Mathematics High School

Find the critical numbers of the function on the interval 0≤ θ < 2π.
f(θ) = 2cos(θ) +(sin(θ))^2

Answers

Answer 1

Critical values of the function f(θ) = 2cos(θ) +(sin(θ))² on the interval 0≤ θ < 2π is 0 and π.

Therefore, the answer is 0 and π.

f(θ) = 2cos(θ) +(sin(θ))²

f'(θ) = -2sin(θ) +2sin(θ)cos(θ)

Critical values of f are points at which f' is zero or not defined.

For all values of θ, we can find that f'(θ) is defined.

f'(θ) = 0

-2sin(θ) +2sin(θ)cos(θ) = 0

cos(θ) - 1 = 0 or sin(θ) = 0

cos(θ) = 1

θ = nπ, n = 0, 1, 2, ...

sin(θ) = 0

θ = nπ, n = 0, 1, 2, ...

Therefore in the interval 0 ≤ θ < 2π, critical values are 0 and π.

2π is not there as it is not included in the interval.

To know more on critical values

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Related Questions

v -10= -9
v= _____

explain how you do it.

Answers

Answer:

v = 1

Step-by-step explanation:

v -10= -9

Add 10 to each side

v -10+10= -9+10

v = 1

Which one is it ? NO LINKS
245
55
180
65

Answers

Answer:

245 is the best answer. I am right ta boy

Answer: 245

Step-by-step explanation:

60 + 120 + 65 = 245

HELP ASAP DUE SOON! GIVING BRAINLIESTT!

Answers

Answer:

1. 40

2. 35.71

Step-by-step explanation:

using

pythagoras theorem

help pleas ..........................

Answers

Answer:

5

Step-by-step explanation:

if the whole segment is 17 and FG is 12, you would do 17-12 to get EF

Answer:

I think its 5

Step-by-step explanation:

You have to add EG and FG. Sorry if its incorrect im not very good at this kind of thing.

What is 60% of 450?
60
75
240
270

Answers

Answer:

270

Step-by-step explanation:

450x60%= 270

         OR

450x0.6=270

Answer:

Step-by-step explanation:

270

 

HELP!!!!!FAST!!!NOW!!!!HURRY!!!!PLS!!!!

The length of the shorter leg of a 30-60-90 Special Right Triangle is 17 yd long. How long is the longer leg of the triangle?
1) 17yd
2) 17√2yd
3) 17√3yd
4) 34yd

Answers

Answer:

[tex]17\sqrt{3}[/tex]

Quiz Results:

The length of the longer leg in the considered 30-60-90 Special Right Triangle is given by: Option 3) 17√3yd

What is a 30-60-90 Special Right Triangle?

The right angled triangle in which, the angles are of the measure 30, 60 and 90 degrees is called 30-60-90 Special Right Triangle.

What is law of sines?

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by law of sines,

[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]

Remember that we took

[tex]\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}[/tex]

The wider the angle is, the larger the side opposite to is.

For this right angled triangle, the side opposite to 60 degrees angle is larger leg (let it be of x yd), and the side opposite to 30 degrees angle is shorter leg (of 17 yd).

As shown in the image below, using the sine law for non right angles,  we get:

[tex]\dfrac{\sin\angle A}{a} = \dfrac{\sin\angle B}{b}\\\\\dfrac{\sin(30^\circ)}{17} = \dfrac{\sin(60^\circ)}{x}\\\\x =\dfrac{17 \times \sin(60^\circ)}{\sin(30^\circ)} = 17\sqrt{3} \: \rm yd[/tex]

Thus, the length of the longer leg in the considered 30-60-90 Special Right Triangle is given by: Option 3) 17√3yd

Learn more about law of sines here:

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Help me please I'm very confused about this!

Answers

Answer:I think it's trying to find the area of which is a 5 times 2 = 10

Step-by-step explanation:

Jackson bought a jar of 240 marbles. The percent bar graph shows the percentage of each color marble in the jar.





