The rate of change of the height of the water in the pool when the depth is 5 feet is approximately 0.089 feet per minute.
Explanation:To find the rate of change of the height of the water in the pool, we can use the formula for the volume of a cylinder.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
So, when the depth of the water is 5 feet, we can find the rate of change of the height by differentiating the volume equation with respect to time.
Let's calculate it:
V = π(5^2)(h)
dV/dt = π(25)(dh/dt)
Since the volume is increasing at a constant rate of 7 cubic feet per minute, we have dV/dt = 7.
Substituting the given values, we have:
7 = π(25)(dh/dt)
dh/dt = 7/π(25)
So, the rate of change of the height of the water in the pool when the depth is 5 feet is approximately 0.089 feet per minute.
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To find the rate of change of the height of the water in the pool, we can use the concept of related rates. The rate of change is approximately 0.089 cubic feet per minute.
Explanation:To find the rate of change of the height of the water in the pool, we can use the concept of related rates. Let's call the height of the water in the pool 'h' and the rate of change of the height 'dh/dt'. We know that the volume of water in the pool is flowing at a constant rate of 7 cubic feet per minute, therefore the rate of change of the volume of water in the pool is also constant at 7 cubic feet per minute. The volume of a cylinder is given by V = πr^2h, where r is the radius of the pool and h is the height of the water. We can differentiate this equation with respect to time to find the rate of change of the volume.
dV/dt = πr^2(dh/dt)
Since the radius of the pool is constant at 5 feet and the rate of change of the volume is 7 cubic feet per minute, we can substitute these values into the equation and solve for dh/dt.
7 = π(5^2)(dh/dt)
dh/dt = 7/(π(5^2))
Therefore, the rate of change of the height of the water in the pool when the depth of the water is 5 feet is approximately 0.089 cubic feet per minute.
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Skylar needs to buy a pair of dress pants for $40, a shirt for $30, and a tie for $20. Skylar has three coupons. The first coupon gives him x percent off on a shirt. The second coupon gives him y percent off on the dress pants. The third coupon gives him z percent off on his total purchase. He cannot combine the coupon for the total purchase with the other two coupons. These expressions give both possibilities for the total cost of Skylar's purchase after the coupons are applied. The variables represent percentages as decimals. (1−x)30+(1−y)40+20 (1−z)(40+30+20) Skylar uses the dress pants coupon. Which part of the expression represents the percent that Skylar will pay for the dress pants?
Answer: Hello there!
As we know, the dress pants cost a total of $40, and we also know that Skylar has a coupon of y percent in the dress pants and a coupon of z percent in the total purchase.
In this problem, the question is:
Skylar uses the dress pants coupon. Which part of the expression represents the percent that Skylar will pay for the dress pants?
Ok, if we have a discount of y percent, (where y is represented as decimals) means that you are paying the total price of something ( the 100%) minus the the decimal y multiplied by the price of the object.
this is: $40 - y*$40 = (1 - y)*$40
then if the dress pants cost $40, and Skylar only uses the dress pants coupon, he will pay (1 - y)*$40 for the dress pants.
1.3 divided by 0.0338 step by step please
The equation of a line is x + 4y = 15.
What is the y-intercept of the line?
415
15
−15
154
Answer:
Option D.
Step-by-step explanation:
Y-intercept form of the equation of a line is given by y = mx + c
Where m = slope of the line
c = y-intercept
Given equation of a line is x + 4y = 15
We will transform this equation into the y intercept form first.
x + 4y = 15
4y = 15 - x
y = [tex]-\frac{x}{4}+\frac{15}{4}[/tex]
Therefore, y - intercept of this equation will be c = [tex]\frac{15}{4}[/tex]
Option D will be the answer.
Find the vertical, horizontal, and slant asymptotes, if any, for f(x)= 3x^3-28x^2+54x-24/x^2-8+7
Consider points R, S, and T. Which statement is true about the geometric figure that can contain these points? No line can be drawn through any pair of the points. One line can be drawn through all three points. One plane can be drawn so it contains all three points. Two planes can be drawn so that each one contains all three points.
Answer: The answer is (c) One plane can be drawn so that it contains all three points.
Step-by-step explanation: We are given three points R, S and T in a coordinate plane. Considering all these three points to be distinct and non-collinear, we can draw the following conclusions.
(i) Since each pairs of points. i.e., (R,S), (S,T) and (T,R) give rise to a straight line when joined, so option (a) is incorrect.
