Find the values of x for which f(x)=g(x).<br><br> a. f(x) = x^2, g(x) = x + 2

A circular backyard pool has a diameter of 26 feet and is 4 feet deep. One cubic foot of water has a capacity of approximately 7

klasskru [66]

Find the water volume of the pool. The formula for a vertical cylinder is V = pi*r^2*h, which here is V = pi(13 ft)^2*(4 ft) = 676*pi cubic feet.

Now convert this 676 cu. ft. to gallons:

Mult (676*pi cu ft) by the conversion factor (7.48 gal) / (1 cu ft):

676*pi cu ft 7.48 gal
--------------- * ------------- = 5056*pi gallons (rounded down from 5056.48 pi)
1 1 cu ft

The cost of filling the pool will be

5056.48*pi gallons $3
--------------------------- * ------------- = $48 (to the nearest dollar)
1 1000 gal

7 0

1 year ago

The area of the surface of the swimming pool is 210 square feet. What is the length d of the deep end in feet

Natali [406]

72 is the length d of how deep end in feet}

6 0

2 years ago

You travel 5 miles downstream in a kayak at a speed of r miles per hour. You turn around and travel 6 miles upstream at a speed

Vlad1618 [11]

Kyle, d = rt, right? This means that t = d/r. If we call the rate of the current c, then her rate upstream is hindered by the current and is 3 - c. Downstream is 3 + c. The total time is 6 hours... 5/(3 - c) + 5/(3 + c) = 6 Once we put everything over the same denominator, we don't need it anymore. 5(3 + c) + 5(3 - c) = 6(3 - c)(3 + c) 15 + 5c + 15 - 5c = 54 - 6c2
30 = 54 - 6c26c2 = 24c2 = 4c = 2 2 mph

3 0

2 years ago

Sean has 15,000 to invest she will put some of it into a fund that pays 4.5% annual interest in the rest in a certificate of dep

DENIUS [597]

Answer:$12500 was invested into the account that pays 4.5% annual interest..

$2500 was invested into the the certificate of deposit that pays 1.8% annual interest..

Step-by-step explanation:

Let x represent the amount invested into the account that pays 4.5% annual interest.

Let y represent the amount invested into the certificate of deposit that pays 1.8% annual interest.

Sean has 15,000 to invest. She will put some of it into a fund that pays 4.5% annual interest and the rest in a certificate of deposit that pays 1.8% annual interest. This means that

x = y + 15000

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time in years

I = interest after t years

Considering the account earning 4.5% interest, the interest would be

I = (x × 4.5 × 1)/100 = 0.045x

Considering the account earning 11% interest, the interest would be

I = (x × 1.8 × 1)/100 = 0.018y

if she wants to earn 4.05% annual interest on the total amount, the amount would be

4.05/100 × 15000 = 607.5

Therefore,

0.045x + 0.018y = 607.5 - - - - - - - - - - -1

Substituting x = 15000 - y into equation 1, it becomes

0.045(15000 - y) + 0.018y = 607.5

675 - 0.045y + 0.018y = 607.5

- 0.045y + 0.018y = 607.5 - 675

- 0.027y = - 67.5

y = - 67.5/- 0.027

y = $2500

x = 15000 - y = 15000 - 2500

x = $12500

6 0

2 years ago

Find the general solution of y''' + 6y'' + y' − 34y = 0 if it is known that y1 = e−4x cos(x) is one solution.

SashulF [63]

Answer:

Step-by-step explanation:

Given is a differential equation of III order,

$y''' + 6y'' + y' - 34y = 0$

The characteristic equation would be cubic as

$m^3+6m^2+m-34=0$

By trial and error, we find that

$f(2) = 2^3+6(2^2)+2-34 =0\\$

Thus m=2 is one solution

Since given that $e^{-4x} cos x$ is one solution we get

m = -4+i and hence other root is conjugate $m=-4-i$

Hence general solution would be

$y=Ae^{2x} +e^{-4x} (Bcosx +C sinx)$

3 0

2 years ago

Find the values of x for which f(x)=g(x). a. f(x) = x^2, g(x) = x + 2