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dusya [7]
3 years ago
9

2. Find the slope of the line.

Mathematics
1 answer:
Airida [17]3 years ago
6 0

Answer:

-1/2

Step-by-step explanation:

Rise(-1) / Run(2)

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The diameter of a bacteria colony that doubles every hour is represented by the graph below. What is the diameter of the bacteri
Nady [450]

Do you notice anything strange about those points ?

(0, 1), 
(1, 2), 
(2, 4),
(3, 8).

The y-coordinate of each point is (2) raised to the  power of the x-coordinate.

First point:       x=0,  y=2⁰ = 1
Second point: x=1,  y=2¹ = 2
Third point:      x=2,  y=2² = 4
Fourth point:    x=3,  y=2³ = 8


The equation of the curve appears to be

                               y = 2 ^ x .

So, after 10 hours,  x=10, and  y = 2¹⁰ = 1,024 .

3 0
3 years ago
Read 2 more answers
A ball of radius 15 has a round hole of radius 5 drilled through its center. Find the volume of the resulting solid. Hint: The u
OverLord2011 [107]

Answer:

The volume of the ball with the drilled hole is:

\displaystyle\frac{8000\pi\sqrt{2}}{3}

Step-by-step explanation:

See attached a sketch of the region that is revolved about the y-axis to produce the upper half of the ball. Notice the function y is the equation of a circle centered at the origin with radius 15:

x^2+y^2=15^2\to y=\sqrt{225-x^2}

Then we set the integral for the volume by using shell method:

\displaystyle\int_5^{15}2\pi x\sqrt{225-x^2}dx

That can be solved by substitution:

u=225-x^2\to du=-2xdx

The limits of integration also change:

For x=5: u=225-5^2=200

For x=15: u=225-15^2=0

So the integral becomes:

\displaystyle -\int_{200}^{0}\pi \sqrt{u}du

If we flip the limits we also get rid of the minus in front, and writing the root as an exponent we get:

\displaystyle \int_{0}^{200}\pi u^{1/2}du

Then applying the basic rule we get:

\displaystyle\frac{2\pi}{3}u^{3/2}\Bigg|_0^{200}=\frac{2\pi(200\sqrt{200})}{3}=\frac{400\pi(10)\sqrt{2}}{3}=\frac{4000\pi\sqrt{2}}{3}

Since that is just half of the solid, we multiply by 2 to get the complete volume:

\displaystyle\frac{2\cdot4000\pi\sqrt{2}}{3}

=\displaystyle\frac{8000\pi\sqrt{2}}{3}

5 0
3 years ago
16(4 1/4) distrubuted
ss7ja [257]

Answer:

68

Step-by-step explanation:

Step 1: Convert fraction to improper

4 1/4 = 16/4 + 1/4 = 17/4

Step 2: Multiply 16 and 17/4

16(17/4) = 272/4 = 68

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3 years ago
Emily spent half of her weekly allowance playing mini-golf. To earn
myrzilka [38]
Emily’s weekly allowance would be $7.
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3 years ago
A = 16, b = 20, mZ B = 40<br> Law of cosines
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What is this ?chfufuykygiufffjfufuf
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