Can someone please explain this in detail?

Mathematics

2 answers:

kykrilka [37]2 years ago

5 0

Factorize the given number:

$5^5 - 5^3 = 5^3 \left(5^2 - 1\right) = 5^3 \times 24 = 2^3 \times 3 \times 5^3$

The first equality follows from

$5^5 = 5^{3 + 2} = 5^3 \times 5^2$

so both 5⁵ and 5³ share a common factor of 5³ that we can pull out as we did.

Then the distinct prime factors are 2, 3, and 5; their sum is 2 + 3 + 5 = 10.

Taya2010 [7]2 years ago

4 0

<h3>Answer: 10</h3>

Work Shown:

$5^5 - 5^3\\\\5^3(5^2 - 1)\\\\5^3(25 - 1)\\\\5^3(24)\\\\5^3(8*3)\\\\5^3(2^3*3)\\\\2^3*3*5^3\\\\$

The distinct prime factors are: 2, 3, 5. We'll ignore the exponents at this point.

Those primes sum to 2+3+5 = 10

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A small plane and a large plane are 6.8km from each other, at the same altitude (height). From an observation tower, the two air

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Answer:

7.9km

Step-by-step explanation:

(a)See attached for the diagram representing this situation.

(b)

In Triangle ABC

$\text{Using Law of Sines}\\\dfrac{\sin A}{a}=\dfrac{\sin C}{c} \\\dfrac{\sin A}{5.2}=\dfrac{\sin 58^\circ}{6.8} \\\sin A=5.2 \times \dfrac{\sin 58^\circ}{6.8}\\A=\arcsin (5.2 \times \dfrac{\sin 58^\circ}{6.8})\\A=40.43^\circ$

Next, we determine the value of Angle B.

$\angle A+\angle B+\angle C=180^\circ\\40.43+58+\angle B=180^\circ\\\angle B=180^\circ-(40.43+58)\\\angle B=81.57^\circ$

Finally, we find b.

$\text{Using Law of SInes}\\\dfrac{b}{\sin B}=\dfrac{c}{\sin C} \\\dfrac{b}{\sin 81.57^\circ}=\dfrac{6.8}{\sin 58^\circ} \\b=\dfrac{6.8}{\sin 58^\circ} \times \sin 81.57^\circ\\b=7.9km $ (to the nearest tenth of a kilometer)$