Given csc(A) = 65/16 and that angle A is in Quadrant I, find the exact value of sec A in simplest radical form using a rational denominator . Someone please help me!

Answer:

[tex]\cos \theta = -\frac{\sqrt{5}}{3}[/tex]

Step-by-step explanation:

Draw a right triangle with angle [tex]\theta[/tex]. In all right triangles, the sine of an angle is equal to its opposite side divide by the hypotenuse of the triangle. Therefore, label the side opposite to [tex]\theta[/tex] as 2 and the hypotenuse (longest side) of the right triangle as 3.

To find the last side, use the Pythagorean Theorem:

[tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse of the triangle.

Solving for [tex]a[/tex]:

[tex]a^2+2^2=3^2,\\a^2+4=9,\\a^2=5,\\a=\pm\sqrt{5}\implies \sqrt{5}[/tex]

In all right triangles, the cosine of an angle is equal to its adjacent side divided by the hypotenuse. However, the cosine of all angles in Quadrant III are negative. Therefore, the desired answer is [tex]\cos \theta=\boxed{-\frac{\sqrt{5}}{3}}[/tex].

Verify:

[tex]\sin \theta =-\frac{2}{3},\\\\\theta=\arcsin(-\frac{2}{3}}),\\\\\cos(\arcsin(-\frac{2}{3}}))=-\frac{\sqrt{5}}{3}\checkmark[/tex]

Answer:

A= -42

B= 3

Step-by-step explanation:

Answer:

39

Step-by-step explanation:

y=arctan(0.8)=38.65=39

Answer:

the answer is true.

4/6

10/15

Answer:

The value of y when x = 8 is -8.

Step-by-step explanation:

y = 8 - 2x

y = 8 - 2*8

y = 8 - 16

y = -8

Have a nice day!

Answer:

21 days

Step-by-step explanation:

101/5=20.2

thus u need 21 days to finish 101 worksheets

Answer:

The answer is "At the 0,10 level, there should be enough proof that the percentage is below 49%"

Step-by-step explanation:

Null and alternative hypothesis:

[tex]H_0 :P \geq 0.49\\\\H_1:P<0.49 \ \ (\text{Left tailed test})\\\\[/tex]

Significance level: [tex]\alpha = 0.10[/tex]

It is decided that the null hypothesis at the defined meaning level is rejected.

Answer: D) 13^(3/5)

Step-by-step explanation: This is assuming that the question is asking the √13^3. With the five as the y root.

Answer:

Mark arrived at school at 9:45 A.M. or either 9:45 P.M.

Answer:

Christy got to school at 9:45am

Step-by-step explanation:

Answer:

[tex]area = (length \times width) \\ = (x + 5) \times 4 \\ = (4x + 20) \: square \: units[/tex]

Answer:

x<−3

Step-by-step explanation:

hope this works

Answer:

C, n < –3 or n > –2

Step-by-step explanation:

Answer:

B and C. can you select more than one?

Answer:

x² + 7x - 4 = 0

Step-by-step explanation:

A quadratic equation in standard form is

ax² + bx + c = 0 ( a ≠ 0 )

Given

- 7x + 4 = x² ( subtract - 7x + 4 from both sides )

0 = x² + 7x - 4 , that is

x² + 7x - 4 = 0 ← in standard form

Answer:

x=1 , y=3

Step-by-step explanation:

y = 4 x − 1

4(y = − x + 4)

y = 4 x − 1

4y= - 4 x +16

5y= 15

y=3

3=4x-1

+1     +1

4=4x

/4  /4

x=1

Answer:

Probability of 100 managers being selected= 100C100*1100C800/1200C900

Probability of selecting just one manager = 1C100*1199C899/1200C900

Explanation:

Given 100 managers, 200 factory workers, 900 miscellaneous workers, and workers bring transferred 900

To find probability of 100 managers leaving given that probability = number of favorable outcomes/total number of outcomes

We use combination since order doesn't matter:

Combination formula= n!/r!(n-r)! Where n= total number of outcomes and r is number of outcome at one time and ! is factorial

Probability of 100 managers using nCr formula for each item = 100C100*1100C800/1200C900

Probability of 1 manager also applying nCr formula as above =1C100*1199C899/1200C900

The probability is the ratio of the favorable event to the total number of events. The probabilities are as follows;

a.  P = ¹⁰⁰C₁₀₀ × ¹¹⁰⁰C₈₀₀ / ¹²⁰⁰C₉₀₀

b.  P = ¹⁰⁰C₁ × ¹¹⁹⁹C₈₉₉ / ¹²⁰⁰C₉₀₀

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen.

