trigonometric identities

Trigonometric Identities

Answers

Answer 1

Answer:

answer B:

[tex]x= \dfrac{\pi}{2}\ or\ \dfrac{\pi}{6}\ or\ x=\dfrac{5\pi}{6}[/tex]

Step-by-step explanation:

[tex]2cos^2 x + 3sin x=3\\\\\Longrightarrow\ 2*(1-sin^2 x)+3sin x -3=0\\\\\Longrightarrow\ 2-2sin^2 x+3 sin x -3=0\\\\\Longrightarrow\ -2sin^2 x+3 sin x -1=0\\\\\Longrightarrow\ 2sin^2 x-3 sin x +1=0\\\\\Delta=3^2-4*2*1=1\\\\sin\ x=\dfrac{3-1}{4} \ or\ sin\ x=\dfrac{3+1}{4}\\\\sin\ x=\dfrac{1}{2} \ or\ sin\ x=1\\\\\Longrightarrow\ x= \dfrac{\pi}{6}\ or\ x= \dfrac{5\pi}{6}\ or\ x=\dfrac{\pi}{2} \\[/tex]


Related Questions

A hundred chickadees can eat 100 kg of seeds in 100 days. How many kg of seeds can 10 chickadees eat in 10 days?

Answers

Answer:

1 kg

Step-by-step explanation:

Number of chickadees = 100

Quantity of seed eaten = 100 kg

Number of days = 100

Quantity of seeds each chickadee eats per day =Number of chickadees ÷ Quantity of seed eaten ÷ Number of days

= 100 ÷ 100 ÷ 100

= 1 ÷ 100

= 0.01 kg of seed

How many kg of seeds can 10 chickadees eat in 10 days?

= Quantity of seeds each chickadee eats per day × number of chickadee × number of days

= 0.01 kg × 10 × 10

= 1 kg

10 chickadees eat 1 kg of seeds in 10 days

Find x round your answer to the nearest integer.

Answers

Answer:

C

Step-by-step explanation:

Note that x is opposite to the given angle and we are also given the hypotenuse.

Since we have an angle and the side opposite to it and the hypotenuse, we can use the sine ratio. Recall that:

[tex]\displaystyle \sin \theta =\frac{\text{opposite}}{\text{hypotenuse}}[/tex]

The opposite side is x, the hypotenuse is 15, and the angle is 53. Substitute:

[tex]\displaystyle \sin 53^\circ = \frac{x}{15}[/tex]

Solve for x:

[tex]x=15\sin 53^\circ[/tex]

Use a calculator (make sure you're in Degrees Mode!). Hence:

[tex]x=11.9795...\approx 12[/tex]

Our answer is C.

Answer:

C. 12

Step-by-step explanation:

Pythagoras Theorem

What's the maximum area you can get for a rectangle with two sides along the x and y axes, and the opposite vertex in the first quadrant along the line y = 20 – 4x?

Answers

Answer:

Remember that a triangle rectangle of length L and width W has an area:

A = W*L

In our rectangle, we have two sides along the x and y axes.

So one of the vertices of our triangle rectangle is the point (0, 0)

And the other vertex, is along the line:

y = -4x + 20

So, if the opposite vertex is at the point:

(x₁, y₁)

We can define the length as the difference between the x-values of each vertex.

L = (x₁ - 0) = x₁

And the width, similarly, as:

W = (y₁ - 0) = y₁

Such that the point (x₁, y₁) is a solution for the equation y = -4x + 20, then we have:

y₁ = -4x₁ + 20

Then we can rewrite the width as:

W = -4x₁ + 20

Now, we can write the area of our rectangle as:

A = (x₁)*(-4x₁ + 20)

A = -4*x₁^2 + 20*x₁

Now we want to maximize the area, notice that the area is given by a quadratic equation with a negative leading coefficient.

Thus, the maximum will be at the vertex of that quadratic equation.

Remember that for a general quadratic equation:

y = a*x^2 + b*x + c

The x-value of the vertex is:

x = -b/(2*a)

so, in our case, the x-value of the vertex will be:

x₁ = -20/(-4*2) = 20/8 = 5/2

Now we can evaluate this in our area equation:

A = -4*(5/2)^2 + 20*(5/2)  = 49.36

This is the maximum area of the rectangle.

solve x
solve x
solve x

Answers

Answer:

x = 25

Step-by-step explanation:

When you combine both angles, you can get a supplementary angle which means that when they are both added, it should add up to be 180 degrees. With that being said, we can create an equation and solve for x.

