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3 years ago

10

Two cities are 400 miles apart.If the scale on the map equals 3/4 inch = 50 miles find the distance between the two cities on th

e map.

1 answer:

alukav5142 [94]3 years ago

4 0

Answer:

6in

Step-by-step explanation:

400/50=8

8*3/4=6

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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:

brainly.com/question/17950304

6 0

2 years ago

Read 2 more answers

Consider the region bounded by 4y=x^2 and 2y=x.

gayaneshka [121]

Answer:

a) ⅓ units²

b) 4/15 pi units³

c) 2/3 pi units³

Step-by-step explanation:

4y = x²

2y = x

4y = (2y)²

4y = 4y²

4y² - 4y = 0

y(y-1) = 0

y = 0, 1

x = 0, 2

Area

Integrate: x²/4 - x/2

From 0 to 2

(x³/12 - x²/4)

(8/12 - 4/4) - 0

= -⅓

Area = ⅓

Volume:

Squares and then integrate

Integrate: [x²/4]² - [x/2]²

Integrate: x⁴/16 - x²/4

x⁵/80 - x³/12

Limits 0 to 2

(2⁵/80 - 2³/12) - 0

-4/15

Volume = 4/15 pi

About the x-axis

x² = 4y

x² = 4y²

Integrate the difference

Integrate: 4y² - 4y

4y³/3 - 2y²

Limits 0 to 1

(4/3 - 2) - 0

-2/3

Volume = ⅔ pi

7 0

3 years ago

The vertices of a triangle are located at X(-2,-1), Y(2,5) and Z(4,3). What is the perimeter of this triangle?

Lana71 [14]

If you plot the points you will find you have to use the distance formula. Pick out 2 pairs label them (x1,y1) (x2,y2) then plug it into the distance formula. The repeat for the other sides. So you should get (2,5) (4,3) plug into distance formula what is get it distance between those two points, then (4,3) (-2,-1) plug into distance formula to get an answer, lastly (-2,-1) (2,5) plug in. Now you have three answers add all together and here is your perimeter of a triangle.

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3 years ago

Which statement below best describes the transformation of parallelogram WXYZ to parallelogram W' X' Y' Z'?

Arisa [49]

The answer is B. A reflection across the x-axis.

6 0

3 years ago

Read 2 more answers

PLEASE HELP :((((

sertanlavr [38]

88(3.7+4.3)-2*2.6

88(8)-2*2.6

704-2*2.6

704-5.2

698.8

I hope it helps!

Please mark Brainliest if it does!:-)

5 0

2 years ago