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MrRa [10]
2 years ago
9

A baseball diamond is a square with side 90 feet. A batter hits the ball and runs toward first base with a speed of 24 ft/sec. A

t what rate is his distance from second base decreasing when he is halfway to first base?
Mathematics
1 answer:
sweet [91]2 years ago
6 0

9514 1404 393

Answer:

  10.73 ft/s

Step-by-step explanation:

When the runner is halfway to first base, the triangle formed by his position and the first and second bases is a right triangle with legs of 45 ft and 90 ft. The angle between the runner's direction and the line from his position to 2nd base is ...

  angle = arctan(90/45) ≈ 63.43°

The "speed made good" in the direction of 2nd base is the product of the cosine of this angle and the runner's speed toward first.

  speed toward 2nd = cos(63.43°)×(24 ft/s) ≈ 10.73 ft/s

The rate the runner's distance to 2nd base is decreasing is 10.73 ft/sec.

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How much more area does a large pizza with a 12 in. diameter have than a small pizza with an 8 in. diameter? Round your answer t
ivolga24 [154]

Answer: About 63 in²

Step-by-step explanation:

<u>Area of circle = π · r²</u>

  • r = radius length
  • π ≈ 3.14

<u>Area of large pizza:</u>

\pi *r^{2} =3.14*6^{2} =3.14*36=113.04

<u>Area of small pizza:</u>

\pi *r^{2} =3.14*4^{2} =3.14*16=50.24

<u>Difference in area:</u>

113.04-50.24=62.8

4 0
2 years ago
I need help please <br>I need this for homework and I need help please <br>​
Natali [406]

Answer:

I think it A I know it try a

6 0
3 years ago
Read 2 more answers
Write 4.5 as a mixed number.
Zolol [24]

Answer:

9/2

Step-by-step explanation:

4.5 = 4 1/2 = 9/2

7 0
2 years ago
Read 2 more answers
There are bytes in a gigabyte. There are bytes in a megabyte. How many times greater is the storage capacity of a 1-gigabyte fla
anzhelika [568]

Answer: third option.

Step-by-step explanation:

You know that:

- There are 10⁹ bytes in a gigabyte.

- There are 10⁶  bytes in a megabyte.

Then, to know how many times greater  the storage capacity of a 1-gigabyte flash drive is than a 1-megabyte flash drive, you must divide 10⁹ bytes by 10⁶ bytes.

Remember the quotient of powers property:

\frac{a^m}{a^n}=a^{(m-n)}

Then:

=\frac{10^9}{10^6}=10^3=1,000 times greater

 

7 0
3 years ago
The number of books sold over the course of the four-day book fair were 190, 100, 272, and 74. Assume that samples of size 2 are
g100num [7]

Answer:

the answer is below

Step-by-step explanation:

We have the total number of possible samples = 4 * 4 = 16 (As 4 choices for each value)

in addition we have to as all sample occur with equal probability, probability of each sample = 1/16, below is samling distribution of mean

x1 x2 probabilityP(x1,x2) sample mean

190 190    1/16                 190

190 100    1/16                 145

190 272    1/16                 231

190 74    1/16                 132

100 190    1/16                 145

100 100    1/16                 100

100 272    1/16                 186

100 74    1/16                        87

272 190    1/16                 231

272 100    1/16                 186

272 272    1/16                 272

272 74    1/16                 173

74 190    1/16                 132

74 100    1/16                 87

74 272    1/16                 173

74 74    1/16                 74

Summarizing above with adding duplicate values

sample mean   probability

       74              1/16

      87               1/8

    100                1/16

    132                1/8

    145                1/8

    173                1/8

   186                1/8

   190               1/16

    231               1/8

   272               1/16

5 0
3 years ago
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