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s344n2d4d5 [400]

3 years ago

13

If you can do your homework at a rate of 5.3 minutes for every problem, how many problems could be done after 9.01 hours? Round

to a whole number.

1 answer:

Deffense [45]3 years ago

8 0

Answer:

I can do 102 problems in 9.01 hours.

Step-by-step explanation:

9.01 hours = 9.01 * 60 = 540.6 minutes

540.6 / 5.3 = 102

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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

Viktor [21]

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

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

6 0

3 years ago

2x-y=3 and y=9-x in substitution methood

raketka [301]

Answer:

By adding equation we get:

2x-y=3

x +y=9

______

3x=12

x=6

Step-by-step explanation:

cut the positive and negative (y)

4 0

3 years ago

A right rectangular prism is 534 cm wide, 1012 cm long, and 8 cm tall. What is the volume of the prism?

Maru [420]

4.32×10^6 will be ur answer I believe or 1012 * 534 * 8 = 4323264

3 0

3 years ago

Read 2 more answers

What is the slope of the line that passes through (-3, 6) and (6, 8)? Type a numerical answer in the space provided. If necessar

shutvik [7]

2/9

Step-by-step explanation:

Slope in calculated as the ratio of change in y values divided by the change in x values

slope, m=Δy/Δx

Δy=8-6=2

Δx=6--3=9

m=2/9

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To calculate slope of a line :brainly.com/question/11267635

Keywords : slope, line, passes

#LearnwithBrainly

8 0

3 years ago

A triangle has an area of 3x^2+9x-54 square centimeters. If the height of the triangle is x+6 centimeters, find the length of th

JulijaS [17]

It should be b = 6(x - 3)

7 0

3 years ago