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Sphinxa [80]
2 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]2 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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3 years ago
Hats and mittens are on sale at the store! One woman was able to buy 5 hats and 4 pairs of mittens for $30.
aalyn [17]

The price of one hat is $2 and one pair of mittens is $5

Step-by-step explanation:

Hats and mittens are on sale at the store!

  • One woman was able to buy 5 hats and 4 pairs of mittens for $30
  • Another woman purchased 3 pairs of mittens and 2 hats for $19
  • The price of one hat is x
  • The price of one pair of mittens is y

We need to find x and y

∵ One woman was able to buy 5 hats and 4 pairs of mittens for $30

∵ The price of one hat is x

∵ The price of one pair of  mittens is y

- Multiply 5 hats by x and 4 pairs of mittens by y and equate

  their sum by 30

∴ 5x + 4y = 30 ⇒ (1)

∵ Another woman purchased 3 pairs of mittens and 2 hats for $19

- Multiply 2 hats by x and 3 pairs of mittens by y and equate

  their sum by 19

∴ 2x + 3y = 19 ⇒ (2)

Now we have a system of equations to solve it

Multiply equation (1) by -2 and equation (2) by 5 to eliminate x

∵ -10x - 8y = -60 ⇒ (3)

∵ 10x + 15y = 95 ⇒ (4)

- Add equations (3) and (4)

∴ 7y = 35

- Divide both sides by 7

∴ y = 5

Substitute the value of y in equation (1) or (2) to find x

∵ 2x + 3(5) = 19

∴ 2x + 15 = 19

- Subtract 15 from both sides

∴ 2x = 4

- Divide both sides by 2

∴ x = 2

The price of one hat is $2 and one pair of mittens is $5

Learn more:

You can learn more about the system of equations in brainly.com/question/2115716

#LearnwithBrainly

8 0
3 years ago
The corr standard form for 100000+2000+500+150+17+0.08
kari74 [83]
<span>100000 + 2000 + 500 + 150 + 17 +0.08

= 102000 + 500 + 150 + 17 + 0.08

= 102500 + 150 + 17 + 0.08

= 102650 + 17 + 0.08

= 102667 + 0.08

= 102667.08 <--</span>
7 0
3 years ago
Read 2 more answers
The top of a mountain is 2,450 feet above sea level a shipwreck was discover 310 feet below sea level what is the distance betwe
arlik [135]

Answer:

d=2,760\ ft

Step-by-step explanation:

Let

x ----> the height of the top of a mountain above sea level

y ----> the deep of a shipwreck below the sea level

we know that

The sea level represent the height equal to zero

In this problem we have

x=2,450\ ft ---> is positive because is above sea level

y=-310\ ft ---> is negative because is below sea level

To find out the distance between the mountain top and the ship wreck, determine the absolute value of the difference between the two values

d=\left|x-y\right|

substitute the values

d=\left|2,450-(-310)\right|

d=\left|2,450+310\right|

d=\left|2,760\right|

d=2,760\ ft

5 0
3 years ago
The coordinates P(0, 1), Q(3, 2), R(5, -4) form a right triangle.
Arisa [49]

Answer:

Yes it forms a right angle triangle.

4 0
3 years ago
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