The advertisement has been printed and is going to be stuck onto the wall.

if f(g(x)) = x and g(f(x)) = x, and f(x) passes through the point (5,-7), and g'(-7) = -2/3, then find the value of f'(5).

Marysya12 [62]

So it is given that f(x) and g(x) are inverse of each other.

Then f(5) = -7 and hence g(-7) = 5

Now let's use f( g( x ) ) = x

Now take deviation. Use chain rule:

f'( g(x) ) g'( x ) = 1

Plug in x = -7

f'( g( -7 ) ) g'( -7 ) = 1

f'( g( -7 ) ) · -2/3 = 1

f'( g( -7 ) ) = -3/2

f'( 5 ) = -3/2

Hope this helps.

5 0

3 years ago

Anyone want to help with this problem

emmasim [6.3K]

Answer:

$2643.06

Step-by-step explanation:

Total purchase = $2436 + 8.5% of $2436

= $2436 + (0.085 * 2436)

= $2436 + $207.06

= $2643.06

5 0

3 years ago

HELP ASAP photo attached

ankoles [38]

Answer:

D. undefined

General Formulas and Concepts:

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Trig Derivative: $\displaystyle \frac{d}{dx}[sinu] = u'cosu$

Derivatives of Parametrics: $\displaystyle \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

Step-by-step explanation:

Step 1: Define

$\displaystyle \frac{dx}{dt} = 5$

$\displaystyle \frac{dy}{dt} = sin(t^2)$

Step 2: Differentiate

[x Derivative] Basic Power Rule: $\displaystyle \frac{d^2x}{dt^2} = 0$
[y Derivative] Trig Derivative [Chain Rule]: $\displaystyle \frac{d^2y}{dt^2} = cos(t^2) \cdot \frac{d}{dt}[t^2]$
[y Derivative] Basic Power Rule: $\displaystyle \frac{d^2y}{dt^2} = cos(t^2) \cdot 2t^{2 - 1}$
[y Derivative] Simplify: $\displaystyle \frac{d^2y}{dt^2} = 2tcos(t^2)$
[Derivative] Rewrite: $\displaystyle \frac{d^2y}{dx^2} = \frac{2tcos(t^2)}{0}$

Anything divided by 0 is undefined.

Topic: AP Calculus BC (Calculus I/II)

Unit: Differentiation with Parametrics

Book: College Calculus 10e

5 0

3 years ago

Given right triangle ABC, what is the value of tan(A)?

Angelina_Jolie [31]

You didn't provide more information regarding triangle but from given options, it seems that triangle has ratio from shortest side to longest side would be 5 : 12 : 13

So 13 would be hypotenuse since it is longest.

Now A cannot be right angle because tangent is not defined at 90°.

Also tan(A) would be ratio of opponent side to adjacent side (think SOH CAH TOA)

So either opposite side would be 5 or 12, and adjacent side would be 12 or 5 respectively.

So the answer is either 5 / 12 or 12 / 5 but only option provided is 12/5 so that would be your answer.

Final answer: 12 / 5

7 0

4 years ago

Read 2 more answers

Suppose that from a standard deck, you draw three cards without replacement. What is the expected number of kings that you will

aksik [14]

I would say... None.
Hope this helps ٩(๑❛▽❛๑)۶

3 0

3 years ago