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ruslelena [56]
3 years ago
8

Consider the circle with an equation in standard form: ( x – 4)² + ( y + 2)² = 36 . Explain in 2-3 sentences or explain the step

s used to find the radius and the center.
Mathematics
1 answer:
iragen [17]3 years ago
4 0

Answer:

The center of this circle is found at (4, -2) and the radius is 6.

Step-by-step explanation:

The equation for a circle in standard for is  ( x – h)² + ( y - k)² = r². In this equation, (h, k) is the center of the circle and r is the radius.

From the given equation, ( x – 4)² + ( y + 2)² = 36, h is already subtracted from x, so h = 4, but the k is not subtracted, so (y + 2) = [y - (-2)], and we see that k is -2. Therefore, the center of the circle is (4, -2) and 36 = r². By taking the square root of 36, we find that r = 6.

The center of this circle is found at (4, -2) and the radius is 6.

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Hi!

We can see here that this is a composition question.

And since the composition of g of f of x is x, we can conclude that g(x) is the inverse of f(x) (if you're confused, search up the definition of an inverse function).

To find an inverse function, we can take the f(x) function and change the positions of the x and y variables.

f(x)=\frac{e^7^x+\sqrt{3}}{2}

y=\frac{e^7^x+\sqrt{3}}{2}

x=\frac{e^7^y+\sqrt{3}}{2}

2x=e^7^y+\sqrt{3}

e^7^y=2x-\sqrt{3}

7y=ln(2x-\sqrt{3})

y=\frac{ln(2x-\sqrt{3})}{7}

Which is answer choice A, to check your work, you can solve the composition of g(f(x)), which will get you x.

g(f(x))

g(\frac{e^7^x+\sqrt{3}}{2})

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2s cancel.

\frac{ln(e^7^x+\sqrt{3})-\sqrt{3}}{7}

The natural log and e cancel.

\frac{7x+\sqrt{3}-\sqrt{3}}{7}

\sqrt{3}s cancel.

\frac{7x}{7}

7s cancel.

x

Hope this helps!

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2 years ago
HURRY PLZ Four friends are collecting money to buy dog food for an animal shelter. The food will cost $150, and each friend will
satela [25.4K]

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Food Cost $150.00

Each Friend Collect the Same amount of Money:  $37.50 each Collected

Just Divide:

$150.00   Divide amongst the  4  friends:

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Answer  ======>   Decimal:    $37.50    Each friend would need to collect to reach their goals.


Check:

$37.50    *     4  

$150.00

150/4   =====>   $37.50





Hope that helps!!!!!!!!!                                                 : )






Hope that helps!!!                                             : )

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