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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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Find the real solutions of the equati<br> √7x+1 - √x-5 = 6
Juliette [100K]

The solution of this equation is x = 5 and   x = 9.

<h3>What is the solution?</h3>

Let us recall that what we have here is a radical equation as follows;

√7x+1 - √x-5 = 6

When we isolate we have';

 √7x+1 = √x-5+6

Taking the square of both sides;

  (√7x+1)^2 = (√x-5+6)^2

Hence;

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Raising this equation to power 2

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5 0
1 year ago
The admission fee at an amusement park is $2.00 for children and $6.80 for adults. On a certain day, 388 people entered the park
san4es73 [151]

Answer: 188 children and 200 adults were admitted

Step-by-step explanation:

Let x represent the number of children that were admitted.

Let y represent the number of adults that were admitted.

On a certain day, 388 people entered the park. It means that

x + y = 388

The admission fee at the amusement park is $2.00 for children and $6.80 for adults. The admission fees collected on that day totaled $1736. It means that

2x + 6.8y = 1736- - - - - - - - - - 1

Substituting x = 388 - y into equation 1, it becomes

2x + 6.8y = 1736

2(388 - y) + 6.8y = 1736

776 - 2y + 6.8y = 1736

- 2y + 6.8y = 1736 - 776

4.8y = 960

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y = 200

x = 388 - y = 388 - 200

x = 188

4 0
3 years ago
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