What is the solution to this linear equation.

What is the approximate surface area of the sphere if circumference is 37.68?

damaskus [11]

The surface area of a sphere is A = 4 π R² .

Sadly, the question doesn't give you 'R', so you have to
back it out of the circumference.

 Circumference = π (diameter)

Divide each side by π : Diameter = circumference / π

Radius = 1/2 diameter: Radius = circumference / (2 π)

 Area = 4 π R² =

 4 π (circumference/2π)² =

 4 π (circumference)² / 4 π²

Divide top and bottom by 4π : Area = (Circumference)² / π

 Circumference = 37.68 units

 Area = (37.68)² square units /π =

 451.93 square units

8 0

2 years ago

A young couple purchases their first new home in 2011 for $95,000. They sell it to move into a bigger home in 2018 for $105,00

mart [117]

Given:

The value of home in 2011 is $95,000.

The value of home in 2018 is $105,000.

To find:

The exponential model for the value of the home.

Solution:

The general exponential model is

$y=ab^x$ ...(i)

where, a is initial value and b is growth factor.

Let 2011 is initial year and x be the number of years after 2011.

So, initial value of home is 95,000, i.e., a=95,000.

Put a=95000 in (i).

$y=95000b^x$ ...(ii)

The value of home in 2018 is $105,000. It means the value of y is 105000 at x=7.

$105000=95000b^7$

$\dfrac{105000}{95000}=b^7$

$\dfrac{21}{19}=b^7$

Taking 7th root on both sides, we get

$\left(\dfrac{21}{19}\right)^{\frac{1}{7}}=b$

Put $b=\left(\dfrac{21}{19}\right)^{\frac{1}{7}}$ in (ii).

$y=95000\left(\left(\dfrac{21}{19}\right)^{\frac{1}{7}}\right)^x$

$y=95000\left(\dfrac{21}{19}\right)^{\frac{x}{7}}$

Therefore, the required exponential model for the value of home is $y=95000\left(\dfrac{21}{19}\right)^{\frac{x}{7}}$ , where x is the number of years after 2011.

5 0

3 years ago

Please help I need to do this for homework but I have zero clue what to do.

Serhud [2]

Answer:

$20$