(ii) Through any two given points, we can always draw a line. If we consider a third point and since we are dealing with non-collinear points, so one line cannot be drawn through three points.
(iii)We can always draw a line by joining two points and when we join the two ends of the line to a third point which does not lie on the line, it will give rise to a plane. So, option (c) is correct.
(iv) We cannot draw two different planes through three given points. If we do so, the new plane will coincide with the previous one. This proves that option (d) is not correct.
Please see the attached figure, where P, Q and R are three non-collinear points. They give rise to a plane.
Thus, the correct option is (c).
Which is the best estimate of each percent 48% of 199
Eliminate the parameter. x = square root of t, y = 3t + 7
Answer:
y = x divided by three + 7
Step-by-step explanation:
What is R such that PR : RQ = 2/5
Express as a coordinate
Solve the inequality.
-x/4 ≤ 2
4x -y =1
I need to get the variable y by its self.
Describe the transformation of ΔABC.
A) rotation of 90° about the origin
B) rotation of 60° about the origin
C) rotation of 180° about the origin
D) rotation of 270° about the origin
Answer:
Transformation of ΔABC rotation of 180° about the origin .
Step-by-step explanation:
Given : Coordinates of Δ ABC ,=A ( 3,5) , B( 6,1) , C( 0,1) .
Coordinates of Δ A'B'C' = A' ( -3,-5) , B'(- 6,-1) , C'( 0,-1) .
To find :
Describe the transformation of ΔABC.
Formula used : 180° rotation (clock wise and counter clock wise)
( x , y ) -------> ( -x , -y ).
Solution :
A ( 3,5)-------> A' ( -3,-5).
B( 6,1)---------> B'(- 6,-1).
C( 0,1).---------> C'( 0,-1) .
Therefore, the transformation of ΔABC rotation of 180° about the origin .
After the drama club sold 100 tickets to a show, it had $300 in profit. After the next show, it had sold a total of 200 tickets and had a total of $700 profit. Which equation models the total profit, y, based on the number of tickets sold, x?
a. y – 300 = 4(x – 100)
b. y + 300 = 4(x + 100)
c. y + 300 = 2.5(x + 100)
d.y – 300 = 2.5(x – 100)
HELPPPPPPPPPPP
Answer:
Option a : [tex]y-300 = 4(x - 100)[/tex]
Step-by-step explanation:
Given :
The drama club sold 100 tickets to a show, it had $300 in profit.
The next show, it had sold a total of 200 tickets and had a total of $700 profit.
To Find : Equation models the total profit, y, based on the number of tickets sold, x
Solution :
For 100 tickets he had $300 in profit .
⇒ ([tex]x_{1} ,y_{1}[/tex])=(100,300)
For 200 tickets he had $700 in profit .
⇒ ([tex]x_{2} ,y_{2}[/tex])=(200,700)
We will use point slope form i.e.
[tex]y-y_{1} = m(x - x_{1})[/tex] --(A)
Now, to calculate m we will use slope formula :
[tex]m = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
[tex]m = \frac{700 -300}{200-100}[/tex]
[tex]m =4[/tex]
Now, putting values in (A)
[tex]y-300 = 4(x - 100)[/tex]
Thus Option a is correct i.e. [tex]y-300 = 4(x - 100)[/tex]
observation often starts the scientific process observation is useful because it helps scientist_____
a) form questions
b) develop opinions
c) summarize data
d) write laws
How do you solve this equation?
5 (x+2) = 7 (4 - x)
Express in scientific notation. Make sure your answer has the same number of significant figures as the starting value. 1,645.6 = _____
i need to know 725 miles in 8 hours miles per hour
divide total miles by time
725/8 = 90.625 miles per hour
Match the following items.
1.) 2x + x + 4 = -17
2.) 3x + 4 = -17
3.) 3x = -21
4.) x = -7
Given
subtraction
combine like terms
division
The correct explanation for each expression are;
1. 2x + x + 4 = -17 Given
2. 3x + 4 = - 17 Combine like term.
3. 3x = - 21 Subtraction.
4. x = -7 Division.
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.
Given that;
The expression is,
⇒ 2x + x + 4 = -17
Now, Solve the expression for x by using suitable property as;
⇒ 2x + x + 4 = -17
Combine like term;
⇒ 3x + 4 = - 17
Subtract 4 both side;
⇒ 3x + 4 - 4 = -17 - 4
⇒ 3x = - 21
Divide by 3;
⇒ x = - 7
Thus, The correct explanation for each expression are;
1. 2x + x + 4 = -17 Given
2. 3x + 4 = - 17 Combine like term.
