A large energy company produces electricity, natural gas, and oil. The production of a dollar's worth of electricity requires inputs of $0.35 from electricity, $0.15 from natural gas, and $0.25 from oil. Production of a
dollar's worth of natural gas requires inputs of $0.35 from electricity, $0.15 from natural gas, and $0.20 from
oil. Production of a dollar's worth of oil requires inputs of $0.10 from each sector. Find the output for each
sector that is needed to satisfy a final demand of $25 billion for electricity, $15 billion for natural gas, and $20
billion for oil.

E = 64.05

NG = 52.29

O = 35.15

Step-by-step explanation:

With the statement we can create a system of 3X3 equations that would be as follows:

E = electricity

NG = natural gas

O = oil

0.35 * E + 0.15 * NG + 0.25 * O = 25

0.35 * E + 0.15 * NG + 0.2 * O = 15

0.1 * E + 0.1 * NG + 0.1 * O = 20

If we pass this system equations to matrix and subtract it from the identity matrix we would have the following:

0.65 * E - 0.15 * NG - 0.25 * O = 25

-0.35 * E + 0.85 * NG - 0.2 * O = 15

-0.1 * E - 0.1 * NG + 0.9 * O = 20

Solving this system of equations around here can be very long and impractical, therefore, I attach a photo of the process:

And the answer is:

E = 64.05

NG = 52.29

O = 35.15

$9.41

step-by-step explanation:

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).