Answer:
The rate of change of the height is 0.021 meters per minute
Step-by-step explanation:
From the formula
[tex]V = \frac{1}{3}\pi r^{2}h[/tex]
Differentiate the equation with respect to time t, such that
[tex]\frac{d}{dt} (V) = \frac{d}{dt} (\frac{1}{3}\pi r^{2}h)[/tex]
[tex]\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (r^{2}h)[/tex]
To differentiate the product,
Let r² = u, so that
[tex]\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (uh)[/tex]
Then, using product rule
[tex]\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}][/tex]
Since [tex]u = r^{2}[/tex]
Then, [tex]\frac{du}{dr} = 2r[/tex]
Using the Chain's rule
[tex]\frac{du}{dt} = \frac{du}{dr} \times \frac{dr}{dt}[/tex]
∴ [tex]\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h(\frac{du}{dr} \times \frac{dr}{dt})][/tex]
Then,
[tex]\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}][/tex]
Now,
From the question
[tex]\frac{dr}{dt} = 7 m/min[/tex]
[tex]\frac{dV}{dt} = 236 m^{3}/min[/tex]
At the instant when [tex]r = 99 m[/tex]
and [tex]V = 180 m^{3}[/tex]
We will determine the value of h, using
[tex]V = \frac{1}{3}\pi r^{2}h[/tex]
[tex]180 = \frac{1}{3}\pi (99)^{2}h[/tex]
[tex]180 \times 3 = 9801\pi h[/tex]
[tex]h =\frac{540}{9801\pi }[/tex]
[tex]h =\frac{20}{363\pi }[/tex]
Now, Putting the parameters into the equation
[tex]\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}][/tex]
[tex]236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)][/tex]
[tex]236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386][/tex]
[tex]708 = 9801\pi \frac{dh}{dt} + \frac{27720}{363}[/tex]
[tex]708 = 30790.75 \frac{dh}{dt} + 76.36[/tex]
[tex]708 - 76.36 = 30790.75\frac{dh}{dt}[/tex]
[tex]631.64 = 30790.75\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt}= \frac{631.64}{30790.75}[/tex]
[tex]\frac{dh}{dt} = 0.021 m/min[/tex]
Hence, the rate of change of the height is 0.021 meters per minute.
A lender charges 3.25% of the loan amount for closing costs on a $165000 home loan. Determine the closing costs.
Answer:
$5,362.50
Step-by-step explanation:
3.25% = 0.0325
165000 x 0.0325 = 5,362.50 dollars
Answer:
$5,362.50
Step-by-step explanation:
Which expression is equivalent to 9-3?
3(y-1)
3(3y-1)
9(y-3)
9(3y-3)
if its correct I will give brainliest!♡
Answer:
B because 3*3=9 And 3*1=3 so it would be 3(3y-1) foil the answer
Step-by-step explanation:
The answer is B, I took the test.
Please answer correctly !!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!
Answer:
2nd answer
Step-by-step explanation:
I need to find 7/8 of $72
Answer:
63
Step-by-step explanation:
7/8 x 72 = 63
The point (1,0) lies on the graph of
P(x) = x^4 - 2x^3 - x+2
A. True
B. False
Answer:
The given statement is true.
Step-by-step explanation:
Given function is:
[tex]P(x) = x^4 - 2x^3 - x+2[/tex]
And the given point is:
(1,0)
In an ordered pair, the first element is the input and second is the output. If we plug in the input to the function and get the respective output then the point lies on the graph of function.
For (1,0) we will put x = 1 in function and check whether we get 0 as output
[tex]P(x) = (1)^4 - 2(1)^3 - 1+2\\= 1-2(1)-1+2\\= 1-2-1+2\\=0[/tex]
Hence,
The given statement is true.
Answer:
A. True
Step-by-step explanation:
HELP HURRRYYY!!!! If (72)x = 1, what is the value of x? Explain your answer.
Answer:
1/72
Step-by-step explanation:
72 times x equals 1
to find singular value of x, divide both sides by 72.
x=1/72
Answer:
1/72
Step-by-step explanation:
The expression 2y+ 2.6 is equal to ? for y=5
Answer:
Its 12.6
Step-by-step explanation:
first we multiply 2 by 5 and get 10. Then we add 10 to 2.6 and get 12.6 for your answer.
