Which set of points are collinear? P, T, Y D, S, Y H, T, S Y, D, H

Suppose that both the radius r and height h of a circular cone are increasing at a rate of 7 cm/s. How fast is the volume of the

rosijanka [135]

Answer:

The volume of the cone is increasing at the rate oof 3848.45 cm³/s when r=15 cm and h=10 cm.

Step-by-step explanation:

The volume of the cone is given by the following formula:

$V = \frac{r^{2}h\pi}{3}$

In which V is measured in cm³ while r and h are measured in cm.

Suppose that both the radius r and height h of a circular cone are increasing at a rate of 7 cm/s.

This means that $\frac{dh}{dt} = \frac{dr}{dt} = 7$

How fast is the volume of the cone increasing when r=15 cm and h=10 cm?

This is $\frac{dV}{dt}$ when $r = 15, h = 10$ .

$V = \frac{r^{2}h\pi}{3}$

Applying implicit differentiation:

We have three variables, V, r and h. So

$\frac{dV}{dt} = \frac{2r\frac{dr}{dt}h \pi + r^{2}\pi \frac{dh}{dt}}{3}$

$\frac{dV}{dt} = \frac{2*15*7*10\pi + 225*\pi*7}{3}$

$\frac{dV}{dt} = 3848.45$

The volume of the cone is increasing at the rate oof 3848.45 cm³/s when r=15 cm and h=10 cm.

7 0

2 years ago

Which equations are equivalent to log 4x=3

Lady bird [3.3K]

I'm not sure that this is what you wanted, but the solution is x = 2500
$log(4x) = 3 \\ rule > \: log_{a}(b) = x < = > \: b = {a}^{x} \\ 4x = {10}^{3} \\ 4x = 10 \: 000 \\ x = \frac{10 \: 000}{4} \\ x = 2500$
Note: when we have no number as the logarithmic base, it is 10 by default.

6 0

2 years ago

Help me It’s due tomorrow and I can’t figure it out!!!

yuradex [85]

A.) 30+10=40. So, 90-40=50. Your answer is 50 degrees.
B.) 45+4=49. So, 90-49=41. Your answer is 41 degrees.
C.) 8 to the square root of 2+45=56.31. So, 90-56.31=33.69. Your answer is 33.69 or 33.7 if you need to round.
D.) One angle is 30 degrees, and another angle is 60 degrees. Your other angle is 90 degrees.
E.) 60+6=66. 90-66=24. Your answer is 24 degrees.
F.) 45+6=51. 90-51=39. Your answer is 39 degrees.

4 0

3 years ago

A 30-year-old female purchased a 20-Year Endowment insurance policy at the age of 23. The face value of the policy was $78,250.

FrozenT [24]

Answer:

B

Step-by-step explanation:

Annual Premium of $2,957.85; 26 years and 10 days

8 0

2 years ago

Read 2 more answers

Anna has a 30-year, 5.75% mortgage on her $250,000 home. She has been

poizon [28]

Answer:

Her new monthly payment is now $1,378.91¢

Step-by-step explanation:

For us to calculate the new monthly mortgage payment that Anna will start paying from now on, we need to input the formula for calculating monthly mortgage payments.

The formula is:-

$M = P [\frac{r(1+r)^{n} }{(1+r)^{n}-1}]$

Where M is the monthly mortgage payment.

P is the principal

r is the monthly interest rate calculated by dividing your annual interest rate by 12

n is the number of payments(the number of months you will be paying the loan).

In this case, the new principal that Anna must pay back is $231,905.47¢. The annual interest rate has been reduced to 5.17% from 5.75% so the new monthly interest rate will be obtained by dividing the new annual interest rate by 12

= 5.17%/2

= 0.431%

This is the new monthly interest rate.

Since she has been paying her mortgage loan diligently for 5 complete years. It means she now has just 25 years to complete the payment. If 12 months make up one year, then there are - 12 × 25 = 300 more months to go.

300 is therefore "n" that is required for the calculation.

All the terms needed for the calculation of her new monthly mortgage is now complete.

P = $231,905.47¢

r = 0.431%

n = 300

$M = 231,905.47[\frac{0.00431(1+0.00431)^{300} }{(1+0.00431)^{300} -1}]$