5x - 5 + 2x + 10 = 180

~Combine like terms

7x + 5 = 180

~Subtract 5 to both sides

7x = 175

~Divide 7 to both sides

x = 25

Best of Luck!

Answer: x = 25

Step-by-Step Explanation:

We are given a line, hence it is a straight angle being 180°

Therefore,

=> 5x - 5 + 2x + 10 = 180

= 5x - 5 + 2x = 180 - 10 = 170

= 5x + 2x = 170 + 5 = 175

= 7x = 175

=> x = 175/7 = 25

Therefore, x = 25

Additionally, finding the values of each angle :-

=> 5x - 5

= 5(25) - 5

= 125 - 5

=> 120°

=> 2x + 10

= 2(25) + 10

= 50 + 10

=> 60°

Therefore, one angle is 120° and the other is 60°


Which of the following lines is parallel to the line
y = 1/2x -6
Select one:
a) y=-1/2x-6
b) y=2x+1
c) y=-1/2x+5
d) y=1/2x-3

Answers

Answer:

y = 1/2x - 3 (option - d)

Step-by-step explanation:

The lines are parallel if they have the same slope/gradient. So by comparing with y = mx + c (where 'm' is the slope and 'c' is the y-intercept).

Line y = 1/2 x - 6 has the slope m = 1/2

and the line in option 'd'

y = 1/2 x -3 has the slope m = 1/2

Slopes are equal and lines are parallel.

Thank-you.

#Muhib

SOMEONEEEE HELPPP MEEEE OUTTTT!!!!

Answers

Answer:

24°

Step-by-step explanation:

cos ? = 41/45

? = arccos 41/45

? = 24

Answered by GAUTHMATH

The height of a rocket a given number of seconds after it is released is modeled by h (t) = negative 16 t squared + 32 t + 10. What does t represent? the number of seconds after the rocket is released the initial height of the rocket the initial velocity of the rocket the height of the rocket after t seconds The function V(r) = four-thirds pi r cubed can be used to find the volume of air inside a basketball given its radius. What does V(r) represent?

Answers

Answers:

t is the number of seconds after the rocket is released

V(r) is the volume of the ball with radius r.

====================================================

Explanation:

There isn't much to say in terms of explanation. These variables are simply definitions.

Two boys together have $12. One of them has $10 more than the other. How much money does each of them have

Answers

One has $1 and the other has $11

(3.1 x 10^10) X (4.6 x 10^4) divided by (9.4 x 10^-3)

(This is scientific notation)

Answers

Answer:

1.5×10^17

Step-by-step explanation:

it would be better to first multiply the two then divide the answer by 9.4×10^-3

I hope this helps

Hello I’m trying to solve this problem I just don’t know how to do it.

BUT if someone could help and show me step by step that would be great I’m not trying to ask for the answer

I’m just trying learn how to solve it and so step by step there no rush Thank you

Answers

Step-by-step explanation:

To evaluate the proposed, the comprehension of linear data is required,

Slope: The rise/run or the accumulative unit distance between two differentiated points on a linear.

X-intercept: The peculiar point in which the observed linear data intersects the x-axis.

Y-intercept: The peculiar point in which the observed linear data intersects the y-axis.

1. To solve the following systems, first convert the Slope-Intercept formatting to Standard (General) form:

y = -5/3x + 3

3(Y = -5/3x + 3) Product by the denominator to eliminate the fraction.

3y = -5x + 9. Add 5x to the other expression as in standard form, the slope must be positive.

5x + 3y = 9 <== Standard (General) Form.

Y = 1/3x - 3

3(y = 1/3x - 3). Product by the denominator to eliminate the fraction.

3y = x - 9. Subtract by x to place the slope within the other expression of the equation.

-1(-x + 3y = -9). Now, product by -1 to contribute to a positive slope.

X - 3y = 9 <=== Standard (General) Form.

2. To solve for the x and y values, utilize the system of substitution:

1(5x + 3y = 9)Multiply equations by opposite slope to the other, and a positive to other.

-5(X - 3y = 9)

Evaluate,

+ 5x + 3y = 9. Now, add the systems.

-5x + 15y = -45

——————————

18y = -36

Y = -2

Thus, now that y is equated to -2, substitute that to either equation.

X - 3y = 9

X - 3(-2) = 9

X + 6 = 9

X = 3

Thus, x = 3, y = -2. This is their intersection point.

