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netineya [11]
3 years ago
5

Sara goes on a slingshot ride in an amusement park. She is trapped into a spherical ball that has a radius of 3•100 centimeters.

What is the volume of air in the spherical ball.
Mathematics
1 answer:
tankabanditka [31]3 years ago
4 0

Answer: <em>1.1 × 10⁸ cm³</em>


Explanation:


1) Since the ball is spherical, you use the volume formula for a sphere, which is:


Volume = [4/3] π r³


2) r is the radius, which is given and is equal to 3×100cm = 300cm


3) Pluging in the value of r, you get:


Volume = [4/3] π (300 cm)³ = 113,097,335.53 cm³


4) Since, r = 3×100 cm has two significant figures, the result must show only two significant figures.


So, using scientific notation, the right answer must be reported as:<em> 1.1 × 10⁸ cm³</em>

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The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC?(A)
ZanzabumX [31]

Answer:

A:102

Step-by-step explanation:

We are given that the points A(0,0),B(0,4a-5) and C(2a-+1,2a+6) form a triangle.

If angle ABC=90^{\circ}

We have to find the area of triangle ABC

If angle ABC= 90 degree

From given below figure

4a-5=2a+6

4a-2a=6+5

2a=11

a=\frac{11}{2}=5.5

Substitute the values then we get

B(0,17) and C (12,17)

Distance formula

\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

AB=\sqrt{(0-0)^2+(17-0)^2}=17 units

BC=\sqrt{(12-0)^2+(17-17)^2}

BC=\sqrt{144+0}=\sqrt{144}=12 units

Area of triangle =\frac{1}{2}\times b\times h

Substitute the values

Then we get

Area of triangle ABC=\frac{1}{2}\times 17\times 12

Area of triangle ABC=102 square units

Answer: A: 102

8 0
3 years ago
An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The
Dmitry_Shevchenko [17]

Answer:

7 years

Step-by-step explanation:

An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The equation represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use a calculator and round your answer to the nearest whole number.

6 0
3 years ago
What is the difference between divergence and convergence testing outliers?
LuckyWell [14K]
A divergence testing just diverts your mind and imagination into several possibilities and scenarios regarding the same issue.
A divergence test will simply test your imagination and forces your mind  to go into as many directions as possible.

On the other hand, a converge test will sort of converge your imagination and your mind into a set of possibilities or options.
A convergence test will let you sort between a set of possibilities and decide on the best one.
8 0
3 years ago
The roots of the equation 3x²-2x-4=0 are J and K. Evaluate J² + K².
melamori03 [73]

Answer:

28/9

Step-by-step explanation:

If the roots are J and K, then:

3 (x − J) (x − K) = 0

3 (x² − (J+K)x + JK) = 0

So if we factor out the leading coefficient:

3x² − 2x − 4 = 0

3(x² − 2/3x − 4/3) = 0

The coefficient of the second term is the sum of the roots:

J + K = 2/3

And the constant is the product of the roots:

JK = -4/3

If we take the sum of the roots and square it:

(J + K)² = (2/3)²

J² + 2JK + K² = 4/9

And subtract twice the product:

J² + K² = 4/9 − 2JK

J² + K² = 4/9 − 2(-4/3)

J² + K² = 4/9 + 8/3

J² + k² = 28/9

6 0
3 years ago
Use the distributive property to find the product mentally. Show the steps you used.
Licemer1 [7]
I believe this is what is wanted

6 0
3 years ago
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