Mathematics High School

If 5cos^2θ + 6sin^2θ =11/2
, the value of cosecθ =--------

Answers

Answer 1

Answer:

[tex]\csc(\theta)=\sqrt{2}[/tex]

Step-by-step explanation:

Please refer to the attachment below.

We have:

[tex]5\cos^2(\theta)+6\sin^2(\theta)=11/2[/tex]

Remember that cosine is the ratio of the adjacent side to the hypotenuse. Therefore:

[tex]\cos(\theta)=\frac{b}{c}[/tex]

And sine is the ratio of the opposite side to the hypotenuse. Therefore:

[tex]\sin(\theta)=\frac{a}{c}[/tex]

Substitute into our original equation:

[tex]5(\frac{b}{c})^2+6(\frac{a}{c})^2=11/2[/tex]

Square:

[tex]\frac{5b^2}{c^2}+\frac{6a^2}{c^2}=\frac{11}{2}[/tex]

Multiply both sides by c squared:

[tex]5b^2+6a^2=\frac{11}{2}c^2[/tex]

Let’s also multiply both sides by 2 to eliminate the fraction:

[tex]10b^2+12a^2=11c^2[/tex]

Remember that according to the Pythagorean Theorem:

[tex]c^2=a^2+b^2[/tex]

Hence, we can make another substitution:

[tex]10b^2+12a^2=11(a^2+b^2)[/tex]

Distribute:

[tex]10b^2+12a^2=11a^2+11b^2[/tex]

Subtract 10b² from both sides:

[tex]12a^2=11a^2+b^2[/tex]

Subtract 11a² from both sides:

[tex]a^2=b^2[/tex]

Take the square root of both sides:

[tex]a=b[/tex]

Hence, a is equivalent to b.

Then, we must have a 45-45-90 Triangle.

Therefore, our angle θ is 45°.

We can substitute this back into our original equation to make sure. Remember that cos(45)=sin(45)=√2/2:

[tex]\begin{aligned} 5\cos^2(45)+6\sin^2(45)&=11/2 \\ 5(\frac{\sqrt{2}}{2}})^2+6(\frac{\sqrt{2}}{2})^2&=11/2 \\ 5(2/4)+6(2/4)&=11/2 \\ 5(1/2)+6(1/2)&=11/2 \\ 5/2+6/2&=11/2 \\ 11/2&=11/2 \;\checkmark \end{aligned} \\[/tex]

Hence:

[tex]\begin{aligned} \sin(45)&=\frac{1}{\sqrt{2}} \\ \Rightarrow \csc(\theta)&=\sqrt{2} \end{aligned}[/tex]

If 5cos^2 + 6sin^2 =11/2, The Value Of Cosec =--------

Related Questions

need somebody that’s at mathematics. put your social media name below!

Answers

Answer:

Which social media do you have

Baker Jo has 429 apples
Each apple pie requires 8
apples to make If she
makes as many apple ples
as possible, how many
apples will she have
remaning?
apples

Answers

429/8 = 53 5/8
She will have 5 apples remaining

answered
If y = 3x and 2x – 4y = 3, then x=

Answers

Answer:

x= -3/10

Step-by-step explanation:

putting value

2x - 4(3x) =3

2x- 12x = 3

-10x = 3

x = -3/10

The Wildcats scored an average of 56 points per game during their four-game season. If the scores for their first three games were 48, 57, and 52, what was the score of their last game?

Answers

Answer:

67

Step-by-step explanation:

Use the average formula: average = sum of elements / number of elements

Let x represent the score of their last game, and plug in the average, other scores, and number of elements into the equation:

56 = (48 + 57 + 52 + x) / 4

Simplify:

56 = (157 + x) / 4

Solve for x, by first multiplying each side by 4:

224 = 157 + x

Subtract 157 from both sides:

67 = x

So, the score of their last game was 67.

Find the quotient of -132 and 6.

Answers

Answer:

-22

Step-by-step explanation:

Answer:

-22

Step-by-step explanation:

-132 ÷ 6 --- Divide

Can someone help me with this

Answers

Answer:

Step-by-step explanation:

It pretty simple, you need to read the sentence and match the number.

