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3 years ago

12

A cylindrical water tank is being filled with a hose. The depth of the water increases by 1 1/4 ft per hour. How many hours will

it take for the water level in the tank to be 3 1/2 ft deep?

1 answer:

Ray Of Light [21]3 years ago

8 0

It will take 2 hours for the pool to reach 3
1/2 feet

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Which expression is equivalent to y · 48?

gtnhenbr [62]

Answer:

None of the above

Step-by-step explanation:

F - 40y

G - 4y

H - 40y

J y+4

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1 year ago

there are 16 bactiria in a beaker and four hours later there are 228 bacteria in the beaker. what is the rate of change per hour

Dominik [7]

Write and solve the appropriate exponential equation:

228 = 16(r)^4, where r is the change per hour in the number of bacteria:

228

------ = r^4 = 14.25.

16

Taking the fourth root of both sides, we get: r = 1.94 (answer)

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3 years ago

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Find the radius of convergence, r, of the series. ∞ xn 2n − 1 n = 1 r = 1 find the interval, i, of convergence of the series. (e

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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3 years ago

Given the function f, match the function g with a transformation of f.

docker41 [41]

Given the function f, match the function g with a transformation of f.

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b) f(x) + 2

c) f(x) - 2

d) f(x - 2)

The transformation that occured was a horizontal shift to the right of all the x's.

3 0

3 years ago

Can someone help me? And possibley tell me how to solve this as well? I'm totally clueless haha

Bumek [7]

Answer:

? = 3

Step-by-step explanation:

To find the value of ?, substitute one of the ordered pairs from the table [except (0, 0)] into the given formula and solve for ?.

Given formula:

$\sf y=\boxed{?} \:x$

Substitute x = 1 and y = 3 into the formula:

$\sf 3=\boxed{?} \:1$

To isolate ? divide both sides by 1:

$\implies \sf \dfrac{3}{1}=\dfrac{\boxed{?} \:1}{1}$

$\implies \sf 3=\boxed{?}$

Therefore, ? = 3:

$\implies \sf y=3x$

Check by inputting another value of x from the table into the found formula and comparing the calculated y-value:

$\sf x=-2 \implies y=3(-2)=-6 \quad \boxed{\sf correct}$

$\sf x=3 \implies y=3(3)=9 \quad \boxed{\sf correct}$

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1 year ago

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