Maggie's brother is 8 years younger than twice her age. The sum of their ages is 25.

Alan's dogs have a total of 24 legs (l). if each dog has 4 legs, which equation gives the number of dogs (

Slav-nsk [51]

4d = 24 would be the right equation. To double check you would divide both sides by 4 (the number of legs) to find the amount of dogs.

3 0

3 years ago

Find the volume of the solid whose base is the region Ix I Iy I < 1 and whose vertical cross sections perpendicular to the y-

gavmur [86]

Answer:

volume of the solid = $\frac{\pi }{3}$

Step-by-step explanation:

As given , the region : |x| + |y| $\leq$ 1

when y $\geq$ 0 ,

|x| + y = 1

⇒|x| = 1 - y

when y ≤ 0 ,

|x| - y = 1

⇒|x| = 1 + y

The given region is the rectangle with sides (0, 5) , (0, -5), (5, 0), (-5, 0)

As given , the vertical cross section are semicircle

As we know that the area of semi circle = $\frac{1}{2}$ $\pi x^{2}$

Now,

Volume = $\int\limits^0_-1 {\frac{\pi }{2} (1+y)^{2} } \, dy$ + $\int\limits^1_0 {\frac{\pi }{2} (1-y)^{2} } \, dy$

= $\frac{\pi }{2} (\frac{(1+y)^{3} }{3} )$ - $\frac{\pi }{2} (\frac{(1-y)^{3} }{3} )$

= $\frac{\pi }{6}$ [1-0] - $\frac{\pi }{6}$ [0-1]

= $\frac{\pi }{6} + \frac{\pi }{6} = 2\frac{\pi }{6} = \frac{\pi }{3}$

⇒volume of the solid = $\frac{\pi }{3}$

4 0

3 years ago

Helen is putting a fence around her flower garden, which is in the shape of half of a circle and a rectangle. If the semicircle

erastova [34]

Answer:

Part 1) Helen will need 38 feet of fencing

Part 2) The perimeter around the three sides of the rectangular section of the garden is 27 feet

Part 3) The approximate distance around half of the circle is 11 feet

Step-by-step explanation:

Part 1) How much fencing will Helen need?

Find out the perimeter

we know that

The perimeter of the figure is equal to the sum of three sides of the rectangular section plus the circumference of a semicircle

so

$P=2L+W+\frac{1}{2}\pi D$

we have

$L=10\ ft\\W=7\ ft\\D=7\ ft\\\pi =\frac{22}{7}$

substitute

$P=2(10)+7+\frac{1}{2}(\frac{22}{7})(7)$

$P=20)+7+11=38\ ft$

therefore

Helen will need 38 feet of fencing

Part 2) What is the perimeter around the three sides of the rectangular section of the garden?

$P=2L+W$

we have

$L=10\ ft\\W=7\ ft$

substitute

$P=2(10)+7$

$P=20+7=27\ ft$

therefore

The perimeter around the three sides of the rectangular section of the garden is 27 feet

Part 3) What is the approximate distance around half of the circle?

Find the circumference of semicircle

$C=\frac{1}{2}\pi D$

we have

$D=7\ ft\\\pi =\frac{22}{7}$

substitute

$C=\frac{1}{2}(\frac{22}{7})(7)$

$C=11\ ft$

therefore

The approximate distance around half of the circle is 11 feet

4 0

3 years ago

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Can you find the number of triangles in the given figure?

melomori [17]

Answer:

20?

Step-by-step explanation:

4 0

3 years ago

A face of a solid is

gtnhenbr [62]

Answer:

The Second Answer , a pattern of two-dimensional shapes that can be folded to form a solid figure . 

3 0

1 year ago

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