The side of the base of a square pyramid is increasing at a rate of 666 meters per minute and the height of the pyramid is decreasing at a rate of 111 meter per minute. At a certain instant, the base side is 333 meters and the height is 999 meters. What is the rate of change of the volume of the pyramid at that instant (in cubic meters per minute)

Answers

Answer 1

Answer:

[tex]105m^3/min[/tex]

Step-by-step explanation:

We are given that

Base side of square pyramid, a=3 m

Height of square pyramid, h=9m

[tex]\frac{da}{dt}=6m/min[/tex]

[tex]\frac{dh}{dt}=-1/min[/tex]

We have to find  the rate of change of the volume of the pyramid at that instant.

Volume of square pyramid, V=[tex]\frac{1}{3}a^2h[/tex]

Differentiate w.r.t t

[tex]\frac{dV}{dt}=\frac{1}{3}(2ah\frac{da}{dt}+a^2\frac{dh}{dt})[/tex]

Substitute the values

[tex]\frac{dV}{dt}=\frac{1}{3}(2(3)(9)(6)+(3^2)(-1)[/tex]

[tex]\frac{dV}{dt}=105m^3/min[/tex]

Hence, the rate of change of the volume of the pyramid at that instant=[tex]105m^3/min[/tex]


Related Questions

Through (4,-4) parallel to y=3

Answers

Answer:
y = -4

Explanation:
The graph of y = 3 is horizontal.

The slope must be 0 for a line to be horizontal, and thus parallel to y=3.

In slope-intercept form (y = mx + b), “m” is the slope, “b” is the y-intercept.
When the slope, m = 0, the equation becomes y = b.

Point (4,-4) is written (x, y).
y = -4

Since y = b, b = -4.

Therefore, the equation is y = -4.

Answer:

y = -4

Step-by-step explanation:

Because y = b, b = -4, the equation would be written as y = -4.

simplify the expression, 7 (m + 2 + 5)

Answers

Answer:

7m + 49 or 7(m + 7)

Step-by-step explanation:

Distribute the 7 to each integer and simplify.

Answer:

7m+49

Step-by-step explanation:

7m+14+35

7m+49

6/8X2/6=What is the answer to this equation

Answers

Answer:

6

Step-by-step explanation:

The segments shown below could form a triangle.​

Answers

Answer:

true, they can form a triangle.

Step-by-step explanation:

since, sum of two sides is greater than the third side in any case and the difference between two sides is smaller than the third one in all cases.

What is the GCF of a¹²b⁴, a⁴b⁸, a²⁴b¹⁶ and a¹²b²⁰?​

Answers

Given:

a¹²b⁴, a⁴b⁸, a²⁴b¹⁶ and a¹²b²⁰.

To find:

The GCF of given terms.

Solution:

Greatest common factor (GCF): To find the GCF of two or more numbers, we need to find the product of their prime factor with their maximum powers.

The given terms are

[tex]a^{12}b^{4},a^{4}b^8, a^{24}b^{16}, a^{12}b^{20}[/tex]

Here, each term has two prime factors a and b. The highest power of a is 24 and the highest power of b is 20. So, the GCF of given terms is

[tex]GCF=a^{24}\times b^{20}[/tex]

[tex]GCF=a^{24}b^{20}[/tex]

Therefore, the GCF of a¹²b⁴, a⁴b⁸, a²⁴b¹⁶ and a¹²b²⁰ is a²⁴b²⁰.

Identify the ‘false’ statement.
a) (-317) < 603
b) (-333) < (-777)
c) 630 > 234
d) 1250 > (-750)

Answers

Answer:

the false statement would be option b) (-333) < (-777).

Step-by-step explanation:

in negative numbers, the smallest negative number would be considered larger when compared to a large negative number. additionally, when you plot these numbers on a number line, it is evident that -333 would be closest to 0, and -777 would be the farthest. thus, -333 is larger than -777.

Can someone solve this please

Answers

Answer:15. 5/8 = 0.625

Step-by-step explanation:

1. identify the corresponding sides on the figure below

Answers

Answer:

No because one side is 8 and the other is 18

Step-by-step explanation:

No. The sides are not equal to one another, even in fraction form.

