I need help with this , please help

Function Composition: Let the function <img src="https://tex.z-dn.net/?f=f%28x%29%3D%203%2B6x" id="TexFormula1" title="f(x)=

V125BC [204]

Answer:

Given

f(x) = 3 + 6x

A

Find the inverse of f(x):

x = 3 + 6f⁻¹(x)
6f⁻¹(x) = x - 3
f⁻¹(x) = (x - 3) / 6

B

f · f⁻¹( ∛5/6) =
f( f⁻¹( ∛5/6)) =
f((∛5/6 - 3)/6) =
3 + 6((∛5/6 - 3)/6) =
3 + ∛5/6 - 3 =
∛5/6

C

f · f⁻¹(x) =
f(f⁻¹(x)) =
f((x - 3)/6) =
3 + 6(x - 3)/6 =
3 + x - 3 =
x

4 0

2 years ago

A person stands 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 meters

In-s [12.5K]

Answer:

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

Step-by-step explanation:

Given that,

A person stand 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 m/s.

From Pythagorean Theorem,

(The distance between car and person)²= (The distance of the car from intersection)²+ (The distance of the person from intersection)²+

Assume that the distance of the car from the intersection and from the person be x and y at any time t respectively.

∴y²= x²+10²

$\Rightarrow y=\sqrt{x^2+100}$

Differentiating with respect to t

$\frac{dy}{dt}=\frac{1}{2\sqrt{x^2+100}}. 2x\frac{dx}{dt}$

$\Rightarrow \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}. \frac{dx}{dt}$

Since the car driving towards the intersection at 13 m/s.

so, $\frac{dx}{dt}=-13$

$\therefore \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}.(-13)$

Now

$\therefore \frac{dy}{dt}|_{x=24}=\frac{24}{\sqrt{24^2+100}}.(-13)$

$=\frac{24\times (-13)}{\sqrt{676}}$

$=\frac{24\times (-13)}{26}$

= -12 m/s

Negative sign denotes the distance between the car and the person decrease.

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

8 0

2 years ago

How many solutions does 10+5x=5x+10 have?

Arturiano [62]

Simplifying
10 + 5x = 5x + 10

Reorder the terms:
10 + 5x = 10 + 5x

Add '-10' to each side of the equation.
10 + -10 + 5x = 10 + -10 + 5x

Combine like terms: 10 + -10 = 0
0 + 5x = 10 + -10 + 5x
5x = 10 + -10 + 5x

Combine like terms: 10 + -10 = 0
5x = 0 + 5x
5x = 5x

Add '-5x' to each side of the equation.
5x + -5x = 5x + -5x

Combine like terms: 5x + -5x = 0
0 = 5x + -5x

Combine like terms: 5x + -5x = 0
0 = 0

Solving
0 = 0
Answer: 0 solutions

3 0

3 years ago

NEEDS TO BE DONE TODAY SOMEONE PLEASE

eduard

Answer:

Step-by-step explanation:

16.

RT=17.885

RS=9.741

Angle T=33°

17

AB=7.077

Angle B= 47.291°

Angle A= 42.709°

19

∠A = 180° - B - C = 1.36944 rad =

A=78.463°

8 0

3 years ago

Please help and explain if so thank you

AVprozaik [17]

How many days are in a year? 365. it started out as 88 inches subtracted that by 115 then add the 3.

7 0

3 years ago