Without computing, decide whether the value of each expression is much smaller than

sarah can complete a project in 90 minutes and her sister betty can complete it in 120 minutes if they both work on the project

alukav5142 [94]

Answer:

It will take them approximately 51.43 minutes to complete the project together

Step-by-step explanation:

This is what is called a "shared job" problem.

The best way to work on them is to start by finding the "portion" of the job done by each of the people in the unit of time.

So, for example, Sarah completes the project in 90 minutes, so in the unit of time (that is 1 minute) she completed 1/90 of the total project

Betty completes the project in 120 minutes, so in the unit of time (1 minute) she completes 1/120 of the total project.

We don't know how long it would take for them to complete the project when working together, so we call that time "x" (our unknown).

Now, when they work together completing the entire job in x minutes, in the unit of time they would have done 1/x of the total project.

In the unite of time, the fraction of the job done together (1/x) should equal the fraction of the job done by Sarah (1/90) plus the fraction of the job done by Betty. This in mathematical form becomes:

$\frac{1}{x} =\frac{1}{90} +\frac{1}{120}\\\frac{1}{x} =\frac{4}{360} +\frac{3}{360}\\\frac{1}{x} =\frac{7}{360} \\x=\frac{360}{7} \\x=51.43\,\,min$

So it will take them approximately 51.43 minutes to complete the project together.

8 0

4 years ago

Find a formula for cos(tan−1(2x)) in terms of x

aleksklad [387]

$~\cos\left( \tan^{-1} 2x\right)\\\\\\=\cos \left[\cos^{-1} \dfrac{1}{\sqrt{(2x)^2+1^2}} \right]~~~~~~~~~~~~~~~~~~~~~~~~~~;[\text{Pythagorean theorem}]\\\\\\=\cos \left( \cos^{-1} \dfrac{1}{\sqrt{4x^2 +1}} \right)\\\\\\=\dfrac{1}{\sqrt{4x^2 +1}}$

4 0

2 years ago

Are these two correct? If not, please correct me and tell me how u figured it out.

goldfiish [28.3K]

Yes, those are correct.

6 0

4 years ago

Read 2 more answers

Suppose two adjacent endpoint of a rotated square are located at (-4, -6) and (5, -1) on the coordinates axes. What is the lengt

Rufina [12.5K]

To find the length of the side of the square, we just need to find the distance between the two endpoints. This problem can quickly be solved by using the distance formula, but for those who are not familiar with it, we can simply solve it by analyzing a triangle.

Take a look at the diagram below. We are interested in x. To find this we have created a right triangle. The horizontal component is just the distance between the x coordinates of the two points while the vertical component is the distance between the y coordinates.

The horizontal component is 9 and the vertical component is 5. We can now get x by using the pythagorean theorem:

$x^{2}= 9^{2} + 5^{2} =81+25=106$
$x= \sqrt{106}$ which is approximately equal to 10.30 units.

ANSWER: The length of the side of the square measures 10.30 units.

8 0

3 years ago

PLEASE I NEED HELP!!!!!!!!!!?

sergiy2304 [10]

Answer:

35

Step-by-step explanation:

8 0

3 years ago