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3 years ago

Simplify (4^7/5^2)^3

Mathematics

2 answers:

Vlad [161]3 years ago

6 0

Answer:

281474976.7

Step-by-step explanation:

4⁷=16384

5²=25

16384/25=655.36

(655.36)³=281474976.7

Nuetrik [128]3 years ago

5 0

Answer:

4²¹/5⁶ or 4398046511104/15625

Step-by-step explanation:

Remember, when raising a term with an exponent to some power, you must multiply the powers.

$(\frac{4^{7} }{5^{2} })^{3} \\\\ = (\frac{(4^{7})^{3} }{(5^{2})^{3} }) \\\\= \frac{4^{7 * 3} }{5^{2* 3} } \\\\= \frac{4^{21} }{5^{6} } \\\\=\frac{4398046511104}{15625}$

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3 years ago

The height of a triangle is 5 cm shorter than its base. If the area of the triangle is 25 cm2, find the height of the triangle.

Olin [163]

Answer:

$h = 5\ cm$

Step-by-step explanation:

Let's call B at the base of the triangle and call h at the height of the triangle. Then we know that:

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For this triangle we know that $A = 25\ cm^2$ and $h = B-5$ . We substitute these values in the equation and solve for B.

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For an equation of the form $ax ^ 2 + bx + c = 0$ the quadratic formula is:

$B=\frac{-b\±\sqrt{b^2-4ac}}{2a}$

In this case note that: $a=0.5,\ \ b=-\frac{5}{2}\ \ c=-25$

Then:

$B=\frac{-(-\frac{5}{2})\±\sqrt{(-\frac{5}{2})^2-4(0.5)(-25)}}{2(0.5)}$

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The solutions are:

$B_1=\frac{5}{2}+\frac{15}{2}=10$

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For this problem we take the positive solution.

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3 years ago