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Sindrei [870]
3 years ago
15

Differentiate the function: y=x^3+2x-1

Mathematics
1 answer:
RUDIKE [14]3 years ago
7 0

Answer:dy/dx=3x^2 + 2

Step-by-step explanation:

y=x^3 + 2x - 1

dy/dx=3x^2 + 2

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-8x + x + 15 = -7x + 12\\\\-8x+x+7x=12-15\\\\0=-3\\\\x\in\emptyset

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Let f and g be two functions defined as
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a) \: (f \times g)(x) = (2x + 5)( {x}^{2} - 7x + 5) \\ b) \: (f \times g)(4) = (2 \times 4 + 5)( {4}^{2}  - 7 \times 4 + 5) = 13( - 7) =  - 91

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2(5 + y) = 18 what does y=​
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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
2 questions here. What does the equation of line mean on number 7? And how do I do 8?
ycow [4]

Equation of line is doubling

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