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-BARSIC- [3]
3 years ago
13

The slope of the tangent line to the curve x^3y+y^2-x^2=5 at the point (2,1) is

Mathematics
1 answer:
zheka24 [161]3 years ago
5 0

Answer:

-4/5

Step-by-step explanation:

To find the slope of the tangent to the equation at any point we must differentiate the equation.

x^3y+y^2-x^2=5

3x^2y+x^3y'+2yy'-2x=0

Gather terms with y' on one side and terms without on opposing side.

x^3y'+2yy'=2x-3x^2y

Factor left side

y'(x^3+2y)=2x-3x^2y

Divide both sides by (x^3+2y)

y'=(2x-3x^2y)/(x^3+2y)

y' is the slope any tangent to the given equation at point (x,y).

Plug in (2,1):

y'=(2(2)-3(2)^2(1))/((2)^3+2(1))

Simplify:

y'=(4-12)/(8+2)

y'=-8/10

y'=-4/5

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Kenji's town voted on a new speed limit. Of the votes received, 39 were in favor of the new speed limit and 13 were opposed. Wha
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Answer:

75%

Step-by-step explanation:

You need to find the total number of votes first. Just add 13 and 39 which would equal 52.

Then divide the number of people in favour by the total number of voters and multiply by a 100 to find the percentage.

39 + 13 = 52

39/52 = 0.75

0.75 x 100 = 75.0

75%

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3 years ago
A 5 pound bag of dog food costs $8.65 . what is the unit price?
inessss [21]
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4 0
3 years ago
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A train travels 80 miles per hour. If its speed remains the same, how far will the train have gone in 90 minutes?
Nataly_w [17]
Hello! So, the train travels 80 miles in an hour. 90 minutes is equivalent ot 1 ½ hours. In case you don't know, ½ of 80 is 40. To find the distance gone in 90 minutes, we can just add 80 and 40. 80 + 40 is 120. Another way to solve it is to multiply 80 by 1.5 and you would still get the same answer. There. The train will have gone 120 miles in 90 minutes.
3 0
3 years ago
An online company wants to establish ratings for the products they provide. To do so, they ask visitors to their website to eval
Lemur [1.5K]

Answer:

This is a group specific influence sample, it only shows a demographic sample of those that are influenced by the reviews in the first place.

Step-by-step explanation:

8 0
3 years ago
Find the points on x-axis where the circle with equation X square + Y square - 8 x - 8 Y - 9 = 0
Mamont248 [21]

Answer:

(- 1, 0) and (9, 0 )

Step-by-step explanation:

To find the x- intercepts let y = 0 in the equation and solve for x, that is

x² + y² - 8x - 8y - 9 = 0

x² - 8x - 9 = 0 ← in standard form

(x - 9)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

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