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denpristay [2]
3 years ago
13

Shortern this expression pls​

Mathematics
1 answer:
pogonyaev3 years ago
4 0

Answer:

c =\frac{8}{3}

Step-by-step explanation:

Given

c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7}} +  \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}}

Required

Shorten

We have:

c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7}} +  \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}}

Rationalize

c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7} * \frac{4 + \sqrt 7}{4 + \sqrt 7}} +  \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}*\frac{4 - \sqrt 7}{4 - \sqrt 7}}

Expand

c = \sqrt{\frac{(4 + \sqrt 7)^2}{4^2 - (\sqrt 7)^2}} +  \sqrt{\frac{(4 - \sqrt 7)^2}{4^2 - (\sqrt 7)^2}

c = \sqrt{\frac{(4 + \sqrt 7)^2}{16 - 7}} +  \sqrt{\frac{(4 - \sqrt 7)^2}{16 - 7}

c = \sqrt{\frac{(4 + \sqrt 7)^2}{9}} +  \sqrt{\frac{(4 - \sqrt 7)^2}{9}

Take positive square roots

c =\frac{4 + \sqrt 7}{3} +  \frac{4 - \sqrt 7}{3}

Take LCM

c =\frac{4 + \sqrt 7 + 4 - \sqrt 7}{3}

Collect like terms

c =\frac{4  + 4+ \sqrt 7 - \sqrt 7}{3}

c =\frac{8}{3}

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An airplane is preparing to land at an airport. It is 50400 feet above the ground and is descending at the rate of 3000 feet per
Dovator [93]

Answer:

let t = no of minutes when they are at the same altitude

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52200 - 3300t = 2500t

52200 = 3300t + 2500t

52200 = 5800t

t = 52200/5800

t = 9 minutes they will be at the same altitude

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The altitude:

9*2500 = 22500 ft

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Check on other train

52200 - 9(3300) =

52200 - 29700 = 22500 ft

3 0
2 years ago
I need help pls !!!!
Phantasy [73]

Answer:

See Below

Step-by-step explanation:

Ok, so in this problem you have some vertical angles. These are angles oppisites from each other. Therefore; d = 52, f = ?, and e = 77. All the angles added together will = 360. Let's add up the angles we know and subtract the whole from 360.

52 + 52 + 77 + 77 = ?

104 + 154 = 258

360 - 258 = 102

Since we know that f and the unlabeled angle are the same, we need to divide this total between the two of them.

102/2 = 51

Therefore;

d = 52

e = 77

f = 51

3 0
3 years ago
PLEASE HELP ME ASAP!!
tatuchka [14]

Answer:

36 feet

Step-by-step explanation:

6 0
3 years ago
Somebody help me ASAP
mixer [17]

Answer:

6

Step-by-step explanation:

6.5 lined up to x is 6

4 0
2 years ago
Read 2 more answers
5/3 - 1/6 and i need it now because im in school now
Vlad [161]

Answer:

9/6 or 1 1/2

Step-by-step explanation:

Make the denominators the same...

<u>5</u> x2     ----> 10/6 -------> 10/6 -1/6 = 9/6

3 x2

5 0
2 years ago
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