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2 years ago

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Draw the unit circle with center (0,0)and plot the point P=(6,2). Observe there are TWO lines tangent to the circle passing thro

ugh the point P.
1)the tangent line on top of the circle(L1) has coordinates?

a) what is the equation for L1?

2) the tangent line below the circle(L2) has coordinates?

b)what is the equation for L2?

1 answer:

scZoUnD [109]2 years ago

8 0

Answer:

Step-by-step explanation:

Given that a tangent is drawn from P (6,2) to unit circle with center at the origin.

The tangent passing through (6,2) would have equaiton of the form

$y-6 = m(x-2)\\y =mx-2m+6$ for suitable m.

Because this line is tangent, distance of centre of circle namely origin is the radius 1.

i.e. $|\frac{-2m+6}{\sqrt{1+m^2} } |=1\\(-2m+6 )^2 = 1+m^2\\3m^2-24m+35=0\\\\m=1.918, 6.082$

the coordinates are the intersection of the tangent with the circle

They are (-0.162, 0.987) and (0.462,-0.887)

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"Immediately after a ban on using hand-held cell phones while driving was implemented, compliance with the law was measured. A r

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Answer:

(a) Null Hypothesis, $H_0$ : $p_1-p_2=0$ or $p_1= p_2$

Alternate Hypothesis, $H_A$ : $p_1-p_2\neq 0$ or $p_1\neq p_2$

(b) We conclude that there is a statistical difference in these two proportions measured initially and then one year later.

Step-by-step explanation:

We are given that a random sample of 1,250 drivers found that 98.9% were in compliance. A year after the implementation, compliance was again measured to see if compliance was the same (or not) as previously measured.

A different random sample of 1,100 drivers found 96.9% compliance."

<em />

<em>Let </em> $p_1$ <em> = proportion of drivers that were in compliance initially</em>

$p_2$ <em> = proportion of drivers that were in compliance one year later</em>

(a) <u>Null Hypothesis</u>, $H_0$ : $p_1-p_2=0$ or $p_1= p_2$ {means that there is not any statistical difference in these two proportions measured initially and then one year later}

<u>Alternate Hypothesis</u>, $H_A$ : $p_1-p_2\neq 0$ or $p_1\neq p_2$ {means that there is a statistical difference in these two proportions measured initially and then one year later}

The test statistics that will be used here is <u>Two-sample z proportion statistics</u>;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{ \frac{\hat p_1(1-\hat p_1)}{n_1} + \frac{\hat p_2(1-\hat p_2)}{n_2}} }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of drivers in compliance initially = 98.9%

$\hat p_2$ = sample proportion of drivers in compliance one year later = 96.9%

$n_1$ = sample of drivers initially = 1,250

$n_2$ = sample of drivers one year later = 1,100

(b) So, <u><em>the test statistics</em></u> = $\frac{(0.989-0.969)-(0)}{\sqrt{ \frac{0.989(1-0.989)}{1,250} + \frac{0.969(1-0.969)}{1,100}} }$

= 3.33

<u>Now, P-value of the test statistics is given by;</u>

P-value = P(Z > 3.33) = 1 - P(Z $\leq$ 3.33)

= 1 - 0.99957 = <u>0.00043</u>

Since in the question we are not given with the level of significance so we assume it to be 5%. Now at 5% significance level, the z table gives critical values between -1.96 and 1.96 for two-tailed test.

<em>Since our test statistics does not lies within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which </em><u><em>we reject our null hypothesis.</em></u>

Therefore, we conclude that there is a statistical difference in these two proportions measured initially and then one year later.

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2 years ago

A right pyramid with a square base has a base edge length of 12 meters and slant height of 6StartRoot 2 EndRoot meters. The apot

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Answer:

Volume of the right pyramid = 288 m²

Step-by-step explanation:

Volume of the pyramid = $\frac{1}{3}\times {\text{Area of the rectangular base}\times height(h)$

From the ΔAOB,

By Pythagoras theorem,

AB² = AO² + OB²

(6√2)² = AO² + (6)²

72 = AO² + 36

AO = √(36) = 6 m

Since base of the pyramid is a square so area of the base = (Length × Width) = (side)²

Now volume of the pyramid = $\frac{1}{3}[(Length)(width)]\times height$

= $\frac{1}{3}(12\times 12)\times 6$

= 288 m²

Therefore, volume of the right pyramid is 288 m².

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2 years ago

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Craig has $1850 dollars in a bank account that he uses to make automatic payments of $400.73 on his car loan. If Craig stops mak

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Given:

Amount in the bank account = $1850

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To find:

When would automatic payments make the value of the account zero?

Solution:

Craig stops making deposits to that account. So, amount $1850 in the bank account is used to make monthly payment of can loan.

On dividing the amount by monthly payment, we get

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It means, the amount is sufficient for 4 payment but for the 5th payment the amount is not sufficient.

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2 years ago

Nadia is mountain climbing. She started at an altitude of 19.26 feet below sea level and then changed her altitude by climbing a

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Answer:

5,418.2 feet

Step-by-step explanation:

Nadia is carrying out mountain climbing.

She started climbing the mountain at an altitude of 19.26 feet below the sea level.

Nadia changed her altitude by climbing a total of 5,437.8 feet from her starting position.

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= 5,437.8-19.6

= 5,418.2

Hence Maria's altitude at the end of her climb is 5,418.2 feet

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2 years ago

The house Trevor's family lives in has 6 66 people (including Trevor) and 3 33 bathrooms. In the past month, each person showere

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Answer:

The amount Trevor's family pay per minute on shower water is $0.005.

Step-by-step explanation:

The cost of water is,

Cost = $0.20/liter

Amount of water used over the entire month:

Amount of water used = 72 liters

Compute the total water cost as follows:

Total water cost = Amount of water used × Cost

= 72 × 0.20

= $14.4/liter

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Compute the total amount of time the 6 person showered as follows:

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