To plot these lines on the graph, execute the following,

Y = -5/3 x + 3

Start with the y-intercept. Draw a point on number 3 on the y-axis (vertical).

Starting with that point, go down 5 units, right 3 units.

* Remember, if there is a negative rise, go down. Positive, go up. If there is a negative run, go left. Positive, go right.

* Keep going 5 units down, right 3 units, until the graph allows.

2. Y = 1/3 x - 3

Similarly, conduct the same steps:

Starting with the y-intercept, draw a point on -3 on the vertical, or y-axis.

Beginning on that point, go up 1 unit, right 3 units.

Keep going up 1 units and 3 units right until the graph permits.

*I hope this helps.

∛3x+7=∛2x+1
solve it please

Answers

Answer:

x = -6

Step-by-step explanation:

cube each side :

3x + 7 = 2x + 1

solve for x:

x = -6

Whats the correct answer?

Answers

Answer:

Actually the answer is "A"

this is a very strange way to present a problem...

this issue her is that [tex](x^{a}) ^{b} = x^{a*b}[/tex]

so you need 1/3 * 3 in the answer... none of them have 1/3 * 3

BUT !!!!! 1/3 + 1/3 + 1/3  is the same as  1/3 * 3 So "A" is the solution

Step-by-step explanation:

Find the value of m.

A. 7
B. 2
C. 42
D. 14

Answers

Answer:

A. 7

Step-by-step explanation:

3m + 21 = 6m

Move variables to one side to get:

3m + 21 = 6m

-3m         -3m

21 = 3m

Then isolate variable by dividing by 3

21/3 = 3m/3

m = 7

Choice A is the correct answer

if (p+2q)/p = 7/5 , find the value of q/p , where p ≠ 0​

Answers

Answer:   1/5

Work Shown:

(p+2q)/p = 7/5

(p/p)+(2q/p) = 7/5

1 + 2(q/p) = 7/5

2(q/p) = 7/5 - 1

2(q/p) = 7/5 - 5/5

2(q/p) = (7-5)/5

2(q/p) = 2/5

q/p = (2/5)*(1/2)

q/p = (2*1)/(5*2)

q/p = 1/5

Answer:

q/p = 1/5

Step-by-step explanation:

(p+2q)/p = 7/5

Multiply each side by p

(p+2q)/p *p = 7/5*p

(p+2q) = 7p/5

Multiply each side by 5

(p+2q)*5 = 7p/5 *5

5p + 10q = 7p

Subtract 5p from each side

5p + 10q -5p = 7p -5p

10 q = 2p

divide each side by p

10q/p = 2p/p

10 q/p = 2

Divide each side by 10

q/p = 2/10

q/p = 1/5


The marked price of a radio was 40% above the cost price. When it was sold allowing 30% discount on it, there was loss of RS. 100. What was the marked price of the radio.​

Answers

Answer:

7000

Step-by-step explanation:

70/100 * marked price = original price - 100

marked price = 140/100* og price

70/100 * 140/100 * og price = original price - 100

49/50 * og price = orignal price - 100

1/50 of original price = 100

orignal price = 5000

marked price = 140/100 * 5000 = 7000

out of 500 bulbs, 0.2 are defective. how many are defctive

Answers

Answer:

100

Step-by-step explanation:

0.2*500=100

100 bulbs 500•0.2=100

Dwight wants to build a new rectangular beet farm, but he is first making a list of items he needs to purchase from the store. Dwight decides he will get 160 feet of
fencing to go around the farm that will have a length of 50 feet.
a. Find the width of the farm that Dwight wants to make. Include units.
b. Dwight decides that he will plant 1 beet seed for every square foot of land in this farm and he does not want to purchase any extra seeds. Exactly how many beet seeds should he purchase? Include units.

Answers

Answer:welcome

Step-by-step explanation: sorry I jsit really needed the points

What is another name for a relation that has each element in its domain paired with exactly one element in its range?​

Answers

A function is a relation in which each element of the domain is paired with exactly one element of the range.

Please help with question thank you

Answers

Answer:

The answer is 3x=50-10y

this is the answer 3x = 50 - 10y

first answer gets marked brainliest!!

Answers

Actually they are not the same because it has 25 dots in each much BUT Group A has LESS music ages because there is 5 to 10 years old and the other group has 20 and over.