Isabella is cooking a meal for 14 friends. Each person gets
6
of a cup of vegetables.
How many cups of vegetables does Isabella need?

Answers

I’m pretty sure that says 6 cups of vegetables so 84 cups but if you meant 1/6 of a cup then 7/3 cups or 2/1/3

HELP ASAP PLEASE! GIVING AWAY 30 POINTS AND BRAINLIEST!

Answers

Answer:

DB!

Step-by-step explanation:

Question a: 3+3+2+2 = 10 dinners

Question b: 15-30 and 30-45, because most people choose that range.

Hope I helped!

Answer:

a) 10 b) 2-3 dollars

Step-by-step explanation:

a) 3+3+2+2

b) (2+2+3+3)/2 equal 2.5 mean, range between them is 2 to 3

solve and you will get brain list ​

Answers

Answer:

No solutions

Step-by-step explanation:

what is the difference between 1 and o.1978​

Answers

Answer:

0,8022

Step-by-step explanation:

guess it helped

Calculate the distance between the points J=(4, -2) and E = (7. – 7) in the coordinate plane.
Give an exact answer (not a decimal approximation).

Answers

Answer:

Step-by-step explanation:

√[(7-4)^2+{-7-(-2))^2] = √36 = 6

The distance between the points J=(4, -2) and E = (7. – 7) in the coordinate plane is 6.

What is coordinate plane ?

"A coordinate plane is a two-dimensional plane formed by the intersection of two number lines. One of these number lines is a horizontal number line called the x-axis and the other number line is a vertical number line called the y-axis. These two number lines intersect each other perpendicularly and form the coordinate plane.

The plane is called two-dimensional because anywhere on this plane where you can put your finger, the location of that point will need two things– its distance on the x-axis and its distance on the y-axis."

Using the distance formula between the points

Given, J = (4,-2) and E = (7,-7)

Distance formula = [tex]\sqrt((x1 - x2)^2 -(y1 - y2)^2)[/tex]

[tex]= \sqrt((4-7)^2 + (-2 - (-7))^2)\\\\= \sqrt(9 + 25) = 6[/tex]

Hence, distance between the points J and E = 6

To know more about coordinate plane here:

https://brainly.com/question/13611766

#SPJ3

plzzzzz i vill give 5 stars a heart brainlyest if you can anwser this write 5(2j+3+1j)= using the commutive property

Answers

Answer:

The answer would be 5 (3j + 3)

Step-by-step explanation:

The 5 outside the partheness would stay the same

2j + 1j = 3j

The 3 remains the same.

So our answer is

5(3j + 3)

if the figures below are similar give the scale factor of figure a to b,20,17.5,16,14

Answers

Answer:

Step-by-step explanation:

a wildlife photographer photographs a crocodile and then paddles against a river current for 6 km. Then, hoping to photograph a hippopotamus, she paddles 15 km across a lake. She paddles across the lake for one hour longer than she paddled up the river. find the speed of the boat as she paddles the lake if the river current is 2 km/h. Pls answer. You'll get 100 points.

Answers

Answer:

5 km/h or 6 km/h

Step-by-step explanation:

Let the speed of the boat be xSpeed against the current in the river is x - 2

Time in the river:

6/(x - 2)

Time in the lake:

15/x

The difference:

6/(x - 2) = 15/x - 1

Solve for x to find the speed of the boat

Multiply both sides by x(x - 2) to clear the fraction:

6x = 15(x - 2) - x(x - 2)6x = 15x - 30 - x² + 2xx² - 11x + 30 = 0(x - 5)(x - 6) =0x -5 = 0, x - 6 = 0x = 5 km/h, x = 6 km/h

Answer:

5km/hr or 6km/hr

Step-by-step explanation:

A little help with this math problem

Answers

Answer:

The length of the last side is 9 metres

Step-by-step explanation:

Plzzz help me it would mean a lot I willl mark you brainliest if you are right plz and ty ​

Answers

Answer:

