Homework help!!!!!!!

We want to find the rate of change of the surface for a cube of increasing volume.

When the side length is equal to 20 inches, the surface area is increasing at a rate of 439.29 in^2 per minute.

We know that for a cube of side length S, the volume is:

V = S^3

And the surface area is:

A = 6*S^2

Here we know that the volume increases at a rate of 12in^3/min.

Because the volume depends on the side length cubed, we can say that the side length increases at a rate of:

∛(12in^3)/min = 2.29 in/min

Then, as a function of time t in minutes, we can write the side length as:

S(t) = (2.29 in/min)*t

Then the surface area equation is:

A(t) = 6*((2.29 in/min)*t)*((2.29 in/min)*t)

A(t)  = (31.46 in^2/min^2)*t^2

The rate of change is given by direct differentiation, we get:

A'(t) = 2*(31.46 in^2/min^2)*t

Now we need to evaluate this in the value of t such that the side length is equal to 20 in:

S(t) = 20in = (2.29 in/min)*t

         (20in)/(2.29 in/min) = t = 8.73 min

Then we will get:

A'(8.73min) =  2*(31.46 in^2/min^2)*8.73min = 439.29 in^2/min

This means that when the side length is equal to 20 inches, the surface area is increasing at a rate of 439.29 in^2 per minute.

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The degree of a polynomial is the highest power of the polynomial.

The polynomial is [tex]\mathbf{P(x) = (x + 3)^4}[/tex]

The degree is given as:

[tex]\mathbf{n = 4}[/tex]

The zero is given as:

[tex]\mathbf{x = -3}[/tex]

Add 3 to both sides

[tex]\mathbf{x + 3= 0}[/tex]

From the question, we understand that the polynomial has a single zero.

So, the polynomial is:

[tex]\mathbf{P(x) = (x + 3)^n}[/tex]

Substitute 4 for n

[tex]\mathbf{P(x) = (x + 3)^4}[/tex]

Hence, the polynomial is [tex]\mathbf{P(x) = (x + 3)^4}[/tex]

Read more about polynomials at:

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Answer:

Step-by-step explanation:

Your answer is A.

Anytime you have a variable or something that changes such as the month that is a variable so that means its going to be your x/m in this case

Answer:

251,734.

Step-by-step explanation:

Answer:

x= 10

Step-by-step explanation:

C(x) = 2,000x + 60,000

R(x) = 8,000x

Set the solution to zero.

R(x) - C(x) = 0

8,000x - (2,000x  + 60,000) = 0

6,000x - 60,000 = 0

x=10

Given :-

To find :-

Solution :-

Common difference ,

As we know that ,

Answer:

30th

Step-by-step explanation:

There is a common difference between consecutive terms, that is

- 2 - (- 13) = 9 - (- 2) = 20 - 9 = 31 - 20 = 11

This indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 13 and d = 11 , then

[tex]a_{n}[/tex] = - 13 + 11(n - 1) = - 13 + 11n - 11 = 11n - 24 ← equate to 306

11n - 24 = 306 ( add 24 to both sides )

11n = 330 ( divide both sides by 11 )

n = 30

The 30th term is 306

Answer:

784.19(1 + .15/12) = 793.99

Step-by-step explanation:

Answer:

104.364

Step-by-step explanation:

Product means multiplication so:

44.6×2.34 = 104.364

the answer to this question is -6&5

Answer:

I cant help you

Step-bBecause i just c

y-step explanation:

Answer:

1.03

Step-by-step explanation:

Per capita just means per unit of population, or per person. This question is asking how many cell phones there were in the United States per person in 2014. We can use simple division to determine that the answer is 327.6/317.9 or about 1.03 when rounded to the nearest hundredth.

Answer:

1.03

Step-by-step explanation:

Answer:

it looks like a positive correlation?

Step-by-step explanation:

I really don't know much but it looks like the y in increasing in a positive direction when the x is as well

Answer:

but where is the question please type your full questions

Answer:

7.5

Step-by-step explanation:

because 7.5 x 16 = 120

Answer:

21/40.

Step-by-step explanation:

There are 3 geometry and 7 algebra books.

If the geometry book is drawn first probability = 3/10

If the second is algebra P = 7/9.

If the third is algebra P = 6/8 = 3/4.

So the probability  of all three being drawn in this order = 3/10 * 7/9 * 3/4

= 63/360

= 7/40.

Now there are a total of 3 ways in the order they are drawn, That is:

GAA

AGA

AAG.

So the required probability = 3 * 7/40

= 21/40.

