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3 years ago

14

There are two different maps of ohio. The scale on the first map is 1 cm to 10 km. The distance from cleveland to clncinnati is

40 cm. The scale on the second map is 1 to 50 km what is the distance from cleveland to cincinnati on the second map explain your reasoning

1 answer:

Ivanshal [37]3 years ago

6 0

1. To answer this question we must keep on mind that we already have the distance from Cleveland to Cincinnati.

2. They tell us that it is 40 centimeters on the first map.

3. If on the first map $1cm = 10km$ then:

$40cm = 10km * 40 = 400km$

4. Then the distance from Cleveland to Cincinnati is 400 kilometers.

5. On the second map $1cm = 50km$

6. Then we want to know how many centimeters represents 400 kilometers on the second map. Therefore:

$400/50= 8$

The answer is: 8 centimeters.

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Step-by-step explanation:

how I see the problem I just put the 1 over the 8 because you can't really do anything else with the problem

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3 years ago

7 and - 1 1/2 on the number line?

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Show that the set of points that are twice as far from the origin as they are from (2, 2, 2) is a sphere. Find the center and ra

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Answer:

This is a sphere with a center $(\dfrac{8}{3},\dfrac{8}{3},\dfrac{8}{3} )$ and radius $\dfrac{4 \sqrt{3}}{3}$

Step-by-step explanation:

Given that: (x,y,z)

where;

d₁ is the distance from the origin = $\sqrt{x^2+y^2+z^2}$

d₂ is the distance from (2,2,2) = $\sqrt{(x-2)^2+(y-2)^2+(z-2)^2}$

Also;

d₁ = 2d₂

$\sqrt{x^2 + y^2 +z^2 } = 2 \sqrt{(x-2)^2 +(y-z)^2+(z-2)^2}$

By squaring both sides;

$x^2 + y^2 +z^2 = 2^2((x-2)^2 +(y-z)^2+(z-2)^2)$

$x^2 + y^2 +z^2 = 4(x-2)^2 +4(y-z)^2+4(z-2)^2$

$x^2 + y^2 +z^2 =4(x^2 -2x -2x +4) + 4(y^2 -2y -2y +4) + 4(z^2 -2z-2z+4)$

$x^2 + y^2 +z^2 =4x^2 -16x +16 + 4y^2 -16y +16 + 4z^2 -16z+16$

Collect the like terms:

$0 = 4x^2 -x^2 -16x +16 + 4y^2 -y^2 -16y +16 +4z^2 -z^2 -16z +16$

$0 = 3x^2 -16x +16 + 3y^2 -16y +16 +3z^2 -16z +16$

Divide both sides by 3

$\dfrac{0}{3} = \dfrac{3x^2 -16x +16}{3} + \dfrac{3y^2 -16y +16 }{3} + \dfrac{ +3z^2 -16z +16}{3}$

$0 = {x^2 - \dfrac{16x}{3} +\dfrac{16}{3} + {y^2 - \dfrac{16y}{3} +\dfrac{16}{3}+{z^2 - \dfrac{16z}{3} +\dfrac{16}{3}$

Using the completing the square method;

$3(\dfrac{160}{9}) -16 = {x^2 - \dfrac{16x}{3} +\dfrac{160}{9} + {y^2 - \dfrac{16y}{3} +\dfrac{160}{9}+{z^2 - \dfrac{16z}{3} +\dfrac{160}{9}$

$\dfrac{16}{3}= (x - \dfrac{8}{3})^2+ (y - \dfrac{8}{3})^2+ (z - \dfrac{8}{3})^2$

∴

This is a sphere with a center $(\dfrac{8}{3},\dfrac{8}{3},\dfrac{8}{3} )$ and ;

radius; $\sqrt{\dfrac{16}{3}}$

$= \dfrac{4 \sqrt{3}}{3}$

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3 years ago

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Mazyrski [523]

Answer:

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Hence, the speed of conveyor is 7.07 feet per second.

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Read 2 more answers

Witch of the following equations could be used to solve the problem? x2+2=36 2x+2=36 2x=36 2x+1=36

Tomtit [17]

Answer:

There is no problem stated, but here is the x's for every equations provided:

Step-by-step explanation:

a.) x²+2=36

x²=34

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b.) 2x + 2 =36

2x= 34

x= 17

c.)2x=36

x= 18

d.) 2x+1=36

2x=35

x=35/2

6 0

3 years ago