45

Step-by-step explanation:

x÷3=15

=×*1/3=15

=x=15*3

x=45

Answer:

15 x 3 = 45

So, x = 45

Pls mark the brainliest :)

Step-by-step explanation:

A wire is attached to the top of a tower and to a point on the ground that is 35 m from the base of the tower. If the wire makes a 65 degree angle with the ground, how long is the wire? Round your answer to the nearest tenth

Answers

Answer:

83 m

Step-by-step explanation:

The computation of the length of the wire is shown below:

Let us assume the length of the wire be x

Given that

There is 35m from the base of the tower

And, the angle with the ground is 65 degree

So, the length of the wire is

cos 65 = 35 ÷ x

x = 35 ÷ cos 65

= 83 m

Exercise 2.4.4: Showing a statement is true or false by direct proof or counterexample. About Determine whether the statement is true or false. If the statement is true, give a proof. If the statement is false, give a counterexample. (a) If and are even integers, then is an even integer. Solution (b) If is an even integer, then and are both even integers. (c) If , then . Solution (d) If x and y are real numbers and , then . Solution (e) If and are positive real numbers and , then . (f) The average of two odd numbers is an odd integer. (g) The average of two even numbers is even. (h) The average of two odd numbers is an integer. Solution

Answers

Answer:

Step-by-step explanation:

and ok thats the deal

Find the perimeter and area of the figure

Answers

Answer:

Step-by-step explanation:

Perimeter = Add

Area= x

Use this solution to figure the area & Perimeter out.

Answer:

perimeter = 76 ft

area = 338 sq ft

Step-by-step explanation:

Does this look right? Explain why


5/6


6.565656…


0.23


-5 3/8

Answers

Answer:

Yes

Step-by-step explanation:

Yes ,a rational number is a number that can be expressed as a fraction. Repeating and terminating decimal are rational number so

5/6 is right since it is a fraction

6.565646 is right since it is a repeating decimal

0.23 is right since it is a terminating decimal

-5 3/8 is right since it is a mixed number

Sqr root of 11 and 0.32416.... is wrong since it creates multiple random unknown digits

Help, please it's due soon?

Answers

9514 1404 393

Answer:

  398,765

Step-by-step explanation:

If s represents the number sold to date, the given relation is ...

  0.081s = 32300

  s = 32300/0.081 ≈ 398,765 . . . . . . divide by the coefficient of s

398,765 copies have been sold to date.

Simplify. 2√6−4√24+√96What is the greatest common factor of 12xy^5+60x^4y^2−24x^3y^3?

Answers

Answer:

greatest common factor is 12xy² .

Step-by-step explanation:


a- 10
b- 70
c- 110
d- 170

Answers

Step-by-step explanation:

step 1. 2x + 50 and 7x are vertical angles

step 2. vertical angles are equal

step 3. 2x + 50 = 7x

step 4. 5x = 50, x= 10

step 5. <AEB = 2x + 50 = 2(10) + 50 = 70.

1. What is the result when 3x2 - 4x + 5 is subtracted
from 3x3 – 13x + 4?

Answers

i think it would be 2-9x

What is a multiple of 1/7 I need a answer quickly. its due tonight please help

Answers

Answer:

2/7

Step-by-step explanation:

Hope that helps! (Brainliest please!)

A new pair of Nike shoes costs $95. It is on sale for 25% off! How much will you pay (not including taxes)?

Answers

Answer:

23.75

Step-by-step explanation:

95 is the 100 so to find 25% divide it by 4 and you get 23.75

Ex. What is the theoretical probability of rolling 5 or higher on a six sided die?​

Answers

since they can roll a 5 or a 6 there’s 2 options
then there are 6 total options
so 2/6 = 1/3

n=7, x=4, p=0.45, find p4

Answers

Answer:

1.8

Step-by-step explanation:

All you need to do is use substitution....

p4

They gave us the value of p and it is 0.45, now we need to substitute it, into the expression to find the value

p4 = (0.45)4

0.45 * 4 = 1.8

so p4 = 1.8

Hope this helped!

Have a supercalifragilisticexpialidocious day!

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