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Sphinxa [80]
3 years ago
10

What is the slope of the line tangent to the curve y+2 = (x^2/2) - 2siny at the point (2,0)?

Mathematics
1 answer:
Aleksandr-060686 [28]3 years ago
6 0
Implicit differentiation
take the deritivive with respect to x

first
y+2=(1/2)(x^2)-2sin(y)
take deritivitive
dy/dx+0=1/2(2x)-2(cosy)dy/dx
dy/dx=x-2cosy(dy/dx)
add 2cosy(dy/dx) to both sides
dy/dx+2cosy(dy/dx) =x
undistribute dy/dx
dy/dx(1+2cos(y))=x
divide both sides by 1+2cos(y)
\frac{dy}{dx}= \frac{x}{1+2cos(y)}
at (2,0)
x=2
y=0

\frac{dy}{dx}= \frac{2}{1+2cos(0)}
\frac{dy}{dx}= \frac{2}{1+2(1)}
\frac{dy}{dx}= \frac{2}{1+2}
\frac{dy}{dx}= \frac{2}{3}
the slope is 2/3
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Answer:

2 \frac{5}{12}

gallons of paint was used by Lucy.

Step-by-step explanation:

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3 years ago
Richard has enrolled in a 401(k) savings plan. He intends to deposit $250 each month; his employer does not contribute to his ac
astraxan [27]

Answer:

Richard will have $60,000 in his account in 20 years.

Step-by-step explanation:

(1) Multiply $250 x 12

(2) Multiply the answer of $250 x 12 which is 3000 by 20

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A circle has a radius of 7.5 centimeters and a central angle AOB that measures 90 degrees. What is the length of the intercepted
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This means that the length of the intercepted arc \stackrel{\frown}{AB} is \frac{1}{4} of the circumference of the circle. So,

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6 0
3 years ago
1. Regina. Phil and Joseph each wrote expressions to represent their hourly
aleksandrvk [35]

Answer:

15

Step-by-step explanation:

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Phil: 3(2.5h+5)

When you plug in the number of hours, you get the weekly pay.  In order to get the same weekly pay, set the equations equal to each other.

6.5h=3(2.5h+5), This is an equation to find the number of hours it will take for them to get equal pay. Now, simplify.

6.5h=7.5h+15

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Phil has a higher rate and starting value, this means that Regina will never make the same amount working the same hours.

6 0
3 years ago
Each lap around the track is 1/4 of a mile. How many laps will Quadir need to jog if he wants to jog 3 1/8 miles? Helpppp
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Answer:

  12 1/2 laps

Step-by-step explanation:

To find the number of laps, divide the distance by the distance per lap.

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Quadir needs to jog 12 1/2 laps if he wants to jog 3 1/8 miles.

5 0
3 years ago
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