In Exercise, describe how the graph of g is related to the graph of f. g(x)=-1+f(x)

Mathematics

1 answer:

Jet001 [13]3 years ago

7 0

Answer:

The graph of g is the graph of f shifted down 1 unit.

Step-by-step explanation:

Suppose you have a function y = f(x), you can do these following operations on the function:

Shift up a units: y = f(x) + a

Shift down a units: y = f(x) - a

Shift left a units: y = f(x + a)

Shift right a units: y = f(x - a)

In this problem, we have that:

g(x) = -1 + f(x) = f(x) - 1

So the graph of g is the graph of f shifted down 1 unit.

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The city council plans to build a new water storage tank for the community. The tank is cylindrical with a base diameter of 25 f

Stella [2.4K]

Answer:

a. $14726.216ft^{3}$

b. $110446.62gal$

Step-by-step explanation:

I attach the diagram of the new water tank.

a. In order to find the volume of the tank in cubic feet, we will need to calculate the volume of a cylinder. We know that its base measures $25ft$ and its height is $30ft$ .

The volume ''V'' of a cylinder is :

$V=(\frac{\pi D^{2}}{4}).(H)$

Where '' $D$ '' is the diameter of the base and '' $H$ '' is the height of the cylinder.

If we replace all the data in the equation :

$V=\frac{\pi .(25ft)^{2}}{4}.(30ft)=14726.216ft^{3}$

We found out that the volume of the tank in cubic feet is $14726.216ft^{3}$

b. We know that 1 cubic foot of water is equal to 7.5 gallons. To find the amount of gallons that the new tank can hold, we need to do an unit conversion.

This equivalence is given to us :

$1ft^{3}=7.5gal$ ⇒ Using the equivalence ⇒