Answer: 12.6
Step-by-step explanation:
2(5)+2.6
10+2.6
12.6
how many boys perfer the ferris wheel?
Answer:
10 Boys
Step-by-step explanation:
10 boys prefer the Ferris wheel because the total amount of boys is 35, but 23 of those 35 boys prefers the Super Slide, meaning what's left is who prefers the Ferris wheel since there are only 2 options for them to choose from.
35 boys - 23 boys (who like the Super Slide) = 10 boys (the remainder who likes the Ferris wheel).
≧◡≦
Mocha here! If this answer helped you, please consider giving it brainliest because I would appreciate it greatly. Have a wonderful day!
write at least four rational numbers between -2/5 and -1/3.
Answer:
-47/120 -23/60 -3/8 -11/30
Step-by-step explanation:
fractions are always rational. give both numbers the same denominator and list any numbers between the two. (-2/5 is equal to -6/15) (-1/3 is equal to -5/15) make sure to simplify though
Answer ASAP!! There is only a blank circle on the left
Answer:
i think its 1000
Step-by-step explanation:
The function y - 3 = 4(x + 2) is in point-slope form. Select the equivalent equation in slope-intercept form
All we need to do is solve for y.
[tex]y - 3 = 4(x + 2)\\\\y - 3 = 4x + 8\\\\y = 4x + 11[/tex]
The answer is A. y = 4x + 11.
please help!!
Find the slope of the line. Enter your answer as
a number, fraction, or undefined. Reduce to
lowest terms where necessary.
Answer:
m = undefined
General Formulas and Concepts:
Algebra I
Vertical Line Test - Tells us if a graph is a functionVertical Lines - slopes are undefinedStep-by-step explanation:
If the slope m was equal to 0, then it would be a horizontal line rather than a vertical line.
Using the Vertical Line Test, we also know that the graph is not a function.
Usually a vertical line has an undefined slope, as x equals a certain number, and m = unknown.
Answer: It's undefined, because it's vertical
A wire is needed to support a vertical pole 4 feet tall. The cable will be anchored to a stake 3 feet from the base of the pole. How
much cable is needed?
4 ft
3 ft
A cable of length
feet is needed.
Enter your answer in the answer box.
Answer:
I think its 5 feet
Step-by-step explanation:
I used Pythagorean theorem
I'm very confused, I don't know where to even start! Please help me!!
Answer/Step-by-step explanation:
✔️Using trigonometric ratio, find width of the rectangle, BD:
Thus:
[tex] tan(\theta) = \frac{opposite}{adjacent} [/tex]
Where,
[tex] tan(\theta) = tan(60) = \sqrt{3} [/tex]
Opposite = BD
Adjacent = 7 cm
Plug in the values
[tex] \sqrt{3} = \frac{BD}{7} [/tex]
Multiply both sides by 7
[tex] 7\sqrt{3} = BD [/tex]
[tex] BD = 7\sqrt{3} [/tex]
✔️Using trigonometric ratio, find height of the rectangle, BF:
Thus:
[tex] tan(\theta) = \frac{opposite}{adjacent} [/tex]
Where,
[tex] tan(\theta) = tan(60) = \sqrt{3} [/tex]
Opposite = 6 cm
Adjacent = BF
Plug in the values
[tex] \sqrt{3} = \frac{6}{BF} [/tex]
[tex] BF = \frac{6}{\sqrt{3}} [/tex]
Rationalize
[tex] BF = \frac{6 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}} [/tex]
[tex] BF = \frac{6\sqrt{3}}{3} [/tex]
[tex] BF = 2\sqrt{3} [/tex]
✔️Perimeter of rectangle BDEF:
Perimeter = 2(BD + BF)
Plug in the values
[tex] Perimeter = 2(7\sqrt{3} + 2\sqrt{3}) [/tex]
[tex] Perimeter = 2(9\sqrt{3}) [/tex]
[tex] Perimeter = 18\sqrt{3} [/tex]
✔️Area of the rectangle BDEF:
Area = BD × BF
Plug in the values
[tex] Area = 7\sqrt{3} \times 2\sqrt{3} [/tex]
[tex] Area = 7 \times 2\sqrt{3 \times 3} [/tex]
[tex] Area = 14 \times 3 [/tex]
[tex] Area = 42 [/tex]
If the base number is 2/3 and the power is 5.
answer must be a fraction
please explain i need this ASAP!!
