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3 years ago

6

The Wilsons have triplets and another child who is eleven years old. The sum of the ages of their children is 32. How old are th

e triplets?

1 answer:

Leno4ka [110]3 years ago

8 0

ANSWER:

The triplets will be 7 years each. 21, divided by 7.

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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

slavikrds [6]

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.

<u>It is assumed that weight of pyramid is proportional to its volume.</u>

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, $W = k *(\frac{1}{3} *A* 5) = 800$

Volume of small pyramid is, $v = \frac{1}{3}* a* h$

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

<u>Since, base and height of small pyramid and original pyramid are in proportion.</u>

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

$(k*\frac{1}{3}* A*5)*\frac{1}{5} *\frac{h^{2} }{25} * h)=400$

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

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

Learn more:

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2 years ago

Read 2 more answers

Which is greater 2 2/3, 2.45, 2 2/5

timofeeve [1]

This is least to greatest

2 2/5 or 2.40

2.45

2 2/3

2 2/5 , 2.45 , 2 2/3

7 0

3 years ago

Read 2 more answers

Write a polynomial f (x) that satisfies the given conditions. Polynomial of lowest degree with zeros of -4 (multiplicity 3), 1 (

yuradex [85]

Answer:

Step-by-step explanation:

Polynomial f(x) has the following conditions: zeros of -4 (multiplicity 3), 1 (multiplicity 1), and with f(0) = 320.

The first part zeros of -4 means (x+4) and multiplicity 3 means (x+4)^3.

The second part zeros of 1 means (x-1) and multiplicity 1 means (x-1).

The third part f(0) = 320 means substituting x=0 into (x+4)^3*(x-1)*k =320

(0+4)^3*(0-1)*k = 320

-64k = 320

k = -5

Combining all three conditions, f(x)

= -5(x+4)^3*(x-1)

= -5(x^3 + 3*4*x^2 + 3*4*4*x + 4^3)(x-1)

= -5(x^4 + 12x^3 + 48x^2 + 64x - x^3 - 12x^2 - 48x - 64)

= -5(x^4 + 11x^3 + 36x^2 + 16x -64)

= -5x^3 -55x^3 - 180x^2 - 80x + 320

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3 years ago

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-0.5x=3.6<br><br> F. -72<br> G. -7.2<br> H. 7.2<br> I. 72

masya89 [10]

Answer:

G

Step-by-step explanation:

3.6÷-0.5 is -7.2, so it's G

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2 years ago

Why is the product of a rational number and an irrational number irrational

prohojiy [21]

Because u r adding irrational to rational its like if u add a whole number to a negative number u get deeper into negatives in this case irrational is the negative and rational is the whole<span />

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3 years ago