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3 years ago

A pendulum is constructed by attaching a 4m rope to a bowling ball. It is then displaced 2m to one side and released.

Mathematics

1 answer:

Arada [10]3 years ago

8 0

Answer:

T = 4.0 s

Step-by-step explanation:

The period of a simple pendulum is given by

$period = 2\pi \sqrt{ \frac{l}{g} }$

where l = length of the pendulum

= 4 m

g = acceleration due to gravity

= 9.8 m/s^2

$period = 2\pi \sqrt{ \frac{(4 \: m)}{(9.8 \: \frac{m}{ {s}^{2} } )} } = 4.0 \: s$

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What are the vertical asymptotes of the function f(x) = the quantity of 2 x plus 8, all over x squared plus 5 x plus 6? x = −3 a

lbvjy [14]

For this question the answer would be x=-3 and x=-2

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3 years ago

When josh planted his bean plant, it stood only 2 inches tall. Since then it has grown 3.25 inches every two weeks. Write the eq

inessss [21]

Answer:

y=3.25x+2

Step-by-step explanation:

Y is the total height after x weeks and since it has grown 3.25 inches per 2 weeks it would be 3.25x and add 2 because the initial height is 2 inches

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3 years ago

Find 10 partial sums of the series. (round your answers to five decimal places.) ∞ 15 (−4)n n = 1

nikklg [1K]

Given

$\Sigma_{n=1}^\infty15(-4)^n$

The first 10 partial sums are as follows:

$S_1=\Sigma_{n=1}^{1}15(-4)^n=15(-4)=\bold{-60} \\ \\ S_2=\Sigma_{n=1}^{2}15(-4)^n=\Sigma_{n=1}^{1}15(-4)^n+15(-4)^2 \\ =-60+15(16)=-60+240=\bold{180} \\ \\ S_3=\Sigma_{n=1}^{3}15(-4)^n=\Sigma_{n=1}^{2}15(-4)^n+15(-4)^3 \\ =180+15(-64)=180-960=\bold{-780} \\ \\ S_4=\Sigma_{n=1}^{4}15(-4)^n=\Sigma_{n=1}^{3}15(-4)^n+15(-4)^4 \\ =-780+15(256)=-780+3,840=\bold{3,060} \\ \\ S_5=\Sigma_{n=1}^{5}15(-4)^n=\Sigma_{n=1}^{4}15(-4)^n+15(-4)^5 \\ =3,060+15(-1,024)=3,060-15,360=\bold{-12,300}$

$S_6=\Sigma_{n=1}^{6}15(-4)^n=\Sigma_{n=1}^{5}15(-4)^n+15(-4)^6 \\ =-12,300+15(4,096)=-12,300+61,440=\bold{49,140}$

The rest of the partial sums can be obtained in similar way.

7 0

3 years ago

Of all sixth graders, 70% sent a text message yesterday. Ten trials of a simulation are conducted and the data are recorded belo

Effectus [21]

Answer:

80%

Step-by-step explanation:

According to the given data, the numbers 0 through 6 represent students who sent a text yesterday while the numbers 7 through 9 represent students who did not send a text yesterday.

Based on this key, we will calculate the number of students who sent the text yesterday and the number of students who did not sent the text yesterday.

The given data is: 62072, 34570, 80983, 04292, 83150, 36330, 96268, 14077, 77985, 13511

For each group we will identify how many students sent the text and how many students did not. According to the key, a number from 0 to 6 will be counted as a student who sent the text and a number from 7 to 9 will be counted as a student who did not send the text. Students who did not sent the text are made bold in the groups below.

62072: 4 students sent the text, 1 did not

34570: 4 students sent the text, 1 did not

80983: 2 students sent the text, 3 did not

04292: 4 students sent the text, 1 did not

83150: 4 students sent the text, 1 did not

36330: All 5 students sent the text

96268: 3 students sent the text, 2 did not

14077: 3 students sent the text, 2 did not

77985: 1 student sent the text, 4 did not

13511: All 5 students sent the text

We need to find the probability that 3 or more of a group of 5 students randomly selected will send a text today.

From the given groups, the number of groups where 3 or more students sent a text = 8

This represents our number of favorable or desired outcomes.

Total number of possible outcomes is the total number of groups = 10

Since, probability is defined as the ratio of number of favorable outcomes to total number of outcomes, based on the simulated data the probability that 3 or more of a group of 5 students randomly selected will send a text today will be = $\frac{8}{10}=0.80=80\%$

Thus, based on the simulated data there is 80% probability that 3 or more of a group of 5 students randomly selected will send a text today

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3 years ago

Read 2 more answers

Asia is buying some CDs. The equation below shows the relationship between x, the number of CDs she buys, and y, the cost. 3. Ho

Svetradugi [14.3K]

She can buy ten CDs.

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3 years ago