WILL GIVE BRAINIEST
Answer:
32/243
Step-by-step explanation:
do 2 to the 5th and put it above 3 to the 5th
A restaurant customer left $ as a tip. The tax was and the tip was % of the after tax cost. Which information is not needed to compute the bill after tax and tip? What was the total bill?
Complete question :
A restaurant customer left $0.90 as a tip. The tax was 8% and the tip was 10% of the after tax cost. Which information is not needed to compute the bill after tax and tip? What was the total bill?
Answer:
The tax percentage
9.9
Step-by-step explanation:
Guven that :
Amount of tip left = 0.90
Tip left = 10% of after tax cost
Tax % = 8%
If tip left = 10% of after tax cost; then ;
If after tax cost = x
10% of x = 0.90
0.1x = 0.9
Hence the percentage tax isn't needed :
To obtain the total bill:
Let total bill = y
y = after tax cost and tip
Hence,
y = x + tip
y = x + 0.9
From : 0.1x = 0.9 ; x = 0.9/0.1 = 9
Hence,
Total bill:
y = 9 + 0.9
y = 9.9
If 4 soap cakes cost Rs 50, find the cost of 3 dozen soap cakes.
50 divided by 4 is 12.5, so it is 12.5 for 1 soap cake, 12.5 x 36 is 45.0
The answer is 45.0
Mark Branliest!
so
How would you write 6.5E4
How do cells maintain homeostasis? Describe one way a cell will maintain stable internal conditions.
Answer:
One way that a cell maintains homeostasis is by controlling the movement of substances across the cell membrane. Cells are suspended in a fluid environment.
A basket contains six apples and five peaches. You randomly select one piece of fruit and eat it. Then you randomly select another piece of fruit.
The first piece of fruit is an apple and the second piece is a peach. What’s the probability?
Answer:
6/11 * 5/10
3/11 or 0.27 repeating
Step-by-step explanation:
Blake sold 17 verses for $3.25 each he spent $16.21 on materials to make the vases what is the profit
Answer:
We can calculate what did he get, as we know he sold 17 vasess for 3.25 dollars each of them, we can multiply:
17 * 3.25 = $55.25
Now, we know he got 55.25 dollars but he spent 16.21, so we substract:
55.25 - 16.21 = $39.04
His profit selling that is of 39.04 dollars..
How much interest will you pay on a loan of $2,620, with a 3% interest rate, paid over 5
years?
Answer:
You'll pay $3013
Step-by-step explanation:
Amount to pay=$2620+Interest accrued
A=$2620+($2620×0.03×5)
A=$2620+$393
A=$3013
what is 149866.37636 rounded to the nearest whole number
Answer:
149866 is the nearest whole number.
Step-by-step explanation:
plzzzz some one help I want step by step I'm confused What's 5⁄6 of £300
Answer: 15
Step-by-step explanation:
Abby has to measure the weight of objects in pounds for her homework, but she only has a scale that measures ounces. If she finds an object weighs 48 ounces, how many pounds does it weigh?
Answer: 3 pounds
Step-by-step explanation: 1 pound=16 ounces
Now that you know what the conversion from ounces to pounds is, you just have to divide the number of ounces in the problem (48) by 16.
48÷16=3
10. In a warehouse, the workers sometimes slide boxes along the floor to move them. Two boxes
were sliding toward each other and crashed. The crash caused both boxes to change speed. Based
on the information in the diagram, which statement is correct? In your answer, explain what the
forces were like and why the boxes changed speed (5pts)
Box 1 has more mass than Box 2.
Box 1 and Box 2 are the same mass.
Box 1 has less mass than Box 2.
Answer:
The Box 1 and Box 2 are the same mass.
Explanation:
It caused both to change speed because they have both the same mass.
Non proportional or proportional
Can you help meh pls
What is the range of {( -1,6), (2,0), (9,-3), (-4,6)}
Answer:
Range: {6,0,-3}
Step-by-step explanation:
Multiply
(1.4 x 105)(2 x 107)
Answer:
31458
Step-by-step explanation:
(1.4 x 105) = 147
(2 x 107) = 247
147 x 247 = 31,458
