Someone please help it’s dueee today!

The surface area of a melting snowball decreases at a rate of3.8cm2/min. Find the rate at which its diameter decreases when the

Scorpion4ik [409]

Answer:

Step-by-step explanation:

This is a pretty basic related rates problem. I'm going to go through this just like I do in class when I'm teaching it to my students.

We see we have a snowball, which is a sphere. We are talking about the surface area of this sphere which has a formula of

$S=4\pi r^2$

In the problem we are given diameter, not radius. What we know about the relationship between a radius and a diameter is that

d = 2r so

$\frac{d}{2}=r$ Now we can have the equation in terms of diameter instead of radius. Rewriting:

$S=4\pi(\frac{d}{2})^2$ which simplifies to

$S=4\pi(\frac{d^2}{4})$ and a bit more to

$S=\pi d^2$ (the 4's cancel out by division). Now that is a simple equation for which we have to find the derivative with respect to time.

$\frac{dS}{dt}=\pi*2d\frac{dD}{dt}$ Now let's look at the problem and see what we are given as far as information.

The rate at which the surface area changes is -3.8, and we are looking for $\frac{dD}{dt}$ , the rate at which the diameter is changing, when the diameter is 13. Filling in:

$-3.8=\pi(2)(13)\frac{dD}{dt}$ and solving for the rate at which the diameter is changing:

$-\frac{3.8}{26\pi}=\frac{dD}{dt}$ and divide to get

$\frac{dD}{dt}=-.459\frac{cm}{min}$ Obviously, the negative means that the diameter is decreasing.

7 0

3 years ago

Find the percent of increase from 12 pencils to 18 pencils.

nalin [4]

18-12/12 *100

6/12*100

1/2*100

50%

7 0

3 years ago

Robin can clean 72 rooms in 6 days how many rooms can robin clean in 9 days

galben [10]

Hello!

Robin can clean 72 rooms in 6 days. How many rooms can Robin clean in 9 days?

We have a proportional magnitude (directly proportional), if we increase the number of days for cleaning, obviously we will have more rooms cleaned, then:

clean rooms __________ days

72 ----------------------------------- 6

y ------------------------------------- 9

$\dfrac{72}{y} = \dfrac{6}{9}$

multiply the means by the extremes

$6*y = 72*9$

$6\:y = 648$

$y = \dfrac{648}{6}$

$\boxed{\boxed{y = 108}}\Longleftarrow(clean\:rooms)\end{array}}\qquad\checkmark$

Answer:

108 clean rooms in 9 days

________________________

I Hope this helps, greetings ... Dexteright02! =)

6 0

3 years ago

Answer please I will give brainiest to the one who answers first.

Lerok [7]

Answer:

$1,094,748.09
$8600.28
11 years, 10 months

Step-by-step explanation:

a) The compound interest formula can be used:

A = P(1 +r/n)^(nt)

where P is the principal invested at annual rate r compounded n times per year for t years.

A = $750,000(1 +.038/4)^(4·10) ≈ $1,094,748.09

Tamsyn's account will have a balance of $1,094,748.09 when she retires.

__

b1) The amortization formula is good for this.

A = P(r/n)/(1 -(1 +r/n)^(-nt))

where P is the amount earning interest at annual rate r compounded n times per year for t years.

A = $1,094,748.09(0.049/12)/(1 - (1 +0.049/12)^(-12·15)) ≈ $8600.28

Tamsyn can withdraw $8600.28 per month for 15 years.

__

b2) The account balance after n months will be ...

B = P(1 +r/12)^n -A((1+r/12)^n -1)/(r/12)

Filling in the known values and solving for n, we have ...

300,000 = 1,094,748.09(1.1.00408333^n) -8600.28(1.00408333^n -1)/.000408333

300,000 = 1,094,748.09(1.1.00408333^n) -2,106,191.02(1.00408333^n -1)

-1,806,191.02 = -1,011,442.93(1.00408333^n)

1.785757 = 1.00408333^n

n = log(1.785757)/log(1.00408333) = 142.3

After about 11 years 10 months, the account balance will be $300,000.

4 0

3 years ago

Can you answer question 29, please?

timurjin [86]

From the table, for every 6 containers of water, you need 8 containers of red dye. So, for every one container of red dye you need 0.75 containers of water (6/8). Then, multiply that by 100 (since you wanted to know water necessary for 100 containers of red dye). For 100 containers of red dye, you would need 75 containers of water.

5 0

3 years ago