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's 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

A salesman earns 6% commission on all the merchandise that he sells. Last month he sold $9000 worth of merchandise. How much
commission (in dollars) did he earn last month?

Answers

$540

6% = .06
“of” = multiply
so 6% of 9000 can be written as .06 x 9000 , which is 540

The commission (in dollars) did he earn last month is 540$.

We have given

A salesman earns 6% commission on all the merchandise that he sells.

Last month he sold $9000 worth of merchandise.

Salesman earns 6% =6/100=0 .06

What is the meaning of commission?

Earning a commission means that a portion of your salary is based on the amount of sales revenue you generate or another similar performance-based goal.

So we have to determine 6% of 9000

We can be written as

=0.06 x 9000,

= 540$

The commission (in dollars) did he earn last month is 540$.

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Evaluate the function when X=3 , X=0 , and x=-2.

Answers

Answer:

12)f(x)=2x-6

=》f(3)=2(3)-6

=》6-6=0

f(×)=2x-6

f(0)=-6

=》f(-2)=2(-2)-6

=》-4-6

=-10

13)h(3)=6(3)+2

=》18+2

=20

h(0)=0+2

=2

h(-2)=6(-2)+2

=》-12+2

=-10

Find the slope of the line contains (-2, -2) and (-10, -9)

Answers

Answer:

The slope is m = 7/8 or 0.975

Step-by-step explanation:

Answer:

7/8

Step-by-step explanation:



1. What is your gross bi-weekly income if you are paid an annual salary of $85,700?

Answers

Answer:

Your gross bi-weekly incomeis of $824.

Step-by-step explanation:

An year has 52 weeks.

In this problem:

Bi-weekly payments, that is, 52*2 = 104 payments during the year, combining $85,700.

Your bi-weekly income will be of:

$85700/104 = $824

Your gross bi-weekly incomeis of $824.

X=y-3
2x-2y=-6
No solution, one solution, or infinite solution?

Answers

Answer:

No solution

Step-by-step explanation:

2y - 3 - 2y = -6

2y - 2y - 3 = -6

-3 = -6

No solution

Find the area of the rhombus

Answers

Answer:

[tex] Area \: of \: rhombus =96\: cm^2 [/tex]

Step-by-step explanation:

[tex] d_1= 2\times 8 = 16\: cm[/tex]

[tex] d_2= 2\times 6 = 12\: cm[/tex]

[tex] Area \: of \: rhombus =\frac{1}{2} d_1d_2[/tex]

[tex] Area \: of \: rhombus =\frac{1}{2}\times 16 \times 12[/tex]

[tex] Area \: of \: rhombus =8 \times 12[/tex]

[tex] Area \: of \: rhombus =96\: cm^2 [/tex]

What is the area of a rectangle that is 4 inches by 2 inches?

Answers

Answer:

8

Step-by-step explanation:

What is the probability of picking a rod marble at
random?
What is the probability of picking'a red marble at
random, and without replacing it, then picking a blue
one?

Answers

Answer:

1) 7/12

2) 35/132

Step-by-step explanation:

1) 7/12

2) 7/12x5/11=35/132

Graph the solution set of the inequality 1/4 x >= - 2

Answers

Answer:

-8 is one point and the arrow goes to 10

Step-by-step explanation:

The solution of the inequality is x≥ -8.

What is Inequality?

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

1/4 x ≥ - 2

Now, the solving the inequality for x we get

x ≥ -2 (4)

x≥ -8

So, the value of x should be the region where values of x should be equal to -8 and greater than -8.

That means x ≠ -7, -6, -5, ....0,1, 2, 3....

The inequality graph is attached below.

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Find the slope of the following graphs?

Answers

Answer:

the gradient is 2/3

Step-by-step explanation:

you find the difference in the height and length, so in this case 2 divided by 3

On hot, sunny, summer days, Jane rents inner tubes by the river that runs through her town. Based on her past experience, she has assigned the following probability distribution to the number of tubes she will rent on a randomly selected day.



x 25 50 75 100 Total
P(x) .27 .33 .29 .11 1.00

Answers

Answer: 11.25.16 iykyk


What is the value of the angle x?

Answers

X= 66

Explanation: you would take 180-114 and that would give you an angle of 66

A(-2,-2) B(-1,2) C(2,1) / A (-4,-4) (-2,4) C(4,2)

Answers

Answer:

umm lettders dont go in math pst this in englash

Step-by-step explanation

yeet

Please help!!!!! 20pts

Answers

Answer:

vertically Angle is correct answer

The first one is none of these.

