Question

For items number 9-11, refer to the following:
Marx is standing on the ground to take a series of photographs of a kite rising
vertically. The distance between Luis at (B) and the launching point of the kite (A)
is 800 meters. Luis must keep the kite on sight and therefore its angle of elevation
must change with height x of the kite.

9. Find the angle t as a function of the height x.
a. t = tan^-1(x/800)
c. t = tan^-1(500x/300)
b.t = tan^-1(800x/500)
d. t =tan-(800)

10. Find the angle tin degrees when x is equal to 150 meters
a. 31.6
b. 21.6
c. 11.6
d. 10.6
11. Find the angle tin degrees when x is equal to 300 meters.
a. 20.6
b. 21.6
c. 22.6
d. 23.6
For items number 12-13, refer to the following:
The function defined by (x)=x/5.3 converts a volume of x liters into g(x) gallons.
12. Which of the following is the inverse of g(x)?
a. g^-1(x) =5.3x
b. g^-1(x)=x/5x+3
c.g^-1(x)=5.3x/5.3+x
d. g^-1(x)=3x/5.3
13. Find the equivalent volume in liters of a 7.5-gallon cooking oil.
a. 43
b.42
c.40
d.50​​

Answer 1

Given:

Marx is standing on the ground to take a series of photographs of a kite rising  vertically. The distance between Luis at (B) and the launching point of the kite (A)  is 800 meters. Luis must keep the kite on sight and therefore its angle of elevation  must change with height x of the kite.

To Find:

9. Find the angle t as a function of the height x.

a. t = tan^-1(x/800)

c. t = tan^-1(500x/300)

b.t = tan^-1(800x/500)

d. t =tan-(800)

10. Find the angle tin degrees when x is equal to 150 meters

a. 31.6

b. 21.6

c. 11.6

d. 10.6

11. Find the angle tin degrees when x is equal to 300 meters.

a. 20.6

b. 21.6

c. 22.6

d. 23.6

Solution:

(9) We need to find the angle t in terms of tan as mentioned in the options so we can observe that the base is 800m and perpendicular is x

$tan(t)=\frac{p}{b}\\tan(t)=\frac{x}{800} \\\\t=tan^{-1}(\frac{x}{800} )$

Hence, option (a) is the correct answer.

(10) using a similar way to find the angle t when x=150m

$t=tan^{-1}(\frac{x}{800} )\\=tan^{-1}(\frac{150}{800} )\\=tan^{-1}(0.1875)\\=10.6^{\circ}$

Hence, option (d) is the correct answer.

(11) using a similar way to calculate t when x=300

$t=tan^{-1}(\frac{x}{800} )\\=tan^{-1}(\frac{300}{800} )\\=tan^{-1}(0.375 )\\=20.6^{\circ}$

Hence, option (a) is the correct answer.

Given:

The function defined by (x)=x/5.3 converts a volume of x litres into g(x) gallons.

To Find:

12. Which of the following is the inverse of g(x)?

a. g^-1(x) =5.3x

b. g^-1(x)=x/5x+3

c. g^-1(x)=5.3x/5.3+x

d. g^-1(x)=3x/5.3

13. Find the equivalent volume in litres of 7.5-gallon cooking oil.

a. 43

b.42

c.40

d.50​​

Solution:

(12) For converting a function into its reverse we just need to convert it into x in terms of y

$g(x)=\frac{x}{5.3}\\y=\frac{x}{5.3} \\x=y*5.3\\so,\\g^{-1}(x)=x*5.3$

Hence, option (a) is the correct answer.

(13) using the previous equation to find the value when x=7.5

$g^{-1}(x)=5.3*x\\=7.5*5.3\\=39.75$

Hence, option(c) is the correct answer.