If you're trying to solve for x, keep in mind the ln (natural log) of e is 1. So take the natural log of both sides, which will give you ln Y = ln e^x. The ln and e essentially cancel out, so you're left with x = ln Y.

6 0

3 years ago

Use the given information to find the unknown value:y varies directly as the square of z. When x = 2, then y= 20. Find y when 2

Vladimir79 [104]

Answer

y = 45 when x = 3

Step-by-step explanation:

$\begin{gathered} \text{Given that y varies directly as the square of x} \\ \text{This implies that there is a positive relationship betwe}en\text{ y and the square of z} \\ \text{Mathematically, this can be expressed as} \\ y\text{ }\propto x^2 \\ To\text{ turn this expression into an equation, we n}eed\text{ to introduce a proportionality constant k} \\ y=kx^2 \\ \text{ According to the question, y = 20 and x = 2} \\ \text{From the above informaion we can find our k} \\ y=kx^2 \\ 20\text{ = k }\cdot2^2 \\ 20\text{ = k }\cdot\text{ 4} \\ \text{Divide both sides by 4} \\ \frac{20}{4}\text{ = }\frac{k\cdot\text{ 4}}{4} \\ k\text{ = 5} \\ \text{ Find y when }x\text{ = 3} \\ y=kx^2 \\ y\text{ = 5 }\cdot(3)^2 \\ y\text{ = 5 }\cdot\text{ 9} \\ y\text{ = 45} \end{gathered}$

8 0

1 year ago

For the function defined by y = StartFraction 1 Over x squared EndFraction, if x is doubled, what is the effect on y?

olchik [2.2K]

Answer:

a. y is quartered.

Step-by-step explanation:

y=1/x^2

when x is doubled, the equation becomes:

y=1/(2x)^2=1/(4x^2)

3 0

1 year ago