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Daniel [21]
3 years ago
8

5/x=7/21 what is x please help

Mathematics
1 answer:
wlad13 [49]3 years ago
6 0

I think it is 7 because 7×3 =21  Put 7in for x then ×it by 3

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3 years ago
A 4-foot tall child walks directly away from a 12-foot tall lamppost at 2 mph. How quickly is the length of her shadow increasin
xz_007 [3.2K]

Answer:

The length of the shadow is increasing with the rate of 1.5 feet per sec

Step-by-step explanation:

Let AB and CD represents the height of the lamppost and child respectively ( shown below )

Also, let E be a point represents the position of child.

In triangles ABE and CDE,

\angle ABE\cong \angle CDE    ( right angles )

\angle AEB\cong \angle CED  ( common angles )

By AA similarity postulate,

\triangle ABE\sim \triangle CDE

∵ Corresponding sides of similar triangles are in same proportion,

\implies \frac{AB}{CD}=\frac{BE}{DE}

We have, AB = 12 ft, CD = 4 ft, BE = BD + DE = 6 + DE,

\implies \frac{12}{4}=\frac{6+DE}{DE}

12DE = 24 + 4DE

8DE = 24

DE=3

Now, the speed of walking = 2 mph = \frac{2\times 5280}{3600}\approx 2.933\text{ ft per sec}

Note: 1 mile = 5280 ft, 1 hour = 3600 sec

Thus, the time taken by child to reach at E  

= \frac{\text{Walked distance}}{\text{Walking speed}}

=\frac{6}{2.933}

= 2.045 hours

Hence, the change rate in the length of shadow

= \frac{\text{Length of shadow}}{\text{Time taken}}

=\frac{3}{2.045}

= 1.5 ft per sec.

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3 years ago
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Fiesta28 [93]
(cube root of 5)  * sqrt(5)
--------------------------------- = ?
(cube root of 5^5)

This becomes easier if we switch to fractional exponents:


  5^(1/3) * 5^(1/2)         5^(1/3 + 1/2)       5^(5/6)
------------------------ = --------------------- = ------------- = 5^[5/6 - 5/3]
[ 5^5 ]^(1/3)                  5^(5/3)                 5^(5/3) 

Note that 5/6 - 5/3 = 5/6 - 10/6 = -5/6.

                                                            1
Thus,  5^[5/6 - 5/3] = 5^(-5/6)  =  --------------
                                                        5^(5/6)

That's the correct answer.  But if you want to remove the fractional exponent from the denominator, do this:

    1            5^(1/6)         5^(1/6)
---------- * ------------- = --------------    (ANSWER)
5^(5/6)       5^(1/6)              5
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3 years ago
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