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1 year ago

Find a formula for the nth term in this arithmetic sequence first term -2 common difference an=

Mathematics

1 answer:

malfutka [58]1 year ago

3 0

The formula for the problem is: An = 8(n-1) - 2

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Suppose it takes 18 hours for a pipe to fill a tank of water, if the tank

Lemur [1.5K]

Answer:

Step-by-step explanation:

Let the volume of tank be x

In 18 hours volume of tank filled = x

we have to find the volume of tank which is filled in 1 hours.

For that we divide LHS and RHS by 18

In 18/18 hours volume of tank filled = x/18

In 1 hours volume of tank filled = x/18

In 30 hours volume of tank emptied = x

we have to find the volume of tank which is emptied in 1 hours.

For that we divide LHS and RHS by 30

in 30/30 hours volume of tank filled = x/30

In 1 hours volume of tank filled = x/30

If tank is empty and one starts to fill it, two things will happen

it will start filling at rate of x/18 hours

But there is leak which will start to empty the tank at x/30 hours

So , at any given time rate if filling of water will be rate of filling the tank- rate of emptying the tank

In 1 hour volume of tank filled if both filling and leaking takes place simultaneously = x/18 -x/30 = (30-18)x/18*30 = 12x/18*30 = x/3*15 = x/45

In 1 hour volume of tank filled = x/45

in 1*45 hour volume of tank filled = x/45*45 = x

Thus, it will take 45 hours to fill the leaky tank .

4 0

3 years ago

Please help solve this system of equations

stepan [7]

Make a substitution:

$\begin{cases}u=2x+y\\v=2x-y\end{cases}$

Then the system becomes

$\begin{cases}\dfrac{2\sqrt[3]{u}}{u-v}+\dfrac{2\sqrt[3]{u}}{u+v}=\dfrac{81}{182}\\\\\dfrac{2\sqrt[3]{v}}{u-v}-\dfrac{2\sqrt[3]{v}}{u+v}=\dfrac1{182}\end{cases}$

Simplifying the equations gives

$\begin{cases}\dfrac{4\sqrt[3]{u^4}}{u^2-v^2}=\dfrac{81}{182}\\\\\dfrac{4\sqrt[3]{v^4}}{u^2-v^2}=\dfrac1{182}\end{cases}$

which is to say,

$\dfrac{4\sqrt[3]{u^4}}{u^2-v^2}=\dfrac{81\times4\sqrt[3]{v^4}}{u^2-v^2}$

$\implies\sqrt[3]{\left(\dfrac uv\right)^4}=81$

$\implies\dfrac uv=\pm27$

$\implies u=\pm27v$

Substituting this into the new system gives

$\dfrac{4\sqrt[3]{v^4}}{(\pm27v)^2-v^2}=\dfrac1{182}\implies\dfrac1{v^2}=1\implies v=\pm1$

$\implies u=\pm27$

Then

$\begin{cases}x=\dfrac{u+v}4\\\\y=\dfrac{u-v}2}\end{cases}\implies x=\pm7,y=\pm13$

(meaning two solutions are (7, 13) and (-7, -13))

8 0

3 years ago

Which of the following choices lists the values of the side longths of a triangle with 45-45-90 degree angles and a hypotonuso -

Ivenika [448]

Answer:

D 12rad2 12rad2 24

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Is 2.7 < 1.9 reasonable? Explain

Butoxors [25]

Answer:

no because 1.9 is less then 2.7 so the thing is wrong

7 0

2 years ago

Read 2 more answers

If one pound of shrimp cost $6 what does 7/8 pound cost

Marizza181 [45]

6 / 8 = 3/4
3/4 x 7 = 5 1/4
5 1/4 = $5.25

So, 7/8 of a pound of shrimp costs $5.25.

7 0

2 years ago