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3 years ago

the form ula for the area of a circle can be found by using a parallelogram. explain the way to derive the formula

Mathematics

2 answers:

USPshnik [31]3 years ago

7 0

Answer:

Sample response: The circle can be cut into slices, separated, and fit together to form a parallelogram that has the same area. The height of the parallelogram is the radius and the base is half the circumference, which is

vladimir2022 [97]3 years ago

4 0

Answer:

Explanation: As you make the segments smaller and smaller, the parallelogram becomes more of a rectangle with shorter side equal to the radius of the circle r and longer side πr - half of the circumference of the circle. Hence we get the formula πr2 for the area of a circle of radius r .

Step-by-step explanation:

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If x 60 and 30 find the unknown sizes of angle

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3 years ago

The operations manager of a manufacturer of television remote controls wants to determine which batteries last the longest in hi

Margarita [4]

Answer:

$t=\frac{107.75-116.75}{\sqrt{\frac{2.75^2}{4}+\frac{9.604^2}{4}}}}=-1.802$

The degrees of freedom are given by:

$df=n_{1}+n_{2}-2=4+4-2=6$

The p value for this case would be given by:

$p_v =2*P(t_{(6)}$

Since the p value is higher than the significance level we have enough evidence to FAIl to reject the null hypothesis and we can conclude that the true mean is not significantly different between the two types of battery

Step-by-step explanation:

Information given

Battery 1 106 111 109 105

Battery 2 125 103 121 118

We can calculate the mean and the deviation with the following formulas"

$\bar X =\frac{\sum_{i=1}^n X_i}{n}$

$s =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X_{1}=107.75$ represent the mean for the Battery 1

$\bar X_{2}=116.75$ represent the mean for the Bettery 2

$s_{1}=2.75$ represent the sample standard deviation for the Battery 1

$s_{2}=9.604$ represent the sample standard deviation for the battery 2

$n_{1}=4$ sample size selected for the Battery 1

$n_{2}=4$ sample size selected for the Battery 2

$\alpha=0.1$ represent the significance level

t would represent the statistic

$p_v$ represent the p value

System of hypothesis

We want to check if the difference in longevity between the two batteries, the system of hypothesis would be:

Null hypothesis: $\mu_{1} = \mu_{2}$

Alternative hypothesis: $\mu_{1} \neq \mu_{2}$

The statistic is given by:

$t=\frac{\bar X_{s1}-\bar X_{2}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}$ (1)

The statistic is given by:

$t=\frac{107.75-116.75}{\sqrt{\frac{2.75^2}{4}+\frac{9.604^2}{4}}}}=-1.802$

The degrees of freedom are given by:

$df=n_{1}+n_{2}-2=4+4-2=6$

The p value for this case would be given by:

$p_v =2*P(t_{(6)}$

8 0

3 years ago

A rectangular gift box is 10 inches long, 7 inches wide, 1.25 inches high, and had a surface area of 182.5 square inches. gift w

valkas [14]

The measurements of the box actually aren't needed since they already gave you the surface area. Just multiply the given surface area by the price of wrapping paper per square inch: 182.5 x $0.012 = $2.2224. If you round that answer, you'll know that it costs $2.22 to wrap the gift.

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3 years ago

Read 2 more answers

the form ula for the area of a circle can be found by using a parallelogram. explain the way to derive the formula​

the form ula for the area of a circle can be found by using a parallelogram. explain the way to derive the formula