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gizmo_the_mogwai [7]
3 years ago
12

Carrie started at the southeast corner of

Mathematics
1 answer:
Marina CMI [18]3 years ago
3 0

Answer:

9600 sq. yards.

Step-by-step explanation:

Carrie walked north 240 yards, turned and walked west 80 yards, and then turned and  walked diagonally back to where she started.

Therefore, the path traced by Carrie is a right triangle with base and heights are 240 yards and 80 yards.

Now, the area of the triangle traced by Carrie while walking is

= \frac{1}{2}\times \textrm {Base}\times \textrm {Height}

= \frac{1}{2} \times 240 \times 80 = 9600 sq. yards. (Answer)

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<h3>Answers:</h3>

f(g(x)) = \sqrt{x^2+5}+5\\\\g(f(x)) = x+30+10\sqrt{x-1}

================================================

Work Shown:

Part 1

f(x) = \sqrt{x-1}+5\\\\f(g(x)) = \sqrt{g(x)-1}+5\\\\f(g(x)) = \sqrt{x^2+6-1}+5\\\\f(g(x)) = \sqrt{x^2+5}+5\\\\

Notice how I replaced every x with g(x) in step 2. Then I plugged in g(x) = x^2+6 and simplified.

------------------

Part 2

g(x) = x^2+6\\\\g(f(x)) = \left(f(x)\right)^2+6\\\\g(f(x)) = \left(\sqrt{x-1}+5\right)^2+6\\\\g(f(x)) = \left(\sqrt{x-1}\right)^2+2*5*\sqrt{x-1}+\left(5\right)^2+6\\\\g(f(x)) = x-1+10\sqrt{x-1}+25+6\\\\g(f(x)) = x+30+10\sqrt{x-1}\\\\

In step 4, I used the rule (a+b)^2 = a^2+2ab+b^2

In this case, a = sqrt(x-1) and b = 5.

You could also use the box method as a visual way to expand out \left(\sqrt{x-1}+5\right)^2

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