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Alina [70]
3 years ago
10

Chan is throwing a ball from the ground at an initial velocity of 22.1 meters per seconds. He threw the ball so high that on it'

s way down it got stuck in a tree 10 meters high. How long was the ball in the air before it got stuck in the tree?
a.4 sec
b.4.51 sec
c.24.9 meters
d.2.25 sec
Mathematics
1 answer:
Nookie1986 [14]3 years ago
7 0

The ball's height <em>y</em> at time <em>t</em> is

<em>y</em> = (22.1 m/s) <em>t</em> - 1/2 <em>gt</em> ²

where <em>g</em> = 9.80 m/s² is the magnitude of the acceleration due to gravity.

Solve for <em>t</em> when <em>y</em> = 10 m:

10 m = (22.1 m/s) <em>t</em> - 1/2 <em>gt</em> ²

→   <em>t</em> = 0.510 s or <em>t</em> = 4.00 s

The first time refers to when the ball first reaches 10 m on its way up, so <em>t</em> = 4.00 s and the answer is A.

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An egg of a certain kind of insect called a Tachinidae is 0.00002 meters
postnew [5]

The length in scientific notation is 2 \times 10^{-5} meters

<em><u>Solution:</u></em>

Given that egg of a certain kind of insect called a Tachinidae is 0.00002 meters long

<em><u>To find: length in scientific notation</u></em>

Given length in meters = 0.00002 meters

<em><u>Let us understand about scientific notation</u></em>

Scientific notation is a mathematical expression used to represent a decimal number between 1 and 10 multiplied by ten, so you can write large numbers using less digits

<em><u>Rules for scientific notation:</u></em>

Move the decimal point in your number until there is only one non-zero digit to the left of the decimal point. The resulting decimal number is a.

Count how many places you moved the decimal point. This number is b.

If you moved the decimal to the left b is positive.

If you moved the decimal to the right b is negative.

If you did not need to move the decimal b = 0.

Write your scientific notation number as a x 10^b and read it as "a times 10 to the power of b."

Remove trailing 0's only if they were originally to the left of the decimal point.

<em><u>Converting 0.00002 meters to scientific notation:</u></em>

Here we move the decimal point to right side. Move the decimal point 5 times so that only "2" is present to left of decimal point

Since decimal point is moved to right, the exponent 5 is negative(-5)

\rightarrow 2 \times 10^{-5}

Thus the length in scientific notation is 2 \times 10^{-5} meters

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3 years ago
A checking account earns 2.5% simple interest. How much would be earned by an account with $3,400 in after 3 years? *
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an environmental agency is analyzing soil samples from 50 farms for lead contamination. eight of the farms have dangerously high
shutvik [7]

Number of ways , two contaminated and 8 non- contaminated farms be choosen is 3,304,845,180.

Permutation and Combination

Combination is a mathematical way to arranging the set of values randomly.

ⁿCᵣ = n! / r! (n-r)!

we have given that ,

total number of farms for lead contamination = 50

Number of farms have dangerously high level of lead = 8

so, number of non- containmated farms ( no high level of lead ) = 50-8 = 42

We have to find the number of ways to choose two contaminated farms and eight non- contaminated farms. Two containmated farms are selected from 8 containated farms and 8 non- contaminated farms are selected from 42 farms .

Number of ways for selecting two containmated farms = ⁸C₂ = 8!/2!×6! = 8×7/2 = 28

Number of ways for selecting eight non-containmated farms from 42 farms = ⁴²C₈

= 42! / 8! 34! = 42×41×---×35/8×7×----×1

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The total number of ways to obtain 2 containmated farms and 8 non- contaminated farms in 10 farms selected is then product of number of ways to select the 2 containmated farms and number of ways to select 8 non-containmated farms .

= 118030185× 28 = 3,304,845,180

To learn more about Combination and Permutation, refer:

brainly.com/question/28065038

#SPJ4

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