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4 years ago

Write an equation of a line using point-slope form that goes through the point (4, 7) and has a slope of 3

Mathematics

1 answer:

sveta [45]4 years ago

4 0

Y - y1 = m(x - x1)
slope(m) = 3
(4,7)....x1 = 4 and y1 = 7
now we sub
y - 7 = 3(x - 4) <==

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Find the number that makes the ratio equivalent to 12:1.<br> ?:6

Naily [24]

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3 years ago

Workout the median of 83,73,76,72,75,86,79,76

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The median is 76

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Alexxandr [17]

Answer:

a ) dAt/dt = 50,24 in/min

dh/dt = - 0,125 in/min

Step-by-step explanation:

The area of the top is At :

At = π*r²

a) Tacking derivatives with respect to time:

dAt/dt = 2* π*r * dr/dt

At t = t₁ r = 16 in and dr/dt = 0,5

Then

dAt/dt = 2*3,14*16*0,5 in/min

a ) dAt/dt = 50,24 in/min

b) The volume of the cylinder is:

Vc = π*r²*h ( where h is the heigh of the cylinder )

Tacking derivatives with respect to time

dVc/dt = 2* π*r*h*dr/dt + π*r²*dh/dt

But dVc/dt = 0 since the volume remains constant, then:

π*r²*dh/dt = - 2* π*r*h*dr/dt

r*dh/dt = - 2*h*dr/dt

dh/dt = - 2*0,5*2/16 in/min

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3 years ago

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Bingel [31]

Assuming the series is

$\displaystyle\sum_{n\ge1}\frac{x^n}{2n-1}$

The series will converge if

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{x^{n+1}}{2(n+1)-1}}{\frac{x^n}{2n-1}}\right|$

We have

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{x^{n+1}}{2(n+1)-1}}{\frac{x^n}{2n-1}}\right|=|x|\lim_{n\to\infty}\frac{\frac1{2n+1}}{\frac1{2n-1}}=|x|-\lim_{n\to\infty}\frac{2n-1}{2n+1}=|x|$

So the series will certainly converge if $-1$ , but we also need to check the endpoints of the interval.

If $x=1$ , then the series is a scaled harmonic series, which we know diverges.

On the other hand, if $x=-1$ , by the alternating series test we can show that the series converges, since

$\left|\dfrac{(-1)^n}{2n-1}\right|=\dfrac1{2n-1}\to0$

and is strictly decreasing.

So, the interval of convergence for the series is $-1\le x$ .

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4 years ago