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Kaylis [27]
2 years ago
13

The function a(b) relates the area of a trapezoid with a given height of 14 and one base length of 5 with the length of its othe

r base. It takes as input the other base value, and returns as output the area of the trapezoid a(b) = 14 * (b + 5)/2 Which equation below represents the inverse function b(a) , which takes the trapezoid's area as input and returns as output the length of the other base? N(c) = (c + 15)/20; n(c) = (c + 20)/15; n(c) = (c - 20)/15; n(G) = (Q - 15)/20
Mathematics
1 answer:
taurus [48]2 years ago
7 0

Answer:

b(a) = \frac{a}{7} -5

Step-by-step explanation:

Given

a(b) = 14 * \frac{b + 5}{2}

Required

The inverse function

We have:

a(b) = 14 * \frac{b + 5}{2}

a(b) = 7(b + 5)

Rewrite as:

a = 7(b + 5)

Divide by 7

\frac{a}{7} =b + 5

Subtract 5

b = \frac{a}{7} -5

Express as:

b(a) = \frac{a}{7} -5 --- the inverse function

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Which octant contains the image of point A( 1, -3, 4) after a reflection about the xz - plane?
ANTONII [103]

Hi,

Concept: The given problem is based on 3 Dimensional Geometry.

Consider three axes in defined space be x, y & z in their positive directions then - x , -y & -z be their negative axes.

The coordinate of given point A(x1, y1, z1) = (1, -3, 4)

If we take the reflection of point A about xz - plane x and z coordinates will remain same and y-coordinate will give its reflection. It means the value of y-coordinate will be changed which will be +ve 3.

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F(x) = <img src="https://tex.z-dn.net/?f=%5Csqrt%7Bx%2B7%7D%20-%5Csqrt%7Bx%5E2%2B2x-15%7D" id="TexFormula1" title="\sqrt{x+7} -\
elena-s [515]

Answer:

x >= -7  ................(1a)

x >= 3   ...............(2a1)

Step-by-step explanation:

f(x) =  \sqrt{x+7}-\sqrt{x^2+2x-15}  .............(0)

find the domain.

To find the (real) domain, we need to ensure that each term remains a real number.

which means the following conditions must be met

x+7 >= 0  .....................(1)

AND

x^2+2x-15 >= 0 ..........(2)

To satisfy (1),  x >= -7  .....................(1a) by transposition of (1)

To satisfy (2), we need first to find the roots of (2)

factor (2)

(x+5)(x-3) >= 0

This implis

(x+5) >= 0 AND (x-3) >= 0.....................(2a)

OR

(x+5) <= 0 AND (x-3) <= 0 ...................(2b)

(2a) is satisfied with x >= 3   ...............(2a1)

(2b) is satisfied with x <= -5 ................(2b1)

Combine the conditions (1a), (2a1), and (2b1),

x >= -7  ................(1a)

AND

(

x >= 3   ...............(2a1)

OR

x <= -5 ................(2b1)

)

which expands to

(1a) and (2a1)   OR  (1a) and (2b1)

( x >= -7 and x >= 3 )  OR ( x >= -7 and x <= -5 )

Simplifying, we have

x >= 3  OR ( -7 <= x <= -5 )

Referring to attached figure, the domain is indicated in dark (purple), the red-brown and white regions satisfiy only one of the two conditions.

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