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yoongnzl
23.04.2020 •
Mathematics
The volume of a sphere is about 523 cm3. What is the volume, to the nearest tenth, of a smaller sphere that has a scale factor of 1/4? a. 8.2 cm3 c. 9.4 cm3 b. 6.7 cm3 d. 8.5 cm3
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Ответ:
The length of the mat is 30 inches.
Step-by-step explanation:
Let H be the hypotenuse of the incline mat, L its length and h its height.
It is given that H = L + 4 and h = L - 14. Now, using Pythagoras' theorem for right-angled triangles, H² = L² + h²
(L + 4)² = L² + (L - 14)²
Expanding, we have
L² + 8L + 16 = L² + L² -28L + 196
collecting all the terms to the right side, we have
L² + L² -28L + 196 - L² - 8L - 16 = 0
L² - 36L + 180 = 0
Using the quadratic formula, L =
L![\frac{-(-36) +/- \sqrt{(-36)^{2} -4X1X180} )}{2X1} = \frac{36 +/- \sqrt{1296 - 720} }{2} \\= \frac{36 +/- \sqrt{576} }{2} \\= \frac{36 +/- 24 )}{2}\\=\frac{36 + 24}{2} or \frac{36 - 24}{2} \\=\frac{60}{2} or \frac{12}{2} \\= 30 or 6](/tpl/images/0511/5869/d005f.png)
We use the larger answer L = 30 inches since L = 6 would give h = L -14 = 6 - 14 = -8 .
So, the length of the mat is 30 inches.