types recognized by the majority of current computer languages. Within each of these broad categories, numerous particular subtypes are established.
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711
Put the measures of the angles in order from least to greatest
Answer: [tex]m\angle YOZ, m\angle VOS, m\angle UOZ, m\angle XOS, m\angle TOZ[/tex]
Step-by-step explanation:
[tex]m\angle VOS=90^{\circ}\\\\m\angle UOZ=180^{\circ}-56^{\circ}=124^{\circ}\\\\m\angle YOZ=180^{\circ}-143^{\circ}=37^{\circ}\\\\m\angle XOS=126^{\circ}\\\\m\angle TOZ=180^{\circ}-33^{\circ}=147^{\circ}[/tex]
Two friends, Caleb and Hassan, took summer jobs. The equation y=21.5xy=21.5x represents Hassan's earnings in dollars and cents, yy, for working xx hours. Caleb earned $819.40 in 34 hours.
Use the dropdown menu and answer-blank below to form a true statement.
Hassan earns $2.6 per hour more than Caleb. Because the rate of Hassan is more than Celeb.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
Two friends, Caleb and Hassan, took summer jobs. The equation y = 21.5x represents Hassan's earnings in dollars and cents, y, for working x hours. Caleb earned $819.40 in 34 hours.
The rate of Caleb is given as,
Celeb's rate = $21.5 per hour
The rate of Hassan is given as,
Hassan's rate = $819.40 / 34
Hassan's rate = $24.1 per hour
The difference is given as,
⇒ $24.1 - $21.5
⇒ $2.6
Hassan earns $2.6 per hour more than Caleb. Because the rate of Hassan is more than Celeb.
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A firm’s current profits are $900,000. These profits are expected to grow indefinitely at a constant annual rate of 2 percent. If the firm’s opportunity cost of funds is 4 percent, determine the value of the firm: a.The instant before it pays out current profits as dividends. b.The instant after it pays out current profits as dividends
Answer: a. The value of the firm the instant before it pays out current profits as dividends can be calculated using the Gordon Growth Model, which is given by the formula:
Value = Dividends / (Cost of Equity - Growth Rate)
Where Dividends = Current Profits, Cost of Equity = Opportunity Cost of Funds, and Growth Rate = Constant Annual Growth Rate.
Substituting the given values into the formula, we get:
Value = 900,000 / (0.04 - 0.02) = 900,000 / 0.02 = 45,000,000
b. The instant after it pays out current profits as dividends, the firm's value will be reduced by the amount of the dividends paid out. So, the value of the firm after paying out the dividends will be:
Value = 45,000,000 - 900,000 = 44,100,000
Step-by-step explanation:
Use the formula for finding the volume of
a rectangular prism to find the volume of
a rectangular prism that measures 1/2 in x 2 2/3 in x 2/5 in.
Options are
The volume of a rectangular prism is 8/15 in³ option - A is correct.
How can you calculate the volume of a rectangular prism using a formula?Therefore, the area of the base of a rectangular prism is multiplied by the height to determine its volume. The formula for calculating a rectangular prism's volume is Volume (V) = height of the prism base area. It is measured in cubic units like cm³, m³, and in³.
The Rectangular Prism's Volume Formula
The volume of a prism can be calculated by dividing the base area by the height. Consequently, a prism's volume is equal to its base area times its height.
The equation for calculating a rectangular prism's volume is
V = l × w × h
V = 1/2 in × 8/3 in ×2/5 in
V = 8/15 in³.
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The graph shows the cube root parent function.
-5
5-
-5
5
K
Which statement best describes the function?
OA. The function is positive when x < 0 and when x > 0.
B. The function is always positive.
C. The function is positive when x > 0.
OD. The function is positive when x<0
The correct option, C. The function is positive when x > 0, for the graph of cube root parent function.
Define the term cube root parent function?The opposite of such cubic function is the cube root function.
We are aware that its parent cubic function is ascending, one-one, and onto, and that its form is f(x) = x³. It results in a bijection as a result. As a result, its cube root inverse function, of the type f(x) = ∛x, also forms a bijection.The definition of the cube root for all numbers may be found in the introduction, as we have already seen (positive, real, and 0). As a result, there is no x for which any cube root function, f(x), is not defined. Therefore, the set among all real numbers is its domain (R).Similar to the square root function, the range of a cube root function is the set among all real numbers because it produces all values (positive, real, and 0). Consequently, a cube root function is f(x): R → R.Thus, using the domain and range we can see from the graph that, for the positive values of the function, the graph is increasing for positive values.