The second is Vertical, like the person above said.

I think that’s it. Sorry if i’m wrong.

Because of the commutative property of multiplication, it is true that
3/4

×
4
=
4
×
3/4

. However, these expressions can be calculated in different ways even though the solutions will be the same.

Below, show two different ways of solving this problem.

First, show how
3/4*4


can be solved using repeated addition.

Answers

¾ + ¾ + ¾ + ¾ = (3+3+3+3)/4 = 12/4 = 3


¾ × 4 = (3 × 4)/4 = 12/4 = 3

linear function, pls help

Answers

Answer:

A

Step-by-step explanation:

15. Ken is planting vegetables in his garden, He has
20 seeds Determine whether 20 is a prime or
composite number if it is composite, list all of the
ways ken can arrange the seeds in even rows,

Answers

Answer:

20 is a composite number.

Ways that can be arranged:

5 x 4

10 x 2

20 x 1

Answer:

Once upon a time, there was a flock of doves that flew in search of food led by their king. One day, they had flown a long distance and were very tired. The dove king encouraged them to fly a little further. The smallest dove picked up speed and found some rice scattered beneath a banyan tree. So all the doves landed and began to eat.

Suddenly a net fell over them and they were all trapped. They saw a hunter approaching carrying a huge club. The doves desperately fluttered their wings trying to get out, but to no avail. The king had an idea. He advised all the doves to fly up together carrying the net with them. He said that there was strength in unity.

Each dove picked up a portion of the net and together they flew off carrying the net with them. The hunter looked up in astonishment. He tried to follow them, but they were flying high over hills and valleys. They flew to a hill near a city of temples where there lived a mouse who could help them. He was a faithful friend of the dove king.

Becky made 63 carnival masks which is 30 % less than the number her brother made How many carnival masks did beck and her brother make in total?

Answers

Answer:

sorry im not smart

Step-by-step explanation:

sorry

THis is akward lol

Casper write the algebraic expression 5b + 3.79. I represents the total cost, in dollars, of buying 5 bagels and a container of cream cheese. Identify any variables, coefficients, and termsin the expression. Tell me what each represents

Answers

Answer:

5 is a co efficient and b is a variable together is a term, 3.79 is a constant/term the whole equation is an expression.

The total cost of buying 5 bagels and a container of cream cheese is $28.79 and in the expression 5 is constant, b is variable, and 3.79 is constant representing the cost of the container.

What is an expression?

An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that all are constrained and create an equation.

For example 3x +5y

Given the expression for the total cost,

C = 5b + 3.79 where b is the number of bagels.

Cost of 5 bangles

C = 5(5) + 3.79 =$ 28.79

Cost of container = $3.79

Thus b is the only variable and 5b represents the cost of bagels while by the sum of container cost 3.79 total costs are created.

Hence "The total cost is $28.39 and container cost is $3.79 while b is variable".

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Q3
Work out the volume of each of these items:
a) a bag of sugar of mass 1000 g and density 1.6 g/cm
b) a packet of margarine with density 2.8 g/cm and mass 250 g

Answers

Answer:

Step-by-step explanation:

1000 g × (1 cm³)/(1.6 g) = 1000/1.6 cm³ = 625 cm³

:::::

250 g × (1 cm³)/(2.8 g) = 89.3 cm³

please help test due tomorrow. I'll give the correct answer brainliest

solve for x. show your work.​

Answers

Is there any extra information in the question?
X= 45
Right angle =90, then divide by two

what is the answer i need help

Answers

Answer:

90/100

Step-by-step explanation:

both equal 0.9

Answer:

[tex]\frac{90}{100\\}[/tex]

Step-by-step explanation:

[tex]\frac{9}{10}[/tex] equals [tex]\frac{90}{100\\}[/tex]

By multiplying the numerator and denominator of [tex]\frac{9}{10}[/tex] by 10, we get [tex]\frac{90}{100\\}[/tex] .

9 x 10 = 90

10 x 10 = 100

A manufacturing company is shipping a certain number of orders that need to weigh between 193 and 194 pounds in order to ship. Use the dot plot below to answer the following questions.193193.1193.2193.3193.4193.5193.6193.7193.8193.9194Step 1 of 3 : How many orders did the company ship between 193 and 194 pounds

Answers

Answer:

15 orders

Step-by-step explanation:

The computation of the orders did the company ship between 193 and 194 is given below:

= 1 dot + 2 dot + 3 dot + 8 dot + 1 dot

= 15 orders

We just simply count the total dots shown in the attached image in order to determine the number of orders

I need help please ​

Answers

I'm not sure of what your trying to find... but the slope is (10/3). The equation in  slope form is y=(10/3)x-10. The Standard form is 10x-3y=30.