How many of the marbles are yellow?

Answers

Answer:

72 marbles are yellow

Step-by-step explanation:

Find the slope of the line that contains (−3,5) and (3,−9).

If the slope is not an integer, enter it is a fraction in simplest form. Do not enter a mixed number. Remember, a fraction in simplest form never contains a negative sign in the denominator. If the slope is undefined, “undefined” should be entered.

Answers

The slope is this and that

50 Points
Find the value of r in the figure.
Assume that lines a and bare parallel.
(4r - 30)
(2x)
b

Answers

Answer:

A) x = 15

Step-by-step explanation:

4x - 30 = 2x

subtract 2x from each side of the equation:

2x - 30 = 0

add 30 to each side:

2x = 30

x = 15

Answer:

[tex] \displaystyle A) {15}^{ \circ} [/tex]

Step-by-step explanation:

remember that,

when a transversal crosses two parallel lines then the Alternate interior angles are equal that is being said

[tex] \displaystyle 4x - 30 = 2x[/tex]

cancel 2x from both sides:

[tex] \displaystyle 2x - 30 = 0[/tex]

add 30° to both sides:

[tex] \displaystyle 2x = 30[/tex]

divide both sides by 2:

[tex] \displaystyle x =15[/tex]

hence

our answer is A)

Need help thanks
It’s Trigonometry and it’s hard.

Answers

Y should be 9 the same as the opposite side and the third side is the sum of the other two sides which should be 18 hope it helped so I’m sure ur answer is a I’m in 9th grade and working on something similar but that’s geometry not trigonometry

HELP PLEASE ASAP TYSM GOD BLESS YOU AND YOUR FAMILY! 15 BRAINLY POINTS

Answers

Answer:

I'm not religious, but thank you anyways.

The upside down "T" mean perpendicular to.

Perpendicular:

per·pen·dic·u·lar

/ˌpərpənˈdikyələr/

adjective

1.

at an angle of 90° to a given line, plane, or surface.

___________________________________________________________

Since the question is asking you which one has two perpendicular lines, it can be assumed that the picture on the left is the answer, since that is the only of the two pictures that have lines what appear perpendicular.

PLEASE HELP ASAPPP ILL MARK BRAINLY IF CORRECT

Answers

Answer:

I don't really understand this problem from the picture but here is some tips-

Step-by-step explanation:

Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x -axis. The range is the set of possible output values, which are shown on the y -axis.

Use the picture attached. Sorry for not answering the exact question!

Can I get brainliest?

PLEASE HELP!!! Given PQ. Find the measure of arc PQ, if the radius is 30 and chord PQ = 36. Round to nearest degree.

Answers

Answer:

I think the answer is 30.

Tell whether this equation has no solution, one solution, or infinitely
many solutions.
2x+5=5x-1
O no solution
Oone solution
O infinitely many solutions

Answers

Answer:

infinitely many solutions

Step-by-step explanation:

infinity many solutions

Moosa's sister is six years younger than 3 times his age. The sum of their ages is 30. How old is Moosa?

Answers

Suppose Moosa is ( x ) years old ,

Thus Moosa's sister is ( 3x - 6 ) years old .

The sum of their ages is 30 :

( x ) + ( 3x - 6 ) = 30 ==》 4x - 6 = 30

==》 4x = 36

==》 x = 9

So Moosa is 9 years old .

I need help on this question. I tried finding the answer through my own thinking and the Internet, but I still couldn't get it.

Answers

Answer:

your answer is 3x2+10x−7

Step-by-step explanation:

solving by elimination
7x-y=19
2x-3y=19​

Answers

Answer:

2x + y = -2, x + 2y = 2

4x + y - 2z = 0, 2x+ 3z = 9 , -6x - 2y + z = 0

x + y = 4 , x - y = 2

Step-by-step explanation:

Answer:

x=2 and y=−5

Step-by-step explanation:

Let's solve your system by elimination.

