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3 years ago

The variables y and x have a proportional relationship, and y =5 when x=4

Mathematics

1 answer:

patriot [66]3 years ago

3 0

Answer:The value of x is 6.4

Step-by-step explanation:

5/8=4/x use cross product.

5x=32 divide both sides by 5

x = 6.4

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Number sequence 3 6 4 8 6 12 10

Jobisdone [24]

The sequence is times 2 minus 2
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20 - 2 = 18

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3 years ago

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arlik [135]

Answer:

1. 64

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3 years ago

Whats the math equation for a sphere

Lyrx [107]

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4 years ago

Q.04: (11 points) Given the polar curve r = e θ , where 0 ≤ θ ≤ 2π. Find points on the curve in the form (r, θ) where there is a

Citrus2011 [14]

I suppose the curve is $r(\theta)=e^\theta$ .

Tangent lines to the curve have slope $\frac{dy}{dx}$ ; use the chain rule to get this in polar coordinates.

$\dfrac{dy}{dx}=\dfrac{dy}{d\theta}\dfrac{d\theta}{dx}=\dfrac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}$

We have

$y(\theta)=r(\theta)\sin\theta\implies\dfrac{dy}{d\theta}=\dfrac{dr}{d\theta}\sin\theta+r(\theta)\cos\theta$

$x(\theta)=r(\theta)\cos\theta\implies\dfrac{dx}{d\theta}=\dfrac{dr}{d\theta}\cos\theta-r(\theta)\sin\theta$

$r(\theta)=e^\theta\implies\dfrac{dr}{d\theta}=e^\theta$

$\implies\dfrac{dy}{dx}=\dfrac{e^\theta\sin\theta+e^\theta\cos\theta}{e^\theta\cos\theta-e^\theta\sin\theta}=\dfrac{\sin\theta+\cos\theta}{\cos\theta-\sin\theta}$

The tangent line is horizontal when the slope is 0, which happens wherever the numerator vanishes:

$\sin\theta+\cos\theta=0\implies\sin\theta=-\cos\theta\implies\tan\theta=-1$

$\implies\theta=\boxed{-\dfrac\pi4+n\pi}$

(where $n$ is any integer)

The tangent line is vertical when the slope is infinite or undefined, which happens when the denominator is 0:

$\cos\theta-\sin\theta=0\implies\sin\theta=\cos\theta\implies\tan\theta=1$

$\implies\theta=\boxed{\dfrac\pi4+n\pi}$

6 0

4 years ago

Giving 13 points if you help plz

natita [175]

125

2^3 = 8
8 = 1/2 of 16
1/2 of 250 = 125

3 0

3 years ago