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zzz [600]
3 years ago
10

Evaluate the function. f(x) = -x² + 6 Find f(-3)

Mathematics
2 answers:
Rina8888 [55]3 years ago
7 0

Answer:

-3

Step-by-step explanation:

Have x= -3.

f(-3) = -(-3)² + 6

       = -3

madam [21]3 years ago
4 0

Answer:

f(- 3) = - 3

Step-by-step explanation:

To evaluate f(- 3) substitute x = - 3 into f(x) , that is

f(- 3) = - (- 3)² + 6 = - 9 + 6 = - 3

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Find the slope of the line that passes through (5,9) and (3,9)
pshichka [43]

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Step-by-step explanation:

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A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.8 ft/s,
shusha [124]

Answer:

-0.133 radians/s is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall.

Step-by-step explanation:

Let

x= distance between the wall and ladder

Ф = angle between the ladder and ground

The rate of change is: dx/dt = 0.8 ft/s

We need to find dФ/dt when x = 8 ft/s

From the triangle in the figure we see that:

cos Ф = x/10

=> x = 10 cosФ

Now, the rate of change will be

d(x)/dt = d/dt (10cosФ)

dx/dt = -10 sin Ф dФ/dt

dx/dt = 0.8 (given)

to find dФ/dt

we need to find sin Ф when x = 8

By Pythagoras theorem

(hypotenuse)^2 = (Perpendicular)^2+(base)^2

(10)^2 = (8)^2+ (Perpendicular)^2

100 = 64 +  (Perpendicular)^2

=>  (Perpendicular)^2 = 100-64

(Perpendicular)^2 = 36

Perpendicular = 6

sin Ф = Perpendicular/hypotenuse

sin Ф = 6/10 = 3/5

Putting values in:

dx/dt = -10 sin Ф dФ/dt

0.8 = -10(3/5) dФ/dt

0.8 = -6 dФ/dt

=> dФ/dt = 0.8 / -6

dФ/dt = - 0.133 radians/s

So, -0.133 radians/s is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall.

3 0
3 years ago
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