Therefore, The function is positive when x > 0.
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I need the answers ASAP please help
For the complex number (13 - i)(13 + i), The real part is 170 and the imaginary part is 0.
What is an equation?An equation consists of numbers and variables linked together by mathematical operations to form an expression.
The standard form of a complex number is a + bi; where a is a real number and the real part while b is a real number and the imaginary part. Also, i = √(-1)
a) (13 - i)(13 + i)
= 169 + 13i - 13i - i² = 169 - i² = 169 - [√(-1)]²
= 169 + 1 = 170
The real part is 170 and the imaginary part is 0.
b) -9i - 2
The real part is -2 and the imaginary part is -9.
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Drag and drop the numbers to order them from least to greatest. 2.045 2 5/9 -2 2/3 -2.43
Answer:
-2.43, -2, 5/9, 2/3, 2, 2.045
Step-by-step explanation:
Negative numbers are less than positive numbers, and we can go in numerical order from 1, 2, 3 to find which number is greater than the other
on monday the sun was out for 3 3/10 hours. on tuesday the sun was out for 6 1/5 hours. how much longer was the sun out on tuesday than monday
Using Subtraction, The Sun was out for 7 1/30 hours more than Monday.
To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference.
Finding the difference between two numbers is what it entails. The icon is as follows: (minus). We take a number and divide it by a smaller number in this operation.
On monday the sun was out for 3 3/10 hours.
On tuesday the sun was out for 6 1/5 hours.
the sun out on tuesday than monday =
Using Subtraction,
⇒ 31/ 3 - 33/10
⇒ 310 - 99/30
⇒ 211/30
⇒ 7 1/30 hours
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What value of m makes the equation y + m = 6x + 15 a proportional relationship? Please include explanation!
The value of m = 15 makes the equation a proportional relationship.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side
The given equation is y + m = 6x + 15.
If an equation has a proportional relationship, then the two variables will have a constant ratio.
General format of a proportional relationship is y = kx, where k is called the constant of proportionality.
We have to get the given equation in the form of y = kx.
It is possible only if m = 15.
y + 15 = 6x + 15
y = 6x + 15 - 15
y = 6x
Hence the value of m is 15, if the relationship is proportional.
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ILL GIVE BRAINLIEST
Answer: y =1x-5
Step-by-step explanation:
The question asks for the slope form y =mx+b, where m is the slope and b is the y-intercept. The y-intercept is the y value when x = 0, also known as when the line intercepts the verticle origin line. On your graph, this point is (0, -5). So, b = -5. Now, we need to pick two points to find the slope using the equation (y2-y1)/(x2-x1). Any two points on the line will work, so even if you do not pick the same points as me, you should still get the same answer.
point one: (0,-5)
point two: (4,-1)
m = (-1 - -5) / (4 - 0) = (-1+5)/(4) = 4/4 = 1
hope this helps!
what is the probability of getting the same number on two six-sided dice
Answer:
1/36, or approximately 0.028
Step-by-step explanation:
The probability of getting the same number on two six-sided dice is 1/6, or approximately 0.17.
This is because there are six possible outcomes for each dice, and only one of those outcomes results in the same number on both dice (for example, both dice showing a 6).
So, out of the 36 possible outcomes when rolling two dice, only one of them results in the same number on both dice. Therefore, the probability of this happening is 1/36, or approximately 0.028.
There are 4 apples, 3 peaches and 2 plums in a grocery bag. If the the checkout person picks 2 plumbs and 1 peach out of the bag, what is the probability that the next piece of fruit out of the bag will be an apple?
The probability that the next fruit out of the bag will be an apple is 2 / 3.
How to find the probability ?We're trying to figure out the probability of picking an apple at random from a bag of fruits, assuming that the odds are equal for each item.
Keep in mind that the chance is equal to the product of the quantity of apples and the quantity of all the other fruits in the bag.
The fruits taken out already include 2 plums and a peach which means 3 fruit have been taken out, leaving a total of:
= ( 4 + 3 + 2) - 3
= 6 fruits
The probability of the next fruit being an apple is:
= ( 4 apples + 2 peaches ) / 6 fruit
= 4 / 6
= 2 / 3
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In each of the following situations, data are obtained by conducting a statistical study. Classify each statistical study as experimental or correlational. Statistics students collect data on the shower length and gender of the person taking the shower for a random sample of showers. The manager of a tuna canning factory is interested in finding out which set of machine settings results in a smaller variance of the fill weight of the tuna cans. She uses one set of machine settings for the day shift and a second set of settings for the night shift. The next day she uses the second set of settings for the day shift and the first set of settings for the night shift. Data are collected on the fill weights of the tuna cans. For a sample of college students using the ATM in the campus center, data are collected on the dollar amount withdrawn.