7x−y=19;2x−3y=19

Multiply the first equation by -3,and multiply the second equation by 1.

−3(7x−y=19)

1(2x−3y=19)

Becomes:

−21x+3y=−57

2x−3y=19

Add these equations to eliminate y:

−19x=−38

Then solve−19x=−38for x:

−19x=−38

(Divide both sides by -19)

x=2

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

7x−y=19

Substitute2forxin7x−y=19:

(7)(2)−y=19

−y+14=19(Simplify both sides of the equation)

−y+14+−14=19+−14(Add -14 to both sides)

−y=5

y=-5

HELPP asap I’ll mark you as brainlister

Answers

Answer:

65.97

Step-by-step explanation:

Don't really know how to explain how to do this, but Omni Calculator is very helpful.

Hope that this helps!

Each base in this oblique prism is a right triangle.

What is the volume of the figure?

Answers

Answer:

66 cm³

Step-by-step explanation:

From the diagram,

Volume of the prism(v) = Area of the base (A)×Height(h)

v = A×h............... Equation 1

But,

A = bh/2.................... Equation 2

Where b = base of the triangle, h = height of the triangular base.

Substitute equation 2 into equation 1

v = (bh/2)H.................... Equation 3

Also for the diagram,

Given; b = 3 cm, h = 4 cm, H = 11 cm

Substitute these values into equation 3

v = (3×4×11)/2

v = 132/2

v = 66 cm³

Can someone help me on this question?

Answers

Answer:

90°

Step-by-step explanation:

opposite angles of quadrilateral is 180 so

<d is 180-90 = 90

Bill is a painter, who has been hired to paint a house.
• He receives an houry rate of $35 an hour.
• The materials Bill had to purchase cost $50 for the job.
• The amount of money Bill makes in profit, after working "x" hours, is modeled by the function:
f(x) = 352 – 50
Determine Bill's profit after working 10 hours.

Answers

Answer: 300

Step-by-step explanation: Math - 35X10-50

I may be wrong sorry!

Replace x with 10 in the given function.

We are seeking f(10).

f(10) = 35(10) - 50

f(10) = 350 - 50

f(10) = 300

After 10 hours, Bill's profit is $300.

Write the absolute value equations in the form |x-b|=c(where b is a number and c can be either number or an expression) that have the following solution sets:
One solution: x=15

Answers

Answer:

|x-15|=0

Step-by-step explanation:

Obviously.

Answer:

|x-15|=0

Step-by-step explanation:

You roll a 6-sided die. What is P(prime)? Write your answer as a percentage.

Answers

Answer:

50%

Step-by-step explanation:

☆Answer :

n(s) = {1, 2, 3, 4, 5, 6} = 6

n(a) = {2, 3, 5} = 3

p(a) = n(a)/n(s) p(a) = 3/6 p(a) = ½ <==> 50%

I don’t know if this is correct !!!!!!! Please answer correctly !!!!!!! Will mark Brianliest !!!!!!!!!

Answers

Both would be SAS
And it can be proven

Answer:

It is correct how you put it

PLEASE HELP ME ILL GIVE 70 POINTS AND MARK BRAINLIEST

Answers

Answer:

7: 28x+4 6:20x+2

What’s the answer it’s due in 15 mins

Answers

attach a picture? i don’t see anything

Answer:

Well Ima need the question buddy

Step-by-step explanation:

After all shrek can’t answer a question without a question.

I am R80000 pay 42% tax how much money do I pay in tax??​

Answers

Answer:

46400 rands

Step-by-step explanation:

Because it's common sense

63
Which expression is not equivalent to
66
A
62
B
1
216
1
D

Answers

Answer:1216

Step-by-step explanation:

It’s to big and if this helps plz but a brainly :)

what is the answer for C = 12π

Answers

the answer is c= 12*3.14=37.68
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