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3 years ago

Can anyone help me?pls

Mathematics

1 answer:

Mama L [17]3 years ago

8 0

Answer/Step-by-step explanation:

Given:

C = right angle = 90°

BC = a = ?

AB = c = 12

AC = b = 9

Required:

a, <A, and <B

Solution:

✔️Find a using Pythagorean Theorem:

a = √(c² - b²)

a = √12² - 9²) = √63

a = 7.93725393 = 8 (nearest whole number)

✔️Find A by applying trigonometric ratio:

Thus,

Reference angle = A

Hypotenuse = 12

Adjacent = 9

Therefore,

$cos(A) = \frac{adj}{hyp} = \frac{9}{12}$

$cos(A) = 0.75$

$A = cos^{-1}(0.75)$

m<A = 41° (nearest whole number)

✔️Find B:

m<B = 180 - (90 + 41) (sum of interior angles of triangle)

m<B = 49°

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Step-by-step explanation:

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3 years ago

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a pyramid whose altitude is 5ft weighs 800lbs. at what distance from its vertex must it be cut by a plane parallel to its base s

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A structure which has a square base and four triangular sides meeting at a point is called pyramid.

At distance of 3.97 feet from its vertex , pyramid is cut by plane so that the two solids of equal weight will be formed.

It is assumed that weight of pyramid is proportional to its volume.

So, $w = k V$ , where V is volume of original pyramid and v is volume of small pyramid and k is constant.

Let us consider that at h distance, pyramid is cut from its vertex. So a small pyramid is also formed.

Assume that base area of original pyramid is A and base of small pyramid is a.

Volume of original pyramid is, $V= \frac{1}{3} *A* 5$

So, weight of original pyramid, $W = k *(\frac{1}{3} *A* 5) = 800$

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So, weight of small pyramid, $w = k*(\frac{1}{3}* a* h)=400$

Since, base and height of small pyramid and original pyramid are in proportion.

So, $\frac{a}{A} = (\frac{h}{5}) ^{2}$

$a = (\frac{h}{5} )^{2}A$

Substituting value of a in equation $k*(\frac{1}{3}* a* h)=400$

So, $k*(\frac{1}{3}* \frac{h^{2} }{25}A * h)=400$

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Since, $(k *\frac{1}{3} *A* 5) = 800$ , substitute in above equation.

So, $800*\frac{h^{3} }{125}=400\\\\h^{3}=\frac{125}{2}\\\\h=\sqrt[\frac{1}{3} ]{62.5}\\\\h=3.97 feet$

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24= 3*2^3
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8408= 1051 * 2^3 -> 1051= 83+968 -> 968 = 2^3 * 11^2
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