An experimental design involves changing an independent variable and observing the impact on a dependent variable. The results are unaffected by other variables because they are controlled.
What are experimental or correlational statistical study?An experimental design involves changing an independent variable and observing the impact on a dependent variable. The results are unaffected by other variables because they are controlled. Variables are measured in a correlational design without any of them being changed. Without influencing or modifying any of the variables, a correlational study design examines associations between two (or more) variables. This particular quantitative research method is non-experimental. These determine the three categories of correlational research: Archival research, survey research, and observational study conducted naturally.Experimental research is an investigation carried out using two sets of variables and a scientific methodology. You use the first set as a standard against which to compare the differences in the second set. For instance, experimental techniques are used in quantitative research.We would learn them all and associate each song with a certain pizza truck if there were several different pizza trucks in the region, each with its own distinctive melody. In this case, "jingle" and "distance of the truck" are the two variables that are established as having a relationship by correlational study.To learn more about correlational statistical study refer to:
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Show that the set S={(3,2),(−1,1),(4,0)} is linearly dependent by finding a nontrivial linear combination of vectors in the set whose sum is the zero vector. (Use s1, s2, and s3, respectively, for the vectors in the set.)
Is it asking for (0,0)=c1(3,2)+c2(−1,1)+c3(4,0) with the matrix being (32−114000)?
c1 = (-4/5)c3, c2 = (8/5)c3, and c3 = 0. That what i found but in the example problem this is not even close to how the answer was.
The nontrivial linear combination of vectors whose sum is equal to zero vector for the given set of linearly independent vectors is given by :
u = 2v + (5/4)w .
As given in the question,
Given set of linearly independent vectors are:
S={(3,2),(−1,1),(4,0)}
Let us consider vectors u , v , and w represents the given set of linearly independent vectors which is given by :
u = ( 3, 2 )
v = ( -1 , 1 )
w = ( 4, 0 )
To get the nontrivial linear combination of vectors whose sum is equal to zero that is ( 0 ,0 ) is given by :
( 3, 2 ) - 2( -1 , 1 ) - (5 / 4)(4 ,0 ) = (0 , 0)
⇒ u -2v - ( 5 / 4 )w = 0
⇒ u = 2v + ( 5 / 4 )w
Therefore, the nontrivial linear combination of vectors whose sum is equal to zero is given by u = 2v + ( 5 / 4 )w.
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3. label the following points on the ppc: a. a point indicating inefficiency/unemployed resources, labeled as m b. a point indicating efficiency, labeled as n c. an unattainable point, labeled as p 4. calculate the opportunity cost of a movement between each of the following points:
PPF is bowed outward, so that as the quantity of pizza and pasta produced increases, it becomes more costly to produce another unit of pizza.
The PPF is a boundary between the attainable and unattainable combinations of pizza and pasta.
Points inside the PPF and on the PPF are attainable and points outside the PPF are unattainable.
Unattainable points are outside the PPF.
Because the PPF shows the limits to production, it separates attainable combinations from unattainable ones.
PPF is bowed outward, so that as the quantity of pizza and pasta produced increases, it becomes more costly to produce another unit of pizza.
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Which of these glasses contains more liquid?
Glass A contains about twice as much as glass B
Glass A contains about 20% more than glass B
Glass A and B contain about the same amount
Glass B contains about 20% more than glass A
Glass B contains about twice as much as glass A
Submit QuestionQuestion 4
Glass A contains about twice as much as glass B.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
Left Glass, height 10 cm , diameter 5.5 cm
And, Right glass, height 3 cm , diameter 7 cm.
Now, We know that;
⇒ Volume of cylinder = πr²h
Where, 'r' is radius of the cylinder.
For left glass;
Height (h) = 10 cm ,
Diameter = 5.5 cm
⇒ Radius = 5.5 / 2
= 2.75 cm
Hence, Volume = π × 2.75² × 10
= 3.14 × 2.75² × 10
= 237.46 cm³
For right glass;
Height (h) = 3 cm ,
Diameter = 7 cm
⇒ Radius = 7 / 2
= 3.5 cm
Hence, Volume = π × 3.5² × 3
= 3.14 × 3.5² × 3
= 115.39 cm³
Thus, Glass A contains about twice as much as glass B.
