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Kruka [31]
3 years ago
9

ASAP! find the inverse of the function y=2x^2+2

Mathematics
1 answer:
jeka57 [31]3 years ago
3 0

Answer:

\displaystyle y=\sqrt{\frac{1}{2}x -1}

Step-by-step explanation:

We want to find the inverse of the function:

y=2x^2+2

To find the inverse of a function, we will flip the variables and solve for <em>y</em>. So:

x=2y^2+2

Solve for <em>y</em>. Subtract two from both sides:

x-2=2y^2

Divide both sides by two:

\displaystyle y^2=\frac{1}{2}x-1

And take the principal square root of both sides. Therefore:

\displaystyle y=\sqrt{\frac{1}{2}x -1}

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3 years ago
1) The deer population in a national park is expected to decline over time. The park
Lorico [155]

Answer:

Here's what I find.

Step-by-step explanation:

You have 800 deer at the end of Year 1, and you expect the population to decrease each year thereafter.

a) i) The recursive formula

Let dₙ = the deer population n years after the initial measurement.

d_{n} = d_{n - 1}r^{n}

For this situation,

d_{n} = d_{n - 1}(0.5)^{n}

a) ii) Definitions

n = the number of years from first measurement

r = the common ratio, that is, the deer population at the end of one year divided by the population of the previous year.

a) iii) First term of sequence

The first term of the sequence is d₀, the population when first measured.

b) The function formula

The formula for the nth term of a geometric series is

d_{n} =d_{0}r^{n - 1}

c) Value of d₀

Let n = 2; then d₂ = 800

\begin{array}{rcl}800 & = & d_{0}(0.5)^{2 - 1}\\800 & = & d_{0}(0.5)\\\\d_{0} & = & \dfrac{800}{0.5}\\\\& =&\mathbf{1600}\\\end{array}

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3 years ago
What are the steps to solving the inequality 3b + 8 &gt; 14
I am Lyosha [343]

Answer:

b > 2

Step-by-step explanation:

  1. 3b + 8 > 14
  2. Subtract 8 on both sides
  3. 3b > 6
  4. divide by 3 on both sides
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2 years ago
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