Answer:

27:45

Step-by-step explanation:

The ratio is 3:5, so the total is 8. 72/8 is 9. 9*3 is 27, and 9*5 is 45, so the two groups consist of 27 and 45 BAKERY Rolls.

Answer:

Step-by-step explanation:

1.)The 4th picture will be the correct one.

Step-by-step explanation:

The first picture shows the graph of f(x) and in the options there are pictures of graph of g(x) = f(x) -1

So, it is clear from the equation of the functions that the graph of f(x) and g(x) will be similar but the the y value in g(x) will be 1 less than the y value in f(x) corresponding to a certain x value.

So, the graph will translate down by 1 unit.

Therefore, the 4th picture will be the correct one.

2.)-(2^x) - 1 will have a y-intercept of -1-1 = -2, a horizontal asymptote of y=-1, and will be decreasing everywhere. The third selection is the graph that has these characteristics.

Answer:

graph 4

Step-by-step explanation: because I love you <3 ;)

Answer:

x = 11

Step-by-step explanation:

3x-2x=9+2 1st and 2nd principle

X=11

Answer:

6x+2/3-2=4x-4/6

6x-4x = 2-⅔-4/6

2x = 2-(4+4)/6

2x = (12-8)/6

2x = 4/6

12x = 4

x = 4/12

x =⅓

Step-by-step explanation:

brainliest plz

Pokyaa is 31 years, 6 months, while Afriyie

is 20 years, 6 months

The age of Pokyaa's such that Pokyaa is 11 years older than Afriyie is 31 years and 6 months old.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

Let's assume that the age of Pokyaa is P while the age of Afriyie is A.

As per the given,

Pokyaa is 11 years older than Afriyie

Therefore,  P = 11 + A

Altogether P + A = 52

Substitute,A = 52 - P  into P = 11 + A

P = 11 + (52 - P)

P = 11 + 52 - P

P + P = 63

2P = 63

P = 32.5 ⇒ 31 years and 6 months.

Hence "The age of Pokyaa such that Pokyaa is 11 years older than Afriyie is 31 years and 6 months old".

For more about the equation,

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(ii) 3% of students failed all three courses, 12% failed economics and mathematics, 9% in math and business, and 10% in econ and business. In other words, the students in these groups failed at least the two mentioned courses. Then 12% - 3% = 9% failed only econ and math but not business; 9% - 3% = 6% failed math and business but not econ; and 10% - 3% = 7% failed econ and business but not math. These groups are mutually exclusive, so the total percentage of students that failed exactly two courses is (ii) 9% + 6% + 7% = 22%.

32% failed econ, which means 32% - 12% - 10% + 3% = 13% failed only econ. Similarly, 46% failed business, so 46% - 9% - 10% + 3% = 30% failed only business. But we don't know how many students failed math, so we can't determine how many failed only math... And consequently we can't determine the proportion of students that make up the other categories.

Answer:

The graph of g(x) is stretched vertically by a factor of 5/3.

Step-by-step explanation:

f(x) = √x

g(x) = √25/9 x = 5/3 √x

5/3 > 1 .. vertical stretch by a factor of 5/3

Answer:

Step-by-step explanation:

What is the HCF of two consecutive odd numbers?

The HCF of two consecutive odd number is 1.

Hello there!

-8+r>-8

Move all the numbers to the right:

r>-8+8

r>0

Hope it helps!

~Just a joyful teen

[tex]GraceRosalia[/tex]

Answer:

11400000

Step-by-step explanation:

1 whale = 380000 lbs

30 whale weighs 380000×30

30 whales = 11400000

I HOPE IT WILL HELP YOU.

Thank you.

Answer:

Step-by-step explanation:

Given formula:

To solve for k, multiply both sides by 2 and divide by x²:

Answer:

[tex]\sf\longmapsto \: k = \frac{2E}{x {}^{2} } [/tex]

Step-by-step explanation:

The formula given is :

[tex]\sf\longmapsto \: E = \frac{1}{2} kx²[/tex]

Now, multiply (×) both sides by 2 and divide (÷) by x^2

[tex]\sf\longmapsto \: 2E = kx²[/tex]

[tex]\sf\longmapsto \: k = \frac{2E}{x {}^{2} } [/tex]

Answer:

8% is the sales tax rate

Step-by-step explanation:

I'm not the best with math but the way I found the answer was by first using my local sales tax rate and determining how much the tax would be.

490 * 8.75% = 42.875

Knowing that this amount was higher than in the equation, I lowered the sales tax to 8% (0.08)

490 * 8% = 39.2

Hope this was somewhat helpful