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2 years ago

8

After how many audiobooks will they cost the same amount?

1 answer:

KatRina [158]2 years ago

6 0

They will need two audio books each

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Help me this is my question:

creativ13 [48]

Answer:

(.2)(15.75)=3.15

Step-by-step explanation:

8 0

3 years ago

HELPPPPPPPPPPPPPPPPPPPPP

tiny-mole [99]

the answer is x=100°

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4 0

3 years ago

Read 2 more answers

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

algerba write the missing numbers that make these number sentences true . 40+50=60 + ____. __= 89+10

san4es73 [151]

Answer:

it is 9 bc it adds up to 99

Step-by-step explanation:

5 0

3 years ago

The domain of f(x) is the set of all real values except 7, and the domain of g(x) is the set of all real values except –3. Which

bija089 [108]

Answer:

The set of all real values except 7

Step-by-step explanation:

We are given that,

Domain of the function f(x) is 'the set of all real values except 7'.

Domain of the function g(x) is 'the set of all real values except -3'.

It is required to find the domain of $(g\circ f)(x)$ .

Now, we know that,

<em>The composition $(g\circ f)(x)$ of functions $f(x)$ and $g(x)$ will be defined where the function $f(x)$ is defined.</em>

Since, the domain of f(x) is 'the set of all real values except 7'.

Thus, the domain of $(g\circ f)(x)$ is also 'the set of all real values except 7'.

4 0

3 years ago