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Alja [10]
2 years ago
12

What is the slope of the line passing through the points (2,5) and (0,-4)?

Mathematics
1 answer:
Lemur [1.5K]2 years ago
8 0

Answer:

9/2

Step-by-step explanation:

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Pls help being timed
Sloan [31]

He needs 9 hours

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3 0
3 years ago
6k &lt; 100<br> Check all that are true.<br><br> k = 5<br><br> k = 15<br><br> k = 10<br><br> k = 20
Elden [556K]

Answer:

True: 5, 15,  and 10

Step-by-step explanation:

6*5=30 Correct, 30 is less than 100

6*15=90 Correct, 90 is less than 100

6*10=60 Correct, 60 is less than 100

6*20=120 Wrong, 120 is greater than 100

7 0
2 years ago
Read 2 more answers
The hemisphere of radius r is made from a stack of very thin plates such that the density varies with height, r = kz, where k is
Papessa [141]

Answer:

M = ¼ k π R⁴

zG = 8/15 R

Step-by-step explanation:

Note: I'm using lower case r as the radius of each plate and upper case R as the radius of the hemisphere.

The mass of each plate is density times volume:

dm = ρ dV

Each plate has a radius r and a thickness dz.  So the volume of each plate is:

dV = π r² dz

Substituting:

dm = ρ π r² dz

We're told that ρ = kz.  Substituting:

dm = kz π r² dz

Next, we need to write the radius r in terms of the height z.  To do that, we need to look at the cross section (see image below).

The height z and the radius r form a right triangle, where the hypotenuse is the radius of the hemisphere R.

Using Pythagorean theorem:

z² + r² = R²

r² = R² − z²

Substituting:

dm = kπ z (R² − z²) dz

We now have the mass of each plate as a function of its height.  To find the total mass, we integrate between z=0 and z=R.

M = ∫ dm

M = ∫₀ᴿ  kπ z (R² − z²) dz

M = kπ ∫₀ᴿ (R² z − z³) dz

M = kπ (½ R² z² − ¼ z⁴) |₀ᴿ

M = kπ (½ R⁴ − ¼ R⁴)

M = ¼ k π R⁴

Next, to find the center of gravity, we use the weighted average:

zG = (∫ z dm) / (∫ dm)

zG = (∫ z dm) / M

We already found M, we just have to evaluate the other integral:

∫ z dm

∫₀ᴿ kπ z² (R² − z²) dz

kπ ∫₀ᴿ (R² z² − z⁴) dz

kπ (⅓ R² z³ − ⅕ z⁵) |₀ᴿ

kπ (⅓ R⁵ − ⅕ R⁵)

²/₁₅ k π R⁵

Plugging in:

zG = (²/₁₅ k π R⁵) / (¼ k π R⁴)

zG = ⁸/₁₅ R

5 0
3 years ago
Help me solve the Inequality Word Problem and solve ?
viktelen [127]
Let x represent the number
.. 1 +3x . . . . . . one more than three times a number
.. x -5 . . . . . . . the number decreased by 5

.. 1 +3x < x -5 . . . . the relation specified by the problem statement
.. 2x < -6 . . . . . . . subtract x+1
.. x < -3 . . . . . . . . . divide by the coefficient of x. (Positive, so < stays the same.)

5 0
3 years ago
What is the chance that heads will come up more than 55 times in 100 flips of a fair coin?
tankabanditka [31]

Answer:

Step-by-step explanation:

50

4 0
3 years ago
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