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4 years ago

Find f '(a). f(x) = 4x2 − 4x + 3

1 answer:

3 0

Use the power rule
d(x^n)/dx = n·x^(n-1)
to form the derivative.
f'(x) = 4·2x -4
f'(x) = 8x - 4

Now, substitute "a" for "x" to find f'(a):
f'(a) = 8a - 4

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Joylin is writing an equation to model the proportional relationship between y, the total cost in dollars of downloading videos

umka2103 [35]

Joylin is writing an equation to model the proportional relationship between y, the total cost in dollars of downloading videos from a website, and x, the number of videos downloaded. She knows that the total cost to download 3 videos was $12. Her work to find the equation is shown below. Joylin’s Work Step 1 x=3/12=0.25 Step 2 y=0.25x Where did Joylin make her first error? Joylin divided 3 and 12 instead of multiplying the two numbers. Joylin computed the decimal equivalent of 3/12 incorrectly. Joylin used 0.25 as the coefficient of x instead of a product of x and y. Joylin switched the numerator and the denominator when she found k.

Solution:

Joylin switched the numerator and the denominator when she found k.

Joylin should divide 12/3 and not 3/12. As, y is total cost and x is number of videos.

For x=1, number of videos=1, y,or total cost=1*4=4,

For x=2,y=2*4=8

For x=3, y=3*4=12

So, the constant, k=4

So, Answer: Option (D)

Joylin switched the numerator and the denominator when she found k.

4 0

3 years ago

Read 2 more answers

A man standing on the roof of a building 64.0 feet high looks down to the building next door. He finds the angle of depression t

8_murik_8 [283]

Answer:

The height of the next door building is 41.7 feet

Step-by-step explanation:

* Lets study the situation in the problem

- The man standing on the roof of a building 64.0 feet high

- The angle of depression to roof of the next door building is 34.7°

- The angle of depression to the bottom of the next door building

is 63.3°

- We need to find the height of the next door building

* Lets consider the height of the man building and the horizontal

distance between the two building formed a right triangle and the

angle of depression is opposite to the side which represented the

height of the building

- Let the horizontal distance between the two buildings called x

# In the triangle

∵ The length of the side opposite to the angle of depression (63.3°)

is 64.0

∵ The length of the horizontal distance is x which is adjacent to the

angle of depression (63.3°)

- Use the trigonometry function tanФ = opposite/adjacent

∴ tan 63.3° = 64.0/x ⇒ use cross multiplication

∴ x (tan 63.3°) = 64 ⇒ divide both sides by (tan 63.3°)

∴ x = 64.0/(tan 63.3°)

∴ x = 32.1886 feet

- Lets use this horizontal distance to find the vertical distance between

the roofs of the two buildings

* Lets consider the height of the vertical distance between the roofs

of the two buildings and the horizontal distance between the two

building formed a right triangle and the

angle of depression is opposite to the side which represented the

vertical distance between the roofs of the two buildings

- Let the vertical distance between the roofs of the two buildings

called y

# In the triangle

∵ The vertical distance between the roofs of the two buildings is y

and opposite to the angle of depression (34.7°)

∵ The horizontal distance x is adjacent to the angle of

depression (34.7°)

∴ tan (34.7°) = y/x

∵ x = 32.1886

∴ tan 34.7° = y/32.1886 ⇒ use the cross multiplication

∴ y = 32.1886 (tan 34.7°)

∴ y = 22.2884 ≅ 22.3 feet

∴ The vertical distance between the roofs of the two

buildings is 22.3 feet

- The height of the next door building is the difference between the

height of the man building and the vertical distance between the

roofs of the two buildings

∴ The height of the next door building = 64.0 - 22.3 = 41.7 feet

7 0

3 years ago

How do you do this? Huge struggle

AveGali [126]

You plug 13 into where the r is and then solve, using a calculator

7 0

3 years ago

Read 2 more answers

2(x + 1) + 1 = 1 - 2(x - 7)

Rus_ich [418]

Answer:

x = 3.

Step-by-step explanation:

2(x + 1) + 1 = 1 - 2(x - 7)

2x + 2 + 1 = 1 - 2x + 14

4x = 1 + 14 - 2 - 1

4x = 12

x = 3.

4 0

3 years ago

Read 2 more answers

(0,-1) and (-2,0)

VladimirAG [237]

Answer:

slope -1/2

y intercept -1

Step-by-step explanation:

To find the slope given two points

m = (y2-y1)/(x2-x1)

=(0--1)/(-2-0)

= (0+1) /(-2-0)

=1/-2

= -1/2

The y intercept is when x = 0

(0,-1) is when x =0 so the y intercept is -1

3 0

3 years ago

Read 2 more answers