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Mandarinka [93]
3 years ago
5

Which has a steeper slope y-1/2x or y=2/3x?

Mathematics
1 answer:
NeX [460]3 years ago
4 0

Answer:

y=2/3x

Step-by-step explanation:

2/3 is greater than 1/2. It doesn't matter if one of the slopes are negative.

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Find the prime factorization for 100.
OleMash [197]

Answer:

100

Step-by-step explanation:

So, the prime factors of 100 are written as 2 x 2 × 5 x 5 or 25*4

8 0
3 years ago
What is the difference between infinity and forever?
VikaD [51]
When you say something goes on forever, it means that it is going on to infinity.  Infinity is something that can be used as a mathematical concept, but forever is not.  Forever is something people say if they don't know how infinity is used.
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3 years ago
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Hi, help with question 18 please. thanks​
Vadim26 [7]

Answer:

See Below.

Step-by-step explanation:

We are given the equation:

\displaystyle y^2 = 1 + \sin x

And we want to prove that:

\displaystyle 2y\frac{d^2y}{dx^2} + 2\left(\frac{dy}{dx}\right) ^2 + y^2 = 1

Find the first derivative by taking the derivative of both sides with respect to <em>x: </em>

<em />\displaystyle 2y \frac{dy}{dx}  = \cos x<em />

Divide both sides by 2<em>y: </em>

<h3><em />\displaystyle \frac{dy}{dx} = \frac{\cos x}{2y}<em /></h3>

<em />

Find the second derivative using the quotient rule:

\displaystyle \begin{aligned} \frac{d^2y}{dx^2} &= \frac{(\cos x)'(2y) - (\cos x)(2y)'}{(2y)^2}\\ \\  &= \frac{-2y\sin x-2\cos x \dfrac{dy}{dx}}{4y^2} \\ \\ &= -\frac{y\sin x + \cos x\left(\dfrac{\cos x}{2y}\right)}{2y^2} \\ \\ &= -\frac{2y^2\sin x+\cos ^2 x}{4y^3}\end{aligned}

Substitute:

\displaystyle 2y\left(-\frac{2y^2\sin x+\cos ^2 x}{4y^3}\right)  + 2\left(\frac{\cos x}{2y}\right)^2 +y^2 = 1

Simplify:

\displaystyle \frac{-2y^2\sin x-\cos ^2x}{2y^2} + \frac{\cos ^2 x}{2y^2} + y^2 = 1

Combine fractions:

\displaystyle \frac{\left(-2y^2\sin x -\cos^2 x\right)+\left(\cos ^2 x\right)}{2y^2} + y^2 = 1

Simplify:

\displaystyle \frac{-2y^2\sin x }{2y^2} + y^2 = 1

Cancel:

\displaystyle -\sin x + y^2 = 1

Substitute:

-\sin x + \left( 1 + \sin x\right) =1

Simplify. Hence:

1\stackrel{\checkmark}{=}1

Q.E.D.

8 0
3 years ago
Determine the equation of the linear function that generates the following table of values.
Mashutka [201]

Answer:

y = -19x + 14

Step-by-step explanation:

For each increase of x by 1, y decreases by 19, giving us -19x. When x = 0, y = 14, therefore, y = -19x + 14

5 0
2 years ago
What’s is 10 times 10
Alenkasestr [34]

Answer:

100

Step-by-step explanation:

10x10=100

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