Your company is considering offering 600 employees the opportunity to transfer to its new headquarters in Ottawa and, as personnel manager, you decide that it would be fairest if the transfer offers are decided by means of a lottery.

Assuming that your company currently employs 100 managers, 300 factory workers, and 900 miscellaneous staff.

We can use combination since order does not matter;

a)  The probability of all the managers will be offered the opportunity will be

[tex]P = \dfrac{^{100}C_{100} * ^{1100}C_{800}}{^{1200}C_{900}}\\[/tex]

b)  The probability of you will be offered the opportunity will be

[tex]P = \dfrac{^{100}C_{1} * ^{1199}C_{899}}{^{1200}C_{900}}\\[/tex]

More about the probability link is given below.

https://brainly.com/question/795909

Answer: DH and HF correspond.

Answer:

B

Step-by-step explanation:

Start by using the distance formula to find the raidus

The two points are (-2,1) and (-4,1)

√((-4+2)²+(1-1)²)= 2

The radius is two and we have our center which means we can write

(x+2)²+(y-1)²=4

now it's just a matter of expanding everyhting

x²+4x+4+y²-2y-3=0

x²+y²+4x-2y+1=0

This is equal to B

Answer:

it would probably be around 1.8 or either 1.7

Answer: [tex]1\dfrac{1}{4}[/tex]

Step-by-step explanation:

Given

The equation in terms of a is

[tex]\Rightarrow \dfrac{a}{a-1}-\dfrac{a+5}{a}=0\\\\\Rightarrow \dfrac{a}{a-1}=\dfrac{a+5}{a}\\\\\Rightarrow a^2=(a-1)(a+5)\\\\\Rightarrow a^2=a^2+4a-5\\\\ \Rightarrow 4a=5\\\\\Rightarrow a=\dfrac{5}{4}\ \text{or}\ 1\dfrac{1}{4}[/tex]

Answer:

8 1/6

Step-by-step explanation:

that is da answer bbbbb

Answer:

8 1/6

Step-by-step explanation:

3 1/2 X 2 1/3

7/2x7/3

Answer:

7 1/2 miles per half hour

Step-by-step explanation:

First let's find how many miles you travel per hour. To find that, you divide 45 by 3. This gives you 15 miles per hour. Now we need to find how many miles in half an hour. To do this we are going to convert into minutes. We need to find out how many miles per minute. There are 60 minutes in 1 hour, so we will divide 15 by 60. That gives 0.25, or 1/4 mile per minute. So now that we know how many miles per minute, we can find out how many for half an hour. Half an hour is 30 minutes, so we are going to multiply 1/4 by 30. You will get 15/2. We need to make that a mixed number, and that gives us 7 1/2 miles per 30 minutes, or 7 1/2 miles per half hour.

I hope this helped :)

(edit: I just realized I did this the hard way. Sorry. The easier way would be to just divide 15 by 2 since it would take two halves of 15 to make the amount of miles per hour.)

Answer:

x =55 degrees

y = 35 degrees

Step-by-step explanation:

We know that the distance from the center of the circle to the circumference is the radius

that means the triangle starting out from O is isosceles since two of the sides are radii and thus the angle of those sides are the same

Let us call one of the angles z

we know that the sum of the angles in a triangle is 180 degrees

That simply means;

80 + 2z = 180

2z = 180-80

2z = 100

z = 100/2

z = 50 degrees

So the angles at each upper end of the cyclic quadrilateral are;

x + 50 and y + 50

we know that the angles that face each other in a cyclic quadrilateral are supplementary

Thus;

95 + y+ 50 = 180

y= 180-95-50

y= 180-145

y = 35 degrees

Now, for x, the angle supplementary to the angle that faces x+ 50 equals x + 50

Thus;

x + 50 = 105

x= 105-50

x = 55 degrees

Step-by-step explanation:

you can follow the same procedure for others

Answer:

7.57 cm

Step-by-step explanation:

Volume of a cylinder = πr²h

π = 3.14

r= radius

h = height

1,800 = 3.14 x r² x 40

r² = 1800 /(3.14 x 40)

r² = 14.33121

√14.33121 = r

r = 3.785658 cm

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

A radius is half of the diameter

Diameter = 2 x 3.785658 cm = 7.57cm

Step-by-step explanation:

answer is in the image above

Answer:

x = 8 cm

Step-by-step explanation:

Given that,

In a square PQRS, PQ = 2x +3 cm and QR = 3x – 5 cm.

We need to find the value of x.

In a square, all the sides are equal. So,

PQ = QR

2x +3 = 3x – 5

3+5 = 3x - 2x

x = 8

So, the value of x is equal to 8 cm.