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The complete question is this,
Which of these glasses contains more liquid?
Left Glass, height 10 cm , diameter 5.5 cm
And, Right glass, height 3 cm , diameter 7 cm.
Glass A contains about twice as much as glass B
Glass A contains about 20% more than glass B
Glass A and B contain about the same amount
Glass B contains about 20% more than glass A
Glass B contains about twice as much as glass A
Submit QuestionQuestion 4
Is 18p and 3p like terms or terms
Answer: They are like terms and terms
Hope this helps :)
Step-by-step explanation:
18p and 3p are terms that happen to have the same variable to be like terms.
y = (x^2/2) + x + 2; [-5, 3]
For each problem, approximate the area under the curve over the given interval using 4 left endpoint rectangles
The area under the curve over the given interval [-5, 3] can be approximated using 4 left endpoint rectangles.
The formula for this is A = ∑f(xi)∆x. Where A is the area, f(x) is the function, xi is the left rectangles. of the interval, and ∆x is the width of the interval. For this problem, the function is f(x) = (x^2/2) + x + 2 and the given interval is [-5, 3]. So, the left endpoints of the intervals are x1 = -5, x2 = -1, x3 = 3, and x4 = 7 and the width of each interval is ∆x = 4. Plugging these values into the formula, A = (f(-5)∆x) + (f(-1)∆x) + (f(3)∆x) + (f(7)∆x). Simplifying, A = (9*4) + (6*4) + (12*4) + (26*4). Thus, the area under the curve over the given interval is A = 360.
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A car travels 84km in 2 hours. How far does it travel in 3hours
Answer:slow
Step-by-step explanation:
its slow
Answer:
Assuming it stays the same speed, 126km.
Step-by-step explanation:
By doing 84/2, I know it takes the car one hour to go 42km. For three hours, we must do 42x3, which is 126.
An indoor staircase has a 14 inch vertical rise per step to get to the second floor of the house. If the angle of elevation is 47 degrees and there are 13 feet of horizontal space total for each of the landings
combined, answer the following questions showing each step of your work:
a) What is the landing space per step (in inches, rounded to the nearest inch)?b) Find the vertical rise from the 1st floor to the 2nd floor (in feet, rounded to the nearest foot).
The landing space per step for the indoor staircase is solved to be
13 inchesThe vertical rise from first floor to second floor is 14 feet
How to find the landing spaceThe figure defined to be a right triangle and the dimensions are worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The right angle triangle comprises of
opposite = total vertical height
adjacent = total horizontal height = 13 feet
The total vertical height is calculated using tan, TOA
let the angle be x
tan x = opposite / adjacent
tan 47 = opposite / 13
opposite = (13 * tan 47) feet
opposite = 12 * (13 * tan 47) inch
opposite = 167.2895 inch
For a 14 inch vertical rise per step say number of step is y
14 y = total vertical height
14 y = 167.2895
y = 11.9493 steps ≈ 12 steps
The landing space for 12 steps is solved by
= horizontal space total in inch / number of steps
= 13 * 12 / 12
= 13 inches
vertical rise from the 1st floor to the 2nd floor
opposite = (13 * tan 47) feet
opposite = 13.94 feet
opposite = 14 feet (to the nearest foot)
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What is the maximum rate of change of f(x,y,z)=x+y/z at the point (5,−3,5) and the direction in which it occurs.
The maximum rate of change of f(x,y,z)=x+y/z at the point (5,-3,5) can be found using the directional derivative.
The directional derivative of f(x,y,z) in the direction (u,v,w) is given by:
Df(x,y,z) = u∂f/∂x + v∂f/∂y + w∂f/∂z
Since f(x,y,z)=x+y/z, the partial derivatives of f(x,y,z) are ∂f/∂x=1, ∂f/∂y=1/z and ∂f/∂z=-y/z^2. Substituting these values into the above directional derivative equation, we get:
Df(x,y,z) = u + v/z - wy/z^2
At the point (5,-3,5), we get Df(5,-3,5) = u + (-3/5) - (5w)(-3/25)
Simplifying this expression gives us Df(5,-3,5) = u + 0.6w
Therefore, the maximum rate of change of f(x,y,z) at the point (5,-3,5) occurs in the direction (u,0,w) and has a value of 0.6w.
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