If cosx=1/12 and sinx>0 find tan2x

Answers

Answer 1

Answer: $cosx=(1)/(12)\n\nsin^2x+cos^2x=1\n\nsin^2x+\left((1)/(12)\right)^2=1\n\nsin^2x+(1)/(144)=1\n\nsin^2x=1-(1)/(144)\n\nsin^2x=(144)/(144)-(1)/(144)\n\nsin^2x=(143)/(144)\n\nsinx=\sqrt(143)/(144)\n\nsinx=(√(143))/(12)$

$tan2x=(sin2x)/(cos2x)\n\nsin2x=2sinxcosx;\ cos2x=cos^2x-sin^2x\n\nsin2x=2\cdot(√(143))/(12)\cdot(1)/(12)=(2√(143))/(144)\n\ncos2x=\left((1)/(12)\right)^2-\left((√(143))/(12)\right)^2=(1)/(144)-(143)/(144)=-(142)/(144)\n\ntan2x=(2√(143))/(144):\left(-(142)/(144)\right)=-(2√(143))/(144)\cdot(144)/(142)=-(√(143))/(71)$

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How do I solve for x? I tried using law of sines and law of cosines but the angles and sides don't match up.

Answers

Law cosines: $y^(2) =$ 16 + 256 - 128 $√(3) ;$ => y ≈ 16.51;
Law sines: 16/sinx = 16.51/sin30 => sinx = 0.48 => x ≈ 29 degrees;

The registrar keeps an alphabetical list of all undergraduates, with their current addresses. Suppose there are 10,000 undergraduates in the current term. Someone proposes to choose a number at random from 1 to 100, count that far down the list, taking that name and every 100th name after it for the sample. a) Is this a probability method?
b) Is it the same as simple random sampling?
c) Is there selection bias in this method of drawing a sample?

Answers

Answer:

The answer to this question can be defined as follows:

Step-by-step explanation:

Following are the description of the given points:

(a) This is a system of probability, which possibility occurs inside an intended manner whenever they choose this specific point of origin from 1 to 100 with no one reserve the possibility about who gets throughout the survey.

(b) Its method is different from the random sampling technique with the base available. For example, two individuals whose names identical to both the list have no chance to join within the survey.

Can someone help me please which one is it ?
A
B
C
D

Answers

It mentions that angle 1 is congruent to angle 2. They have the same angle measure. This allows us to replace angle 1 with angle 2 (because they're effectively the same thing).

We can say
(angle 1) + (angle 3) = 90
(angle 2) + (angle 3) = 90
notice the replacement in bold

The second equation is an algebraic way of saying "angle 2 and angle 3 are complementary"

Answer: Choice C

SOLVE for r.
V=(1/3)pi r^2 h