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3 years ago

If sin theta = -1/2 and lies in the third quadrant, what is the cos?

Mathematics

1 answer:

never [62]3 years ago

5 0

Sin angle that equals the 1/2 value is the 30 degree on the 1st Quadrant.

The angle of 30 degree on the 3rd Quadrant is equivalent to (formula and circle in the 1st photo) 180 + 30 = 210°.

So theta = 210° (3rd Quadrant) = 30° (1st Quadrant).

$cos \: 30\degree = \sqrt{3} \div 2$

Now just transfer the cos 30° to the 3rd Quadrant and the signal will be negative (as shown in the 2nd photo attached).

$cos \: 210 \degree = - \sqrt{3} \div 2$

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How can one fifth x − 2 = one third x + 8 be set up as a system of equations?

suter [353]

Answer:

none of the above

Step-by-step explanation:

The given equation can be divided into two parts:

... x - 2 = y = (1/3)x +8

Putting the left equation into standard form, it becomes

... y -x = -2

Multiplying it by 5 gives ...

... 5y -5x = -10 . . . . . . . . . . . matches answer choices A or B

Please note there is no obvious reason <em>why</em> the equation is multiplied by 5. (It is no longer in standard form when there is a factor of 5 that can be removed.)

___

Putting the right equation into standard form, it becomes

... y = (1/3)x + 8

... 3y = x + 24 . . . . . multiply by 3

... 3y -x = 24 . . . . . . subtract x . . . . . . matches answer choice D

Solution:

An appropriate system of equations is ...

5y -5x = -10
3y -x = 24

These have solution (x, y) = (15, 13) as the original equation does.

_____

<em>Comment on the question</em>

In cases like this, where none of the offered answers has any relevance to the problem, I suggest you have your teacher show you how to work this problem and check the resulting answer.

3 0

3 years ago

50 POINTS

lesantik [10]

Answer:

Step-by-step explanation:

Area of sector = ½ r² ∅

1/2 ( 9^2) pi/6

81 x pi/6 x 1/2

81 x (0.52359877559) x 1/2

Area of sector = 21.21

3 0

3 years ago

Interval of increase x^(1/3)(x+4)

Agata [3.3K]

Your function f(x)=(x^(1/3))(x+4)

What your going to want to do first is calculate your first derivative.
You will want to use both the power rule and the product rule.

f '(x)=(x+4)/x^(2/3)+x^(1/3)

f '(x)=4/3(x^(-2/3))(x+1)

Now find the critical numbers

4/3(x^(-2/3))=0 x+1=0
x=0, x=-1

Now plug numbers on the intervals (-infinity, -1),(-1,0) and (0,infinity) into the derivative of your function. The numbers I would choose are -2, -1/2 and 1.

Since f '(-2) is negative, f '(-1/2) is positive and f '(1) is positive, (-1,-3) and (1,5) are relative extrema. This means that the function f(x)=(x^(1/3))(x+4) is increasing on the interval (-1,0) U (0,infinity).

7 0

3 years ago

The length of a rectangle is three times its width. If the area of the rectangle is 192 ft^2, find its perimeter

Nikolay [14]

Area(A)=192ft^2
Width (W)=?
Length (L)=3W
First we must find what the width and length are to find perimeter (P=2L+2W).
A=LxW
192=(3W)(W)
192=3W^2
192/3=3W^2/3
64=W^2
8=W can only use positive solution of 8 because distance is positive.
L=3W=3(8)=24

P=2L + 2W
P=2 (24)+2 (8)
P=48+16=64ft

4 0

3 years ago

What is the standard form of the number shown in this calculator display? The calculator shows three point eight two e positive

Volgvan

The answer would be 382000000.

8 0

3 years ago