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3 years ago

the distance between Two Cities on a map is 4.125. find the actual distance if the scale on the map was 2 inches = 40 miles

Mathematics

1 answer:

atroni [7]3 years ago

7 0

Answer:

85 miles.

Step-by-step explanation:

Lets begin by figuring out the number of miles in 4 inches. Since every 2 inches make 40 miles, we can figure out that there are 80 miles in 4 inches. To figure out that .125 part, we multiply 40 by .125, to get 5. We can add 80 plus 5 to get our grand total of 85 miles.

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A triangle has two constant sides of length 5 feet and 7 feet. The angle between these two sides is increasing at a rate of 0.9

o-na [289]

Answer: $12.74 ft^2/s$

Step-by-step explanation:

Given

Two sides of triangle of sides 5 ft and 7 ft

and angle between them is increasing at a rate of 0.9 radians per second

let $\theta$ is the angle between them thus

Area of triangle when two sides and angle between them is given

$A=\frac{ab\sin C}{2}$

$A=\frac{5\times 7\times \sin \theta }{2}$

Differentiate w.r.t time

$\frac{\mathrm{d} A}{\mathrm{d} t}=\frac{35\cos theta }{2}\times \frac{\mathrm{d} \theta }{\mathrm{d} t}$

at $\theta =\frac{\pi }{5}$

$\frac{\mathrm{d} A}{\mathrm{d} t}=\frac{35\times cos(\frac{\pi }{5})}{2}\times 0.9$

$\frac{\mathrm{d} A}{\mathrm{d} t}=12.74 ft^2/s$

4 0

3 years ago

What is the approximate area of the shaded portion of the diagram? (Use 3.14 as an estimate for pi.)

Nadusha1986 [10]

Answer:

218

Step-by-step explanation:

first find the area of the circle-

$A=\pi r^{2} \\A=\pi 10^{2} \\A=100\pi \\A=314$

to find the area of the triangle, we need the base and the height. The base we know is 16, since we don't know the height yet, use the Pythagorean theorem to find the height. One leg is 16 the hypotenuse is 20 (2* the radius).

$a^{2} +b^{2} =c^{2} \\a^{2} +16^{2} =20^{2} \\a^{2} +256=400\\a^{2} =144\\a=12$

Now I know the height is 12. Find the area of the triangle

$A=\frac{1}{2} bh\\A=\frac{1}{2} (16)(20)\\A=96$

subtract the area of the triangle from the area of the circle

314-96=218

6 0

2 years ago

Which equation represents the line that passes through (5,8) and (9,2)

Dahasolnce [82]

ASSUMING This is a straight line so we gotta the formula for a straight line which is y=mx+b, where m represents the slope and b represents the y intercept.

First, we know this line passes through (5,8) and (9,2) we can use these for finding the equations. When we know two points, we use this formula:

y-y=m(x-x)

The first y is 8 and the second one is 2
The first x is 5 and the second one is 9

Plug it in:

8-2=m(5-9)
6=m(-4)
6/-4=m <— simplify this
m= -3/2

*NOTE: another way to find m is by calculating it (y-y)/(x-x)

Now we know m, we have to find b.
All you gotta do is plug everything you know back into the equation y=mx+b

y=mx+b
y=-3/2x+b <— now plug in a point we know(x,y)

8=-3/2(5)+b
8=-15/2+b
8-(-15/2)=b
b=8+15/2
b=16/2+15/2
b=31/2 (now you can write be as a fraction or a decimal in your equation, depending on what your teacher told you to use)
*NOTE: it is best to use fractions instead of decimals as it is more accurate sometimes.

Now we know all the variables that need to be known, we just need to rewrite the formula of the equation so the teacher can see.

m=-3/2
b=31/2

We don’t need to plug in x or y since it could have different values (since a straight line has MANY co-ordinates)

SO OUR EQUATION IS=
y=(-3/2)x+31/2

Hope you understand this, feel free to ask me anything!

6 0

3 years ago

How can i find the volume of a rectangular prism

Lubov Fominskaja [6]

Answer:

Width x height x length

Step-by-step explanation:

You just multiply the width times the height times the length.

4 0

3 years ago

What is the minimum force required to prevent a ball weighing 22.6 lb from rolling down a ramp which is inclined at 39.0 with th

shusha [124]

22.6sin[39.0]= 21.78

3 0

2 years ago