All categories

3 years ago

Somebody please help me?! I'll mark brainliest if you're correct!

1 answer:

8 0

Since the bolts need to be within 0.2 mm of 12 mm, that means that the length of the bolts are anywhere between 12 mm + 0.2 mm and 12 mm - 0.2 mm.

1. Since they are within 0.2 mm, and since it doesn't specify if they are plus or minus, the bolts can be at lengths anywhere from 12.2 mm to 11.8 mm.

a) Since the bolts are within 0.2 mm of 12 mm, that means that the longest would be 12 mm + 0.2 mm which is equal to 12.2 mm.

b) Since the bolts are within 0.2 mm of 12 mm, the shortest bolt possible would be 0.2 mm smaller than 12 mm, which is equal to 12 mm - 0.2 mm which is 11.8 mm.

You might be interested in

Use the drawing tool(s) to form the correct answer on the provided graph.

NikAS [45]

Answer:

Here's one way to do it

Step-by-step explanation:

1. Solve the inequality for y

5x - y > -3

-y > -5x - 3

y < 5x + 3

2. Plot a few points for the "y =" line

I chose

\begin{gathered}\begin{array}{rr}\mathbf{x} & \mathbf{y} \\-2 & -7 \\-1 & -2 \\0 & 3 \\1 & 8 \\2 & 13 \\\end{array}\end{gathered}

−2

−1

−7

−2

You should get a graph like Fig 1.

3. Draw a straight line through the points

Make it a dashed line because the inequality is "<", to show that points on the line do not satisfy the inequality.

See Fig. 2.

4. Test a point to see if it satisfies the inequality

I like to use the origin,(0,0), for easy calculating.

y < 5x + 3

0 < 0 + 3

0 < 3. TRUE.

The condition is TRUE.

Shade the side of the line that contains the point (the bottom side).

And you're done (See Fig. 3).

6 0

3 years ago

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

Sarah ran 26 km in 3 hours. How far could Sarah run in 5 hours.

Digiron [165]

Answer:

43.33 km

Step-by-step explanation:

Step 1: Find the amount of km Sarah can run in 1 hour

26/3

Step 2: Find the amount of km Sarah ran in 5 hours

26/3 * 5

130/3

43.33

Answer: 43.33 km

8 0

3 years ago

250% as a fraction in its simplest form

Anvisha [2.4K]

Answer:

250/100 simplest form 25/10

4 0

3 years ago

Last question! Find the equation of the line Y=__x +__

krek1111 [17]

The answer is y=-2/6x + 5

7 0

3 years ago