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Given tan(theta)= -2 and pi/2 < theta < pi; find cos theta)

Answers

Answer 1

Answer:

Answer:

$\cos \theta=-(1)/(√(5))$

Step-by-step explanation:

$Given\ \tan \theta=-2\ \ \ \ \ -(\pi)/(2)<\theta<\pi$

Hence $\theta$ is in second quadrant.

$\tan \theta=(opposite)/(adjacent)=-2\n\nLength\ of\ opposite=2,\ \ Length\ of\ adjacent=1\n$

Pythagorean Theorem: $hypotenuse^2=opposite^2+adjacent^2$

$hypotenuse^2=(1)^2+(2)^2=1+4=5\nhypotenuse=√(5)$

$\cos \theta=(adjacent)/(hypotenuse)\n\n\cos \theta=(1)/(√(5))$

But in the second quadrant $\cos \theta$ will be negative.

Hence

$\cos \theta=-(1)/(√(5))$

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Carol drew an isosceles triangle that has an angle that measures 62°. Which could be the measures of the other two angles in Carol’s triangle?A. 62° and 62°
B. 56° and 56°
C. 28° and 90°
D. 56° and 62°

Answers

Answer: the answer is B

Step-by-step explanation:

Answer:

56 and 62

Step-by-step explanation:

Please answer 2-5 and 7-9 asap

Answers

Answer:

i dont have that

Step-by-step explanation:

4. Quadrilateral ROPQ is inscribed in a circle. Show all work on no credit. Find x and y. What is the measure of each angle of quadrilateral EFGH? What is the measure of arc HF?

Answers

Answer:

x = 55, y = 60
E = 70°, F = 120°, G = 110°, H = 60°
arcHF = 140°

Step-by-step explanation:

a) The sum of opposite angles of an inscribed quadrilateral is 180°. This lets us use angles E and G to solve for x:

(x+15) + (2x) = 180

3x + 15 = 180 . . .simplify

x +5 = 60 . . . . . divide by 3

x = 55 . . . . . . . . subtract 5

Similarly, we can use angles F and H to solve for y:

(3y -60) + (y) = 180

4y -60 = 180 . . . . simplify

y -15 = 45 . . . . . . divide by 4

y = 60 . . . . . . . . . add 15

___

b) Then the measures of the angles are ...

G = 2x = 2·55 = 110

E = 180 -G = 70

H = y = 60

F = 180 -H = 120

The angle measures are ...

m∠E = 70°, m∠F = 120°, m∠G = 110°, m∠H = 60°

___

c) short arc HF is intercepted by inscribed angle E, so the arc will have twice the measure of the angle.

arc HF = 2·m∠E = 140°

_____

Comment on the problem

Throughout, the only relation being used is that the measure of an arc is twice the measure of the inscribed angle intercepting it. For opposite angles of the quadrilateral, the sum of the two intercepted arcs is 360° (the whole circle), so the sum of the two angles is 180°.

What is the equation of the line

Answers

find the equation of a line given that you know points it passes through

Answer:

picture?

Step-by-step explanation:

An attacker at the base of a castle wall 4 m high throws a rock straight up with speed 7.5 m/s from a height of 1.5 mabove the ground.
(a) Will the rock exceed the top of the wall?
(b) If so, what is its speed when it reaches the top of the wall?
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(c) If we don’t want the stone to exceed the top of the wall (we want the top of the wall to be the maximum height)
what the initial speed that the stone must have?

Answers

Answer:

a) Yes, b) $v\approx 2.686\,(m)/(s)$ , c) $v_(o) \approx 7.002\,(m)/(s)$

Step-by-step explanation:

a) The maximum height reached by the rock is:

$\Delta y = (\left(0\,(m)/(s) \right)^(2)-\left(7.5\,(m)/(s) \right)^(2))/(2\cdot \left(-9.807\,(m)/(s^(2)) \right))$

$\Delta y = 2.868\,m$

$y = 1.5\,m + 2.868\,m$

$y = 4.368\,m$

Yes, the rock will exceed the top of the wall.

b) The speed when the rock reaches the top of the wall:

$v = \sqrt{\left(7.5\,(m)/(s) \right)^(2)+2\cdot \left(-9.807\,(m)/(s^(2)) \right)\cdot (4\,m-1.5\,m)}$

$v\approx 2.686\,(m)/(s)$

c) The initial speed required so that stone does not exceed the top of the wall is:

$v_(o) = \sqrt{\left(0\,(m)/(s) \right)^(2)-2\cdot \left(-9.807\,(m)/(s^(2)) \right)\cdot (4\,m-1.5\,m) }$

$v_(o) \approx 7.002\,(m)/(s)$

Find the difference.
-7 - (-9)

Answers

Answer: The answer is 2.

Step-by-step explanation: If you have 2 minuses together, then that actually means a plus. -7+9 is 2.

Answer:

-7-(-9) a negative and a negative makes a positive so the new question will be -7+9 which should equal -16?

Other Questions

Deanna and Lise are playing game at the arcade. Deanna started with $20 and the the game she is playing costs $0.25 each game. Lise started with $40, and her machine costs $0.75 per game. How many games will it be before they both have the same amount of money left? Make an expression the solves the problem.

5x^2-7x-6=0 in factored form

How to write 7/9 as a decimal

Which solution matches both equations ?