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2 years ago

The sides of ∠A are tangent to circle k(O) with radius r. Find: r, if OA=14 dm, m∠A=90°.

Mathematics

2 answers:

Alex_Xolod [135]2 years ago

6 0

Answer:

r = √98

Step-by-step explanation:

angle A and the diameter form an isosceles right triangle, with OA as the hypotenuse and r as the other sides. You can then make and solve an equation from the Pythagorean Theorem:

r^2 + r^2 = 14^2

2r^2 = 14^2

2r^2 = 196

r^2 = 98

r = √98

Anvisha [2.4K]2 years ago

4 0

Answer:

Step-by-step explanation:

Alright, lets get started.

Please refer the diagram I have attached.

The angle A is 90 degree.

The side OA is 14.

There will be a right triangle formed.

So, Using Pythagorean theorem,

$r^2+r^2=14^2$

$2r^2=196$

Dividing 2 in both sides

$r^2=\frac{196}{2}=98$

$r=\sqrt{98}$

$r=7\sqrt{2}$

So,the answer is $7\sqrt{2}$ : Answer

Hope it will help :)

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Can someone please help with #16

ollegr [7]

Answer:

∠ WZX = 50°

XW is not an altitude.

Step-by-step explanation:

16. See the attached figure.

XW is the angle bisector of ∠ YXZ, hence, ∠ WXY = ∠ WXZ

Now, given that ∠ YXZ = 8x + 34 and ∠ WXY = 10x - 13

Hence, ∠ YXZ = 2 ∠ WXY

⇒ 8x + 34 = 2(10x - 13)

⇒ 8x + 34 = 20x - 26

⇒ 12x = 60

⇒ x = 5.

Hence, ∠ XZY = ∠ WZX = 10x = 50° (Answer)

Now, ∠ WXZ = ∠ WXY = 10x - 13 = 37°

Hence, from Δ WXZ,

∠ WZX + ∠ WXZ + ∠ XWZ = 180°

⇒ 50° + 37° + ∠ XWZ = 180°

⇒ ∠ XWZ = 93° ≠ 90°

Hence, XW is not an altitude. (Answer)

6 0

2 years ago

A pecan pie is being served for dessert. One piece of pie has an arc length of 7.85 in. It has been cut into 8 equal pieces. Wha

pishuonlain [190]

Answer: 10 inches.

Step-by-step explanation:

Since the pecan pie is a circle, you can use this formula:

$arc\ length=r\theta$

Where "r" is the radius and $\theta$ is the central angle of the arc in radians.

If the pecan pie has been cut into 8 equal pieces then the central angle is:

$\theta=\frac{2\pi}{8}\\\\\theta={\frac{\pi}{4}$

Now you know the arc length and the central angle, then, you can solve for "r" from $arc\ length=r\theta$ :

$\frac{arc\ length}{\theta} =r$

Substituting values, you get that the radius of the pecan pie rounded to the nearest whole number is:

$r=\frac{7.85in}{\frac{\pi}{4}}\\\\r=10in$

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2 years ago

Name the place value each number was round 1.974to2.0

Alex

The answer is "tenths"

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2 years ago

] It is claimed that 42% of US college graduates had a mentor in college. For a sample of college graduates in Colorado, it was

Bad White [126]

Answer:

$z=\frac{0.480 -0.42}{\sqrt{\frac{0.42(1-0.42)}{1045}}}=3.930$

The p value for this case would be given by:

$p_v =P(z>3.930)=0.0000443$

For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis so then we can conclude that the true proportion is significantly higher than 0.42

Step-by-step explanation:

Information given

n=1045 represent the random sample selected

X=502 represent the college graduates with a mentor

$\hat p=\frac{502}{1045}=0.480$ estimated proportion of college graduates with a mentor

$p_o=0.42$ is the value that we want to test

z would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to test if the true proportion is higher than 0.42, the system of hypothesis are.:

Null hypothesis: $p \leq 0.42$

Alternative hypothesis: $p > 0.42$

The statistic is given by:

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

Replacing the info we got:

$z=\frac{0.480 -0.42}{\sqrt{\frac{0.42(1-0.42)}{1045}}}=3.930$

The p value for this case would be given by:

$p_v =P(z>3.930)=0.0000443$

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2 years ago

A drug is eliminated from the body through urine. Suppose that for a dose of 10 milligrams, the amount A(t) remaining in the bod

adell [148]

Answer: a - 4.512 hours

b - 1.94 hours

Step-by-step explanation:

Given,

a) A(t) = 10 (0.7)^t

To determine when 2mg is left in the body

We would have,

A(t) = 2, therefore

2 = 10(0.7)^t

0.7^t =2÷10

0.7^t = 0.2

Take the log of both sides,

Log (0.7)^t = log 0.2

t log 0.7 = log 0.2

t = log 0.2/ 0.7

t = 4.512 hours

Thus it will take 4.512 hours for 2mg to be left in the body.

b) Half life

Let A(t) = 1/2 A(0)

Thus,

1/2 A(0) = A(0)0.7^t

Divide both sides by A(0)

1/2 = 0.7^t

0.7^t = 0.5

Take log of both sides

Log 0.7^t = log 0.5

t log 0.7 = log 0.5

t = log 0.5/log 0.7

t = 1.94 hours

Therefore, the half life of the drug is 1.94 hours

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3 years ago