How can you solve an equation with a variable on both sides

Which one is correct?

notsponge [240]

Answer:

The volume of the prism is other; 5.04 m^3

Step-by-step explanation:

Here, we want to get the volume of the prism

What we have to do here is to calculate the area of the trapezoid base and multiply by the height of the prism

The area of the base is;

A = 1/2(a + b) h

a and b are the parallel sides of the trapezoid which is 80 cm and 2 m

h is the height of the trapezoid which is 1.2 m

80 cm is same as 80/100 = 0.8 m (100 cm = 1 m)

A = 1/2( 0.8 + 2)1.2

A = 1/2 * 2.8 * 1.2 = 1.68 m^2

So we proceed to multiply this with the height of the prism which is 3 m

This will be ;

1.68 m^2 * 3 m = 5.04 m^3

5 0

3 years ago

What’s the regions ?

shutvik [7]

Answer:

In mathematical analysis, the word region usually refers to a subset of or that is open (in the standard Euclidean topology), connected and non-empty. A closed region is sometimes defined to be the closure of a region. Regions and closed regions are often used as domains of functions or differential equations.

Step-by-step explanation:

(I got this from the internet.)

3 0

4 years ago

Read 2 more answers

The record high temperature is 41° the record low temperature is -16° what is the difference in the record temperatures

vampirchik [111]

Answer: $57\°$

Step-by-step explanation:

For this exercise it is important to remember that:

1. The word "difference" indicates subtraction (The result of a subtraction is called "difference").

2. The multiplication of signs:

$(+)(+)=+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-$

For this case, according to the data given in the exercise, the records high temperature and the record low temperature are:

$High\ temperature=41\°\\\\Low\ temperature=-16\°$

Therefore, if you want to find the difference in the record temperatures, you need to sutract them.

Then you get the following result:

$High\ temperature-Low\ temperature=41\°-(-16\°)=41\°+16\°=57\°$

4 0

3 years ago

A yo-yo is moving up and down a string so that its velocity at time t is given by v(t) = 3cos(t) for time t ≥ 0. The initial pos

jeka57 [31]

Part A - The average value of v(t) over the interval (0, π/2) is 6/π

Part B - The displacement of the yo-yo from time t = 0 to time t = π is 0 m

Part C - The total distance the yo-yo travels from time t = 0 to time t = π is 6 m.

<h3>Part A: Find the average value of v(t) on the interval (0, π/2)</h3>

The average value of a function f(t) over the interval (a,b) is

$f(t)_{avg} = \frac{1}{b - a} \int\limits^b_a {f(t)} \, dx$

So, since velocity at time t is given by v(t) = 3cos(t) for time t ≥ 0. Its average value over the interval (0, π/2) is given by

$v(t)_{avg} = \frac{1}{\frac{\pi }{2} - 0} \int\limits^{\frac{\pi }{2} }_0 {v(t)} \, dt$

Since v(t) = 3cost, we have

$v(t)_{avg} = \frac{1}{\frac{\pi }{2} - 0} \int\limits^{\frac{\pi }{2} }_0 {3cos(t)} \, dt\\= \frac{3}{\frac{\pi }{2}} \int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt\\= \frac{6}{{\pi}} [{sin(t)}]^{\frac{\pi }{2} }_{0} \\= \frac{6}{{\pi}} [{sin(\frac{\pi }{2})} - sin0]\\ = \frac{6}{{\pi}} [1 - 0]\\ = \frac{6}{{\pi}} [1]\\ = \frac{6}{{\pi}}$

So, the average value of v(t) over the interval (0, π/2) is 6/π

<h3>Part B: What is the displacement of the yo-yo from time t = 0 to time t = π?</h3>

To find the displacement of the yo-yo, we need to find its position.

So, its position x = ∫v(t)dt

= ∫3cos(t)dt

= 3∫cos(t)dt

= 3sint + C

Given that at t = 0, x = 3. so

x = 3sint + C

3 = 3sin0 + C

3 = 0 + C

C = 3

So, x(t) = 3sint + 3

So, its displacement from time t = 0 to time t = π is

Δx = x(π) - x(0)

= 3sinπ + 3 - (3sin0 + 3)

= 3 × 0 + 3 - 0 - 3

= 0 + 3 - 3

= 0 + 0

= 0 m

So, the displacement of the yo-yo from time t = 0 to time t = π is 0 m

<h3>Part C: Find the total distance the yo-yo travels from time t = 0 to time t = π. (10 points)</h3>

The total distance the yo-yo travels from time t = 0 to time t = π is given by

$x(t) = \int\limits^{\pi}_0 {v(t)} \, dt\\= \int\limits^{\pi }_0 {3cos(t)} \, dt\\= 3 \int\limits^{\pi }_0 {cos(t)} \, dt\\ = 3 \int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt + 3\int\limits^{\pi }_{\frac{\pi }{2}} {cos(t)} \, dt\\= 3 \times 2\int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt\\= 6 [{sin(t)}]^{\frac{\pi }{2} }_{0} \\= 6[{sin\frac{\pi }{2} - sin0]\\\\= 6[1 - 0]\\= 6(1)\\= 6$

So, the total distance the yo-yo travels from time t = 0 to time t = π is 6 m.

Learn more about average value of a function here:

brainly.com/question/15870615

#SPJ1

4 0

1 year ago

Laine reads 200 pages in 240 minutes if Laine reads 25 pages at the same rate how long will it take her

Alik [6]

First, we have to calculate how much time it takes Laine to read one page.

240 / 200 = 6 / 5 (six fifths of a minute)

Then, we need to find out how much time it takes her to read 25 pages.

25 * 6 / 5 = 150 / 5 = 30 minutes

A: It will take Laine 30 minutes to read 25 pages at the same rate.

5 0

2 years ago