Does this help?

Answer: The equation of that line is [tex]Y = 3 \frac{1}{3}x -10[/tex]

Step-by-step explanation:

Factor by grouping. 3x³ – 2x²–9x+6​

Answers

Answer:

(3x-2)(x²-3)

Step-by-step explanation:

3x³-2x²-9x+6

=(3x³-2x²)+(-9x+6)

=x²(3x-2)-3(3x-2)

first answer must include the GCF and the second answer consists of the remaining numbers.

The Los Angeles Times regularly reports the air quality index for various areas of Southern
California. A sample of air quality index values for Pomona provided the following
data: 28, 42, 58, 48, 45, 55, 60, 49, and 50.
a. Compute the range and interquartile range.
b. Compute the sample variance and sample standard deviation.
c. A sample of air quality index readings for Anaheim provided a sample mean of 48.5,a sample variance of 136, and a sample standard deviation of 11.66. What comparisons can you make between the air quality in Pomona and that in Anaheim on the basis of these descriptive statistics?

Answers

Answer:

Range = 32 ; IQR = 13 ; Variance = 92.75 ; Standard deviation = 9.63

Step-by-step explanation:

Given the data:

28, 42, 58, 48, 45, 55, 60, 49, 50

Reorderd data: 28, 42, 45, 48, 49, 50, 55, 58, 60

The range: maximum - minimum

Range = 60 - 28 = 32

Interquartile range (IQR) : Q3 - Q1

Q3 = 3/4(n+1) th term. ; n = sample size

Q1 = 1/4(n+1)th term.

Using calculator :

Q3 = 56.5 ; Q1 = 43.5

IQR = 56.5 - 43.5 = 13

The variance :

Σ(X - m)^2 / n-1

m = Σx / n

Mean, m = 435 / 9 = 48.33

Variance :

[(28-48.33)^2 + (42-48.33)^2 + (45-48.33)^2 + (48-48.33)^2 + (49-48.33)^2 + (50-48.33)^2 + (55-48.33)^2 + (58-48.33)^2 + (60-48.33)^2] / 8

= 742.0001 / 8

= 92.75

Standard deviation = sqrt(Variance):

Sqrt(92.75) = 9.63

C.)

Sample mean are very close with a slightly greater Variability in the air quality of Anaheim over Pomona

1. Jerry has 56.92 centimeters (cm) of wire. He uses 2 pieces of the wire. Each piece he uses is 7.37 cm long. What is the length of the remaining wire, rounded to the nearest tenth of a centimeter?




2.

Answers

4.2 because 56.92-7.37(2)=4.18. Then you can just round to the nearest tenth which would make it 4.2 since 8 rounds up. Hope this helped!
The answer to this question is 4.2.

What is the slope of the line shown below?
10
O A. -3
(4,8)
5
O B. - 1
3
(2, 2)
-5
5
10
15
O c. 3
1
O D.
-10 +

Answers

Slope of the line shown is option C. 3.

What is Slope?

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Given is a line.

The two points that the line passes through is given.

(4, 8) and (2, 2)

Slope of a line passing through two points can be found as,

Slope = (Change in y coordinates ) / (Change in x coordinates)

Here the points are (4, 8) and (2, 2),

Slope = (2 - 8) / (2 - 4)

          = -6 / -2

          = 3

Hence the slope of the line given is 3.

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Green lawns uses 33 oz. Of fertilizer for 5.5 acres. Assume the company is fertilizing 0.5 of am acre. How much fertilizer does ot need?

Answers

0.5 acre × 33 oz)/(5.5 acres) = 3 oz fertilizer

What is x in 15 = -3(x -2)

Answers

Answer:

-3

Step-by-step explanation:

15 = -3(x -2)

-5=x-2

-3=x

Answer:

x = -3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Step-by-step explanation:

Step 1: Define

15 = -3(x - 2)

Step 2: Solve for x

[Division Property of Equality] Divide -3 on both sides:                              -5 = x - 2[Addition Property of Equality] Add 2 on both sides:                                  -3 = xRewrite/Rearrange:                                                                                        x = -3
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