Ex:

Seven more than one half = 7 more than 1/2

= 7+ 1/2

Because ‘more’ shows that you’re adding

While difference shows you’re subtracting

Quotient shows you’re dividing

And product shows you’re multiplying

And when it refers to ‘a number’ it means your variable which in this case is ‘n’.

What is the value of x?
In the drawing, lines g and h are parallel.
k
A
32
1200
g
B) 40
h
(2x - 470
42
D
58

Answers

Answer:

D

Step-by-step explanation:

Each square in the grid is a unit square with an area of 1 square unit. What is the area of the figure? square units ​

Answers

Answer:

The total area of the figure is: 16 square units

Step-by-step explanation:

The Area is basically a measure of how much space in square units there is inside an object.

Given that each square in the grid is a unit square with an area of 1 square unit.

The figure clearly shows that there are 14 complete squares and 4 half square units.

Thus, the total area of the figure is:

(1 × 14) + (1/2 × 4)

=14 + 2

= 16 square units

Therefore, the total area of the figure is: 16 square units

The information is in the picture PLEASE HELP ME

Answers

Answer:

The answer is A

Step-by-step explanation:

2t(t-4)

(2t x t)(2t x -4)

2t^2 - 8t

PLEASE HELP ASAP:(.....

Answers

Answer:

5

Step-by-step explanation:

23 - 10 = 13

13 - 8 = 5

Answer:

5

Step-by-step explanation:

p = a + b + c

23 = 8 + 10 + c

23 = 18 + c

5 = c

what is the slope of 1.5x+4.5y=18

Answers

Answer:

The x intercept is (12,0)

Step-by-step explanation:

1.5x+4.5y=18  Subtract 1.5 x from both sides of the equation

4.5y=-1.5x+18  Divide both sides of the equation by 4.5

4.5y/4.5=-1.5x/4.5+18/4.5

y=-1/3x+4

The slope is -1/3

The y intercept is (0,4)

To find the x intercept, yet y=0 and solve.

1.5x+4.5y=18

1.5x+4.5(0)=18

1.5x=18  Divide both sides of the equation by 1.5

1.5x/1.5=18/1.5

x=12

The slope is 1/3. You subtract 1.5x on both sides and you are left with 4.5y = 18-1.5x. Then you divide by 4.5 on both sides and you get y=4-1/3x. The slope is always the number multiplied by x.

What is the value of x pls help

Answers

Answer:

118

Step-by-step explanation:

Answer:

118⁰

Step-by-step explanation:

37⁰+25⁰= 62 ⁰

180⁰-62⁰= 118⁰

a hexagon has interior angles the measure 127, 85, 121, 135, and 139 find the measure of the remaining angle.
Please help i need ths asap

Answers

Answer:

113º

(pls mark brainliest if possible)

Step-by-step explanation:

Hexagon has sum of interior angles as 720º

127+85+121+135+139+x=720

607+x = 720

x= 113º

Cheri has a box of cookies to share with her friends. If she gives each friend 6 cookies, she will have 1 cookie left over. If she gives each friend 4 cookies, she will have 29 cookies left over. How many friends does Cheri have?

Answers

30 because you ads the total remaining/

I NEED HELP ASAP I WILL MARK YOU AS BRAINLYLIST

Answers

Answer:

Step 2 Hope this helps

Step-by-step explanation:

Answer:

step:2

Step-by-step explanation:

12x-6=14+2x it must be there.

If you answer this I'll mark you the brainest

Four bots are preparing for a final click battle.

Order the bots to show how they will place

Answers

Answer:

Bot C, A, D, and B

Step-by-step explanation:

Answer: c,a,d,b

Step-by-step explanation: c is the fastest a is second fastest d is third, b is last

HELP NOW!!?!! who ever gets all three of them right gets brainlist and (15 points) *questions in photo*

Answers

Answer:

1. 1,518,720

2. B = 458

3. Leah

Step-by-step explanation:

1. In order to get the first answer you must multiply 48 by 56 and then multiply that by the cost per feet to get your answer.

