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3 years ago

show that the lines x2-4xy+y2=0 and x+y=3 form an equilateral triangle also find area of the triangle

Mathematics

1 answer:

arlik [135]3 years ago

4 0

Given pair of lines are x² + 4xy + y² = 0

⇒ (y/x) ² + 4 y/x + 1 = 0

⇒ y/x = -4±2√3/2 = -2±√3,

∴ The lines y = (-2 + √3) x and y = (-2 - √3) x and x - y = 4 forms an equilateral triangle

Clearly the pair of lines x² + 4xy +y² = 0 intersect at origin,

The perpendicular distance form origin to x - y = 4 is the height of the

h = 2 √ 2

∵ Area of triangle = h²/√3 = 8/√3

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3 years ago

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In a study of the accuracy of fast food drive-through orders, McDonald’s had 33 orders that were not accurate among 362 orders o

melomori [17]

Answer:

A. We need to conduct a hypothesis in order to test the claim that the true proportion of inaccurate orders p is 0.1.

B. Null hypothesis: $p=0.1$

Alternative hypothesis: $p \neq 0.1$

C. $z=\frac{0.0912 -0.1}{\sqrt{\frac{0.1(1-0.1)}{362}}}=-0.558$

D. $z_{\alpha/2}=-1.96$ $z_{1-\alpha/2}=1.96$

E. Fail to the reject the null hypothesis

F. So the p value obtained was a very high value and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the true proportion of inaccurate orders is not significantly different from 0.1.

Step-by-step explanation:

Data given and notation

n=362 represent the random sample taken

X=33 represent the number of orders not accurate

$\hat p=\frac{33}{363}=0.0912$ estimated proportion of orders not accurate

$p_o=0.10$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

A: Write the claim as a mathematical statement involving the population proportion p

We need to conduct a hypothesis in order to test the claim that the true proportion of inaccurate orders p is 0.1.

B: State the null (H0) and alternative (H1) hypotheses

Null hypothesis: $p=0.1$

Alternative hypothesis: $p \neq 0.1$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

C: Find the test statistic

Since we have all the info required we can replace in formula (1) like this:

$z=\frac{0.0912 -0.1}{\sqrt{\frac{0.1(1-0.1)}{362}}}=-0.558$

D: Find the critical value(s)

Since is a bilateral test we have two critical values. We need to look on the normal standard distribution a quantile that accumulates 0.025 of the area on each tail. And for this case we have:

$z_{\alpha/2}=-1.96$ $z_{1-\alpha/2}=1.96$

P value

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(z$

E: Would you Reject or Fail to Reject the null (H0) hypothesis.

Fail to the reject the null hypothesis

F: Write the conclusion of the test.

So the p value obtained was a very high value and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the true proportion of inaccurate orders is not significantly different from 0.1.

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3 years ago

Please help find the value of x<br> find value angle of WAY <br> find value angle of XAY

stealth61 [152]

Answer:

(x-10)° + (x + 14)° = 180°

=> x° - 10° + x° + 14 ° = 180°

=> 2x° + 4° = 180°

=> 2x° = 176°

=> x° = 176°/ 2

=> x° = 88°

Therefore the magnitude of x° = 88° (ans)

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Input/output machine

Andreas93 [3]

An input is were you put a number to get the answer. a output is were you take away the answer to get the correct

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The distance from around the Earth along a given latitude can be found using the formula C=2∏r cos L , where r is the radius of

guajiro [1.7K]

Answer:

The distance reduces to 0 as you go from 0° to 90°

Step-by-step explanation:

The question requires you to find the distance using different values of L and check the trend of the values.

Given C=2×pi×r×cos L where L is the latitude in ° and r is the radius in miles then;

Taking r=3960 and L=0° ,

C=2× $\pi$ ×3960×cos 0°

C=2× $\pi$ ×3960×1

C=7380 $\pi$

Taking L=45° and r=3960 then;

C= 2× $\pi$ ×3960×cos 45°

C=5600.28 $\pi$

Taking L=60° and r=3960 then;

C=2× $\pi$ ×3960×cos 60°

C=3960 $\pi$

Taking L=90° and r=3960 then;

C=2× $\pi$ ×3960×cos 90°

C=2× $\pi$ ×3960×0

C=0

Conclusion

The values of the distance from around the Earth along a given latitude decreases with increase in the value of L when r is constant

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4 years ago

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