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4 years ago

200 gallon tank fills at 3 gallons/minute and loses 2 gallons/minute how long does it take to fill up

Mathematics

1 answer:

goblinko [34]4 years ago

7 0

it fills at 3 gallons per minute, but loses 2 gallons per minute

3-2 =1, so it fills at 1 gallon per minute

200 gallons at 1 gallon per minute = 200 minutes,

200/60 = 3 hours and 20 minutes

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QS¯¯¯¯¯¯¯ bisects ∠PQR . If m∠PQS = 5x and m∠RQS = 2x + 6, then what is m∠PQR ? m∠PQR is

soldi70 [24.7K]

Answer:

$PQR = 20$

Step-by-step explanation:

Given

Bisector: QS

$PQS = 5x$

$RQS = 2x + 6$

Required

Determine PQR

Since PQR is bisected to PQS and RQS, we have that

$PQS = RQS$

Substitute expressions for PQS and RQS

$5x = 2x + 6$

Collect Like Terms

$5x - 2x = 6$

$3x = 6$

Divide both sides by 3

$x = 2$

Solving for PQR;

$PQR = PQS + RQS$

$PQR = 5x + 2x + 6$

$PQR = 7x + 6$

Substitute 2 for x

$PQR = 7 * 2 + 6$

$PQR = 14 + 6$

$PQR = 20$

4 0

4 years ago

A geometric series has second term 375 and fifth term 81 . find the sum to infinity of series .

Eduardwww [97]

Answer: $\bold{S_{\infty}=\dfrac{3125}{2}=1562.5}$

<u>Step-by-step explanation:</u>

a₁, 375, a₃, a₄, 81

First, let's find the ratio (r). There are three multiple from 375 to 81.

$375r^3=81\\\\r^3=\dfrac{81}{375}\\\\\\r^3=\dfrac{27}{125}\qquad \leftarrow simplied\\\\\\\sqrt[3]{r^3} =\sqrt[3]{\dfrac{27}{125}}\\ \\\\r=\dfrac{3}{5}$

Next, let's find a₁

$a_1\bigg(\dfrac{3}{5}\bigg)=375\\\\\\a_1=375\bigg(\dfrac{5}{3}\bigg)\\\\\\a_1=125(5)\\\\\\a_1=625$

Lastly, Use the Infinite Geometric Sum Formula to find the sum:

$S_{\infty}=\dfrac{a_1}{1-r}\\\\\\.\quad =\dfrac{625}{1-\frac{3}{5}}\\\\\\.\quad =\dfrac{625}{\frac{2}{5}}\\\\\\.\quad = \dfrac{625(5)}{2}\\\\\\.\quad = \large\boxed{\dfrac{3125}{2}}$