All categories

3 years ago

A leaky faucet waste 3600 gallons of water per year.how many quarts does it waste per month

1 answer:

3 0

There are 12 months in a year, so you need to divide 3600 by 12. 3600 / 12 = 300. The faucet wastes 300 gallons of water per month.

You might be interested in

Find the exact value of the expression.<br> tan( sin−1 (2/3)− cos−1(1/7))

Sonja [21]

Answer:

$\tan(a-b)=\frac{2\sqrt{5}-20\sqrt{3}}{5+8\sqrt{15}}$

Step-by-step explanation:

I'm going to use the following identity to help with the difference inside the tangent function there:

$\tan(a-b)=\frac{\tan(a)-\tan(b)}{1+\tan(a)\tan(b)}$

Let $a=\sin^{-1}(\frac{2}{3})$ .

With some restriction on $a$ this means:

$\sin(a)=\frac{2}{3}$

We need to find $\tan(a)$ .

$\sin^2(a)+\cos^2(a)=1$ is a Pythagorean Identity I will use to find the cosine value and then I will use that the tangent function is the ratio of sine to cosine.

$(\frac{2}{3})^2+\cos^2(a)=1$

$\frac{4}{9}+\cos^2(a)=1$

Subtract 4/9 on both sides:

$\cos^2(a)=\frac{5}{9}$

Take the square root of both sides:

$\cos(a)=\pm \sqrt{\frac{5}{9}}$

$\cos(a)=\pm \frac{\sqrt{5}}{3}$

The cosine value is positive because $a$ is a number between $-\frac{\pi}{2}$ and $\frac{\pi}{2}$ because that is the restriction on sine inverse.

So we have $\cos(a)=\frac{\sqrt{5}}{3}$ .

This means that $\tan(a)=\frac{\frac{2}{3}}{\frac{\sqrt{5}}{3}}$ .

Multiplying numerator and denominator by 3 gives us:

$\tan(a)=\frac{2}{\sqrt{5}}$

Rationalizing the denominator by multiplying top and bottom by square root of 5 gives us:

$\tan(a)=\frac{2\sqrt{5}}{5}$

Let's continue on to letting $b=\cos^{-1}(\frac{1}{7})$ .

Let's go ahead and say what the restrictions on $b$ are.

$b$ is a number in between 0 and $\pi$ .

So anyways $b=\cos^{-1}(\frac{1}{7})$ implies $\cos(b)=\frac{1}{7}$ .

Let's use the Pythagorean Identity again I mentioned from before to find the sine value of $b$ .

$\cos^2(b)+\sin^2(b)=1$

$(\frac{1}{7})^2+\sin^2(b)=1$

$\frac{1}{49}+\sin^2(b)=1$

Subtract 1/49 on both sides:

$\sin^2(b)=\frac{48}{49}$

Take the square root of both sides:

$\sin(b)=\pm \sqrt{\frac{48}{49}$

$\sin(b)=\pm \frac{\sqrt{48}}{7}$

$\sin(b)=\pm \frac{\sqrt{16}\sqrt{3}}{7}$

$\sin(b)=\pm \frac{4\sqrt{3}}{7}$

So since $b$ is a number between $0$ and $\pi$ , then sine of this value is positive.

This implies:

$\sin(b)=\frac{4\sqrt{3}}{7}$

So $\tan(b)=\frac{\sin(b)}{\cos(b)}=\frac{\frac{4\sqrt{3}}{7}}{\frac{1}{7}}$ .

Multiplying both top and bottom by 7 gives:

$\frac{4\sqrt{3}}{1}= 4\sqrt{3}$ .

Let's put everything back into the first mentioned identity.

$\tan(a-b)=\frac{\tan(a)-\tan(b)}{1+\tan(a)\tan(b)}$

$\tan(a-b)=\frac{\frac{2\sqrt{5}}{5}-4\sqrt{3}}{1+\frac{2\sqrt{5}}{5}\cdot 4\sqrt{3}}$

Let's clear the mini-fractions by multiply top and bottom by the least common multiple of the denominators of these mini-fractions. That is, we are multiplying top and bottom by 5:

$\tan(a-b)=\frac{2 \sqrt{5}-20\sqrt{3}}{5+2\sqrt{5}\cdot 4\sqrt{3}}$

$\tan(a-b)=\frac{2\sqrt{5}-20\sqrt{3}}{5+8\sqrt{15}}$

4 0

3 years ago

Marisa wants to buy a quality phone for least $200.She has already saved $125 and plans to save an additional $10 each week.Writ

eduard

Answer:

The inequality can be represented as:

$10w+125\geq200$

where $w$ represents the number of weeks in which Maria will be able to buy a phone for least $200.

On solving it we get : $w\geq 7.5$

Step-by-step explanation:

Given:

Maria wants to buy a phone for at least $200.

She has savings of $125.

She plans to save $10 every week.

To write an inequality for the situation.

Solution:

Let the number of weeks in which Maria will be able to buy a phone be = $w$

If she saves $10 each week.

Then, in $w$ weeks she will save in dollars = $10w$

She already has savings = $125

So her total savings in $w$ weeks in dollars will be = $10w+125$

She wants to buy a phone for at least $200.

Thus, the inequality can be represented as:

$10w+125\geq200$

Solving for $w$

Subtracting both sides by 125.

$10w+125-125\geq 200-125$

$10w\geq 75$

Dividing both sides by 10.

$\frac{10w}{10}\geq \frac{75}{10}$

$w\geq 7.5$

Thus Maria needs at least 7.5 weeks to be able to buy a phone for atleast $200.

5 0

3 years ago

Adam currently runs about 40 miles per week, and he wants to increase his weekly mileage by 30%. How many miles will Adam run pe

BigorU [14]

Answer:

52 miles/week (12 more miles per week)

Step-by-step explanation:

In order to know the miles per week with this increasement, we'll use the rule of 3, assuming that 40 miles is the 100% innitially so:

If:

40 miles --------->100%

X miles ----------> 30%

Solving for X we have the following:

X = 30 * 40 / 100 = 12 miles

So, if Adam wants to increase his weekly mileage by 30%, he needs to run 12 more miles, and that makes a total of 52 miles/week

6 0

3 years ago

Jim is building a rectangular deck and wants the length to be 1 ft greater than the width. what will be the dimensions of the de

Travka [436]

Let x = width
x+1 is then the length

2x+2(x+1)=66
2x+2x+2=66
4x=64
x=16
deck will be 16x17, nice for a BBQ. :)

3 0

3 years ago

WILL MARK BRIANLIEST!

gayaneshka [121]

Answer:

(4, - 2 )

Step-by-step explanation:

Given the 2 equations

x + y = 2 → (1)

x - y = 6 → (2)

Adding the 2 equations term by term will eliminate the term in y, that is

(x + x) + (y - y) = (2 + 6)

2x = 8 ( divide both sides by 2 )

x = 4

Substitute x = 4 in either of the 2 equations and solve for y

Substituting in (1)

4 + y = 2 ( subtract 4 from both sides )

y = - 2

Solution is (4, - 2 )

7 0

3 years ago