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3 years ago

Which function represents g(x), a reflection of f(x) = 6(1/3)^x across the y-axis?

Mathematics

2 answers:

LUCKY_DIMON [66]3 years ago

5 0

Answer:

$g(X) = 6\bigg(\displaystyle\frac{1}{3}\bigg)^{-x}$

Step-by-step explanation:

We are given the function:

$f(x) = 6\bigg(\displaystyle\frac{1}{3}\bigg)^x$

We have to find another function g(x) that is reflection of f(x) across, the y-axis.

To find the reflection of the function, we put -x in place of x to find the reflection of given function.

Thus, reflection of f(x) is given by g(x), where,

$g(x)=f(-x) = 6\bigg(\displaystyle\frac{1}{3}\bigg)^{-x}$

The attached image shows the function and the reflection of function across y-axis.

sergejj [24]3 years ago

4 0

Answer:

g(x)= $6(\frac{1}{3})^{-x}$

Step-by-step explanation:

a reflection of f(x) = 6(1/3)^x across the y-axis

Given f(x)= $6(\frac{1}{3})^x$

When graph of f(x) reflects across y axis then f(x) becomes f(-x)

For reflection across y axis we replace x with -x

f(x)= $6(\frac{1}{3})^x$

f(-x)= $6(\frac{1}{3})^{-x}$

f(-x) is a reflection across the y axis that is our g(x)

So g(x)= $6(\frac{1}{3})^{-x}$

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3 years ago

A plane is flying at 20,000 feet and the pilot wishes to take the plane 35000 feet. The angle of elevation that should be used i

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Answer:

40.88 miles

Step-by-step explanation:

Here I attach a draw of the situation.

Our plane is flying at 20,000 ft and we want it to be at 35,000 ft, thus, we need to take it up 15,000 ft high. We will do so with an elevation angle of 4dg. Notice what we have is a triangle, more precisely a right triangle, which angles are 90dg, 4dg and, consequently, 86dg. Also, we know that one of the legs is 15,000. The other legs we do not know yet and neither the hypotenuse. However, we can find this measures using trigonometry.

We know that, given an angle a, it mus be that:

sin(a) = opposite leg / hypotenuse

Take a ad our angle of 4dg. So, sin(a)=sin(4)= 0.070

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0.070 = 15000/hypotenuse

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1 = 15000/0.070 * hypotenuse

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hypotenuse = 15000/0.070

hypotenuse = 215,033.9

So, our plane will need to fly 215,033.9 ft to get to the height of 35000 ft.

However, we need the result in miles. As 1 mile is 5260 ft, we just need to divide our result in ft by 5260:

215,033.9/5260 = 40.88 miles

So, the plane need to fly 40.88 miles at an elevation angle of 4dg to reach a height of 35,000 ft.

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