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3 years ago

The volume of a cylindrical container

Mathematics

1 answer:

Ray Of Light [21]3 years ago

3 0

Answer:

A. $\frac{3}{4}\textrm{ gal}$

Step-by-step explanation:

Given:

Volume of the cylindrical container before dilation, $V_{i}=1\textrm{ gal}$

Scale factor of the dilation, $SF=\frac{3}{4}$

Therefore, the volume of the dilated cylinder is given as:

$V_{f}=SF\times V_{i}$

Plug in 1 gal for $V_{i}$ and $\frac{3}{4}$ for SF. Solve for $V_{f}$ . This gives,

$V_{f}=\frac{3}{4}\times 1\\V_{f}=\frac{3}{4}\textrm{ gal}$

Therefore, the volume of the dilated cylinder is $\frac{3}{4}$ gallons.

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What is the length of the hypotenuse? 55 ft and 48 ft

34kurt

Answer:

$\sqrt{55^2+ 48^2} = 73$

Step-by-step explanation:

$c=\sqrt{a^2 + b^2}$

6 0

2 years ago

Erika worked 18 hours last week and 20 hours this week. If she earns $6 per hour, how much did she earn these two weeks?

Crank

Hi!

If she worked 18 hours last week and 20 hours this week, then she worked 38 hours in total, because 18 + 20 = 38.

If she earns $6 per hour, and she worked for 38 hours, then she got 38 sets of 6, which you can find the answer to by multiplying 38 and 6.

This is essentially 6 + 6 + 6 +...

38 * 6 = $228

So she earned $228 these two weeks.

Hope this helped!

6 0

3 years ago

Read 2 more answers

Place each number on the number line. Use the number line to round the numbers to the nearest 1,000

artcher [175]

Where is the number line

5 0

2 years ago

Help please tysm becuase this is hard

NISA [10]

<h3>Answer: </h3><h3>Overall balance for year 5 after taxes = $1350</h3><h3>The filled out table is shown in the attached image below</h3>

===============================================================

Work Shown:

10% = 10/100 = 0.10

10% of 1000 = 0.10*1000 = 100 is the amount of interest earned in year 1. This goes in the first row of column 1. The overall balance becomes 1000+100 = 1100 after we add on the interest earned. We will write 1100 in row1,column2.

Next, compute the tax: 30% of 100 = 0.30*100 = 30. The 30 will be written in row1,column3. Finally, we subtract the amount taxed (30) from the overall balance in column 2 (which was 1100). So 1100-30 = 1070 will be written in row1,column4.

After finishing row1, we should have these four values: 100, 1100, 30, 1070

----------------------------------------------

Now onto row 2

We earn the same amount in interest because we are not compounding. Write 100 in row2,column1.

The overall balance will be different. Instead of using 1000, we will use 1070 which was the figure in row1,column4. Add the amount of interest earned ($100) onto the updated balance ($1070) to get 1170. Write 1170 in row2,column2

The value in row2,column3 is the same as the value above it. This is because the amount of interest does not change, so the amount taxed doesn't change either. Basically we'll have 30s all the way down column 3. We'll also have 100s all the way down column 1.

Subtract 1170 and 30 to get 1140 which is the balance after taxes for year 2.

------------------------------------------------

Repeat these steps for the third, fourth, and fifth rows and you'll get what you see in the table below.

6 0

3 years ago

Ex 2.8<br> 3. find the maximum value of y for the curve y=x^5 -3 for -2≤x≤1

harkovskaia [24]

$y=x^5-3\\ y'=5x^4\\\\ 5x^4=0\\ x=0\\ 0\in [-2,1]\\\\ y''=20x^3\\\\
y''(0)=20\cdot0^3=0$

The value of the second derivative for $x=0$ is neither positive nor negative, so you can't tell whether this point is a minimum or a maximum. You need to check the values of the first derivative around the point.
But the value of $5x^4$ is always positive for $x\in\mathbb{R}\setminus \{0\}$ . That means at $x=0$ there's neither minimum nor maximum.
The maximum must be then at either of the endpoints of the interval $[-2,1]$ .
The function $y$ is increasing in its entire domain, so the maximum value is at the right endpoint of the interval.

$y_{max}=y(1)=1^5-3=-2$

4 0

3 years ago