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aksik [14]
3 years ago
13

Michelle rode her bicycle from her house to school at an average speed of 8 miles per hour. Later that day, she rode from school

back home along the same route at an average speed of 12 miles per hour. If the round trip took one hour, how many miles long is the round trip?
Mathematics
1 answer:
Crazy boy [7]3 years ago
8 0

9514 1404 393

Answer:

  9.6 miles

Step-by-step explanation:

Let x represent the round trip distance. Then Michelle's time was ...

  t = distance/speed

  1 = (x/2)/8 +(x/2)/12 = x(1/16 +1/24) = x(3/48 +2/48) = x(5/48)

  48/5 = x = 9.6

The round trip is 9.6 miles.

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Montano1993 [528]
Part A - 226.865 or 226.87
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Part C - 106.865
5 0
3 years ago
Using t=tanx/2, write an expression for sinx and cosx in terms of t.
Dafna11 [192]

Assume 0 < <em>x</em>/2 < <em>π</em>/2. Then

tan²(<em>x</em>/2) + 1 = sec²(<em>x</em>/2)   ===>   sec(<em>x</em>/2) = √(1 - tan²(<em>x</em>/2))

===>   cos(<em>x</em>/2) = 1/√(1 - tan²(<em>x</em>/2))

===>   cos(<em>x</em>/2) = 1/√(1 - <em>t</em> ²)

We also know that

sin²(<em>x</em>/2) + cos²(<em>x</em>/2) = 1   ===>   sin(<em>x</em>/2) = √(1 - cos²(<em>x</em>/2))

Recall the double angle identities:

cos(<em>x</em>) = 2 cos²(<em>x</em>/2) - 1

sin(<em>x</em>) = 2 sin(<em>x</em>/2) cos(<em>x</em>/2)

Then

cos(<em>x</em>) = 2/(1 - <em>t</em> ²) - 1 = (1 + <em>t</em> ²)/(1 - <em>t</em> ²)

sin(<em>x</em>) = 2 √(1 - 1/(1 - <em>t</em> ²)) / √(1 - <em>t</em> ²) = 2<em>t</em>/(1 - <em>t</em> ²)

7 0
2 years ago
The length of a log of wood is 90 in. How many cuts do you need to make to obtain
Ilia_Sergeevich [38]

The greatest number of pieces will be 12 where each piece will have a different length and the length of each piece is a whole number, in inches and the remaining piece length will be 12 in(90 - 78).

<h3>What is a sequence?</h3>

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

The total length of the wood = 90 in

We have to cut it into the greatest number of pieces, where each piece will have a different length and the length of each piece is a whole number, in inches.

We can cut it like:

1 in, 2 in, 3 in, 4 in, and so on

The above shows the arithmetic sequence,

The sum of the n natural number is given by:

\rm S_n = \dfrac{n(n+1)}{2}

\rm 90 = \dfrac{n(n+1)}{2}

After solving, we will get a quadratic equation:

n² + n -180 = 0

After solving, we will get:

n = 12.92 and n = -13.92(term can not be negative)

n = 12 (taking whole number)

Thus, the greatest number of pieces will be 12 where each piece will have a different length and the length of each piece is a whole number, in inches and the remaining piece length will be 12 in(90 - 78).

Learn more about the sequence here:

brainly.com/question/21961097

#SPJ1

6 0
2 years ago
One lap around a parking lot is 3/10 mile.this represents 15% of the total distance Gregory ran.what is the total distance in mi
sattari [20]
Given:

One lap around a parking lot = 3/10 mile
3/10 mile is 15% of the total distance Gregory ran.

To determine the total distance (in mile) that Gregory ran, we refer to the given percentage:

3/10 mile / 0.15 = 2 miles

The total distance that Gregory ran is 2 miles. <span />
4 0
3 years ago
Which of the following are measurements for triangles that are similar to a triangle with sides measuring 6, 8, and 12? Check al
kirza4 [7]
For two triangles to be similar the sides need to have the same ratio.

A and C are the correct answers.
7 0
3 years ago
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