Complete the derivation of the formula for a cylinder

The vertices of a parallelogram are A(x1,y1), B(x2,y2), C(x3,y3), D(x4,y4)

Tju [1.3M]

<span>For a parallelogram to be proven to be a rectange, the opposide sides must be parallel and the two adjacent sides must be perpendicular. For two parallel sides, the slope of the two sides is equal. Thus, for the parallelogram to be a rectangle, AB is parallel to CD. The slope of AB = (y2 - y1)/(x2 - x1) while the slope of CD = (y4 - y3)/(x4 - x3) Also, BC is perpedicular to CD. For two perpendicular sides, the product of the slopes is -1. The slope of BC is given by (y3 - y2)/(x3 - x2). Therefore, for the parallelogram to be a rectangle. (y2 - y1)/(x2 - x1) = (y4 - y3)/(x4 - x3) and (y4 - y3)/(x4 - x3) x (y3 - y2)/(x3 - x2) = -1. The third option is the correct answer.</span>

3 0

3 years ago

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Can some help me with this question

Luden [163]

To find the equation of this line in slope-intercept form (y = mx + b, where m is its slope and b is its y-intercept), we naturally need the slope and the y-intercept. We can see that the line intersects the y-axis at the point (0, 4) so our y-intercept is 4, and the line rises 4 along the y-axis for every 2 it runs along the x-axis, so its slope is 4/2 = 2. With this in mind, we can write the line's equation as

y = 2x + 4

7 0

3 years ago

A manufacturer of running shoes knows that the average lifetime for a particular model of shoes is 15 months. Someone in the res

AveGali [126]

Answer:

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is no sufficient evidence to show that the designer's claim of a better shoe is supported by the trial results.

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 15 \ months$

The sample size is n = 25

The sample mean is $\= x = 17 \ months$

The standard deviation is $s = 5.5 \ months$

Let assume the level of significance of this test is $\alpha = 0.05$

The null hypothesis is $H_o : \mu = 15$

The alternative hypothesis is $H_a : \mu > 17$

Generally the degree of freedom is mathematically represented as

$df = n -1$

=> $df = 25 -1$

=> $df = 24$

Generally the test statistics is mathematically represented as

$t = \frac{\= x- \mu }{\frac{s}{\sqrt{n} } }$

=> $t = \frac{ 17 - 15 }{\frac{5.5}{\sqrt{25} } }$

=> $t = 1.8182$

Generally from the student t distribution table the probability of obtaining $t = 1.8182$ to the right of the curve at a degree of freedom of $df = 24$ is

$p-value = P(t > 0.18182 ) = 0.4286$

From the value obtained we see that $p-value > \alpha$ hence

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is no sufficient evidence to show that the designer's claim of a better shoe is supported by the trial results.

7 0

2 years ago

What is 3 1/3 divided by 1/3

saveliy_v [14]

Convert 3 1/3 into a improper fraction:
= 10/3

Then flip the other fraction around and multiply them together:
1/3 -> 3/1
(10*3)/(3*1) = 30/3 = (30/3)/(3/3) = 10/1 = 10

The answer is 10

4 0

3 years ago

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Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 99 people

sertanlavr [38]

Answer:

The probability of getting someone in the 18-21 age bracket or someone who agreed to respond $= 0.365$