3. 3x = - 21 Subtraction.
4. x = -7 Division.
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Find all the real zeros of x3-2x2-5x+6=0.
During a huge snowstorm in the White Mountains last year, it snowed 61.5cm in one day. How much did it snow in meters? Be sure to include the correct unit in your answer.
The snowfall during the snowstorm in the White Mountains was 61.5 cm, which is equivalent to 0.615 meters when converted.
Explanation:To convert the snowfall from centimeters to meters, we need to understand that 1 meter is equivalent to 100 centimeters. With this, to find the snowfall in meters, you simply divide the snowfall in centimeters by 100. So, the snowfall of 61.5 centimeters would be 0.615 meters.
This is because:
1 meter = 100 centimetersTo convert centimeters to meters, divide by 10061.5 cm / 100 = 0.615 metersLearn more about Conversionhttps://brainly.com/question/5561273
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Mrs.Carson pays Kristen $48 for babysitting 6 hours,and Mr.Vaquez pays her $67.50 for babysitting 9 hours,Who pays Kristin the better salary? Explain your answer
A sporting goods store pays $150 for a rubber raft. The percent of markup is 55%. Find the raft’s selling price.
Describe how to derive the quadratic formula from a quadratic equation in standard form. edginuity
Answer:
The quadratic formula is derived from a quadratic equation in standard form when solving for x by completing the square. The steps involve creating a perfect square trinomial, isolating the trinomial, and taking the square root of both sides. The variable is then isolated to give the solutions to the equation.
Step-by-step explanation:
Mr Webster is buying carpet for an exercise room in his basement the room will have an art of 230 square feet the width of the room is 12 1/2 what is the length
The length of Mr. Webster's exercise room is 18.4 feet, calculated by dividing the area (230 sq ft) by the width (12.5 ft).
To find the length of the room, we can use the formula for the area of a rectangle:
[tex]\[ \text{Area} = \text{Length} \times \text{Width} \][/tex]
Given that the area is 230 square feet and the width is 12 1/2 feet, we can plug these values into the formula:
[tex]\[ 230 = \text{Length} \times 12 \frac{1}{2} \][/tex]
To solve for the length, divide both sides by 12.5:
[tex]\[ \text{Length} = \frac{230}{12 \frac{1}{2}} \]\[ \text{Length} = \frac{230}{\frac{25}{2}} \]\[ \text{Length} = 230 \times \frac{2}{25} \]\[ \text{Length} = 18.4 \][/tex]
So, the length of the room is [tex]\( \boxed{18.4} \)[/tex] feet.
What is the range of the following relation?
all real numbers
x ≤ 0
y ≤ 0
y ≤ 0
ExplanationRemember that the range is all the possible y-values that the relation can take. We can see in the picture that the repletion is always bellow of the positive y-axis, so the relation can take only negative y-values or zero. In other words, the range of the relation is all the y-values greater or equal than zero, which we represent with the inequality: y ≤ 0. The domain, on the other hand, is all the real numbers; since x can take any value.
Answer:
y ≤ 0 is the correct answer
Step-by-step explanation:
you gots to see it through mah boi
Answer this question please!
The length of a rectangle is 3 inches more than the width. the perimeter is 30 inches. find the length and width.
How many 2/3
cup servings are there in a 12-cup pitcher of orange juice?
Complete the data set with one value so that the mean of the data is 13.
10,14,8,16,12,____
The value of another number such that mean remains 13 is 18.
What is mean?The mean is the average of a data set. Mean gives us the idea of that how much amount of overall data have.
Mean = sum of data / Number of data
For example, if you have marks in 5 subjects like 40,45,44,46,48 then the mean will be
( 40 + 45+ 44 + 46 + 48) /5 = 44.6.
Let's say that number is x
Then,
Mean = (10 + 14 + 8 + 16 + 12 + x)/6
(60 + x)/6 = 13
x = 18
Hence "The value of another number such that mean remains 13 is 18".
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what is the intersection of plane stxw and plane stv
A storeowner places a “No Smoking” sign in front of their store. This would be classified as a type of what factor.
Answer:
external pressure
Explanation:
This is the full question:
A sign in front of a store says "No Smoking.” What kind of factor is this sign?
external pressure
internal pressure
media influence
peer pressure