[tex]48=56[/tex]

[tex]48\times56=2688[/tex]

[tex]2688\times565=1518720[/tex]

[tex]=1518720[/tex]

2. In order to get the answer to this question you need to find the amount of necklaces both girls created and then multiply that number by the number of beads on those necklaces.

[tex]G=106[/tex]

[tex]106+39=145[/tex]

[tex]L=145[/tex]

[tex]106\times104=210[/tex]

[tex]145\times104=249[/tex]

[tex]210+249=459[/tex]

[tex]=458b[/tex]

3. In order to find the answer to this question you need to calculate how much each the girls made then compare.

[tex]G=106[/tex]

[tex]L=145[/tex]

[tex]106\times14=1484[/tex]

[tex]14+10=24[/tex]

[tex]145\times24=3480[/tex]

[tex]1484 < 3480[/tex]

[tex]=3480L[/tex]

Hope this helps.

For khan academy . Need answer immediately

Answers

It's easy just use y=mx+b form ok?

5.5 cm
What is the circumference of this circle?
cm

Answers

Answer:

23.76

Step-by-step explanation:

The answer is 23.76

Mark me brainlist please don’t need 1 more

What is the kinetic energy of a toy truck with a mass of 0.75kg and a velocity of 4 m/s (Formula: KE= 1/2mv2)​

Answers

Answer:6

Step-by-step explanation:

What is the answer?❤️✌️

Answers

Answer:

b

Step-by-step explanation:

guys if you need to answer a question so you can ask for one just say it please is better then given a wrong answer

C(-1,6);y=2/5x-2 what is the equation of the parallel lines.

Answers

9514 1404 393

Answer:

  y = 2/5x +32/5

Step-by-step explanation:

The given line is in slope-intercept form.

  y = mx + b . . . . . . m is the slope; b is the y-intercept

The value of the slope in the given line is m=2/5. A parallel line will have the same slope. In general, it will have a different y-intercept. That value can be found from the given point.

  y = 2/5x + b

  6 = 2/5(-1) +b

  6 +2/5 = b = 32/5

The equation of the parallel line through (-1, 6) is ...

  y = 2/5x +32/5

Helppppp will give the crown

Answers

-√121
10 1/11
10.13
10.2 repeating
-√121 - 10 1/11 - 10.13 - 10.2

25 POINTS!! PLS HELP

Answers

Answer:

5/13

Step-by-step explanation:

You are meant to find cos which is CAH

That means there is an adjacent and hypotenuse

So it will be 5/13

What is the value of n?
1131
nº
160°
A. 290
B. 490
C. 20°
D. 690

Answers

Answer:

c as 131 -180=49° is the answer

Select an expression that is equivalent to 3(n − 3) + 4. (1 point)

a
3n + 1

b
3n − 5

c
3n + 13

d
3n − 3

Answers

Answer:

C. 3n+13

Step-by-step explanation:

When you simplyfy 3(n-3)+4 you get 3n-9 +4, Then you add 4 to 9 since addition comes before subtraction and you would get the answer 3n+13.

Use f(x) = 2x + 5

Find f^-1 (11)

Answers

Answer:

If you're looking for the inverse, the answer is:

[tex]\frac{x}{2}-\frac{5}{2}[/tex]

The solution shown for the equation is incorrect. What is the correct​ solution? What is the​ error?
-5 (4 - r) = 15
-20 - 5r =15
-5r = 35
r = -7

Answers

r = 7 not -7
-5(4 - r) = 15
-5(4 - r)/-5 = 15/-5
4 - r = -3
4 - r - 4 = -3 - 4
-r = -7
-r/-1 = -7/-1
r = 7

whats 1100 x 100,00 pls help

Answers

Answer:

110000

Step-by-step explanation:

Which angle has a measure equal to the sum of m∠SQR and m∠QRS?

∠RSC
∠SRE
∠DQS
∠QSR

Answers

Answer:

QSR

Step-by-step explanation:

Same letters so its the answer

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