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3 years ago

What two integers are between √88

Mathematics

2 answers:

love history [14]3 years ago

5 0

9 and 10 is the answer ;;

MariettaO [177]3 years ago

4 0

9 and 10
hope this helps!!!

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Use implicit differentiation to find the points where the parabola defined by x2−2xy+y2+4x−8y+20=0 has horizontal and vertical t

Komok [63]

Answer:

The parabola has a horizontal tangent line at the point (2,4)

The parabola has a vertical tangent line at the point (1,5)

Step-by-step explanation:

Ir order to perform the implicit differentiation, you have to differentiate with respect to x. Then, you have to use the conditions for horizontal and vertical tangent lines.

-To obtain horizontal tangent lines, the condition is:

$\frac{dy}{dx}=0$ (The slope is zero)

--To obtain vertical tangent lines, the condition is:

$\frac{dy}{dx}=\frac{1}{0}$ (The slope is undefined, therefore the denominator is set to zero)

Derivating respect to x:

$\frac{d(x^{2}-2xy+y^{2}+4x-8y+20)}{dx} = \frac{d(x^{2})}{dx}-2\frac{d(xy)}{dx}+\frac{d(y^{2})}{dx}+4\frac{dx}{dx}-8\frac{dy}{dx}+\frac{d(20)}{dx}$ = $2x -2(y+x\frac{dy}{dx})+2y\frac{dy}{dx}+4-8\frac{dy}{dx}= 0$

Solving for dy/dx:

$\frac{dy}{dx}(-2x+2y-8)=-2x+2y-4\\\frac{dy}{dx}=\frac{2y-2x-4}{2y-2x-8}$

Applying the first conditon (slope is zero)

$\frac{2y-2x-4}{2y-2x-8}=0\\2y-2x-4=0$

Solving for y (Adding 2x+4, dividing by 2)

y=x+2 (I)

Replacing (I) in the given equation:

$x^{2}-2x(x+2)+(x+2)^{2}+4x-8(x+2)+20=0\\x^{2}-2x^{2}-4x+x^{2} +4x+4+4x-8x-16+20=0\\-4x+8=0\\x=2$

Replacing it in (I)

y=(2)+2

y=4

Therefore, the parabola has a horizontal tangent line at the point (2,4)

Applying the second condition (slope is undefined where denominator is zero)

2y-2x-8=0

Adding 2x+8 both sides and dividing by 2:

y=x+4(II)

Replacing (II) in the given equation:

$x^{2}-2x(x+4)+(x+4)^{2}+4x-8(x+4)+20=0\\x^{2}-2x^{2}-8x+x^{2}+8x+16+4x-8x-32+20=0\\-4x+4=0\\x=1$

Replacing it in (II)

y=1+4

y=5

The parabola has vertical tangent lines at the point (1,5)

4 0

3 years ago

Combine the like terms to create an equivalent expression:<br>4z-(-3z)

Verdich [7]

the answer is 12z²

Step-by-step explanation:

u just multiply the 4z-(-3z).

7 0

2 years ago

Diego has $11 and begins saving $5 each week toward buying a new phone. At the same time that Diego begins saving, Lin has $60 a

ValentinkaMS [17]

Answer:

1. It should be 7

2. They have $46

Step-by-step explanation:

1. You make a system of linear equations from this. So it would be y= 5x+11 where x is the number of weeks and y is the money. And the second linear equation is y=-2x+60. Then you substitute it. You make it 5x+11=-2x+60. Then you solve it normally and you got your answer but remember in this case they are asking for the x. So make sure to submit the x and not the y.

2. For this it is the same thing except they are asking for the y not the x.

3 0

2 years ago

Read 2 more answers

50 decreased by twice craig's score use the variable c to represent craig's score

ikadub [295]

Answer:

50 - 2c

Step-by-step explanation:

i think its incomplete

3 0

3 years ago