Hope this helps :)

Ade thinks of a number He doubles it and then subtract 5 The result cannot be less than 100 find the range of values of x

Answers

Answer: [tex]x\in [53,\infty)[/tex]

Step-by-step explanation:

Given

Ade doubles her number and subtract 5 from it. The result cannot be less than 100

Suppose the number is [tex]x[/tex]

According to the question

[tex]\Rightarrow 2x-5\geq100\\\text{Solve the inequality}\\\Rightarrow 2x\geq105\\\Rightarrow x\geq52.5\\\text{for integer number, the range is given by }\\\Rightarrow x\in [53,\infty)[/tex]

The height of a baseball in feet can be found by the equation -4.982 – 20t + 1000. How far has the
baseball traveled at t = 6?

Answers

Answer:

875.018

Step-by-step explanation:

To solve this, we must plug in 6 for our t value. So, we have the equation:

-4.982 - 20(6) + 1000

Following the rules of PEMDAS, we have:

-4.982 - 120 + 1000 = 875.018

P= 3in
a) find the length of each side of the square
b) find the area of the square

Answers

Step-by-step explanation:

what does P mean ?

I assume it is perimeter ?

what is the perimeter of a square ?

come on, there is practically nothing in math that is easier to solve.

a square has 4 equal sides.

so, to go one time around the whole square, we have to go along every one of its 4 sides (which are all of equal length).

so, when I get the perimeter number, I know this is the result of all 4 sides added together.

and how can we express having 4 times the same number ? exactly how we say it in English : 4 times the number.

therefore

P = 4 × side length

and from there we can immediately deduct

side length = P / 4 = 3/4 in

now we know how long the sides of the square are.

what is the area of the square ?

like for any rectangle the area is length×width. just that length=width, so that we end up with length×length = length².

therefore, the area is

3/4 × 3/4 = (3/4)² = 9/16 in²

this is important : a length is measured e.g. in inches (in). an area is then measured in square-inches = in²

the least common multiple of ½,⅓,⅘ and ³/¹⁰ is a)90 b)50 c)30 d)15 e)10​

Answers

Yhhshussuudhddhhdhdhdhdhfidijenrnrr

Answer:

Step-by-step explanation:

WILL GIVE BRANLIEST AND BE SOOO HAPPY PLEASE HELP!!! 30 POINTS SHARE YOUR SMARTNESS!!

Answers

Answer:

s4 = 270

18+36+72+144 = 270

-- convergent sums to a single value

Step-by-step explanation:

Answer:

S4 = 270

Step-by-step explanation:

The 4th partial sum of the sequence is the sum of the first 4 terms:

S4 = a(1) + a(2) + a(3) + a(4)

Because the sequence is geometric any term can be written in terms of the previous one:

a(n) = r a(n - 1)

And more importantly in terms of the first term a(1) so that

a(2) = r a(1)

a(3) = r a(2) = r^2 a(1)

a(4) = r a (3) = r^3 a(1)

Then the 4th partial sum is

S4 = a(1) + r a(1) + r^2 a(1) + r^3 a(1)

S4 = a(1) (1 + r + r^2 + r^3)

With a a(1) = 18 and r = 2 we have

S4 = 18 (1 + 2 + 4 + 8) = 270

Therefore, the 4th partial sum is 270

Find the perimeter of this semi-circle with diameter, d = 22cm.
Give your answer as an expression in terms of t.

Answers

Answer:

=22tcm

Step-by-step explanation:

Perimeter of a circle =πD

But π=t

hence perimeter; = 22tcm

where t=π

QUESTION 2
In A XYZ, X = 18 cm, y = 14 cm, and z= 17 cm.
Determine the measure of Z to the nearest degree.
a. 66°
b. 63°
c. 57°
d. 60°

Answers

Answer:

B: 63

Step-by-step explanation:

The graph f(x) shown below has the same shape as the graph of g(x)=x^2 which of the following is the equation of f(x)

Answers

Answer:

Choice D. [tex]F(x)=x^2-4[/tex]

Step-by-step explanation:

Since the graph is translated down 4, it cannot be choice A. or C.Since the graph is concave up, choice B. is ruled out.Leaving choice D. the correct answer.

Find the value of both variables.

Answers

[tex] \cos(45) = \frac{5 \sqrt{2} }{x} \\ \frac{1}{ \sqrt{2} } = \frac{5 \sqrt{2} }{x} \\ x = 10 \\ \\ \tan(45) = \frac{y}{5 \sqrt{2} } \\ 1 = \frac{y}{5 \sqrt{2} } \\ y = 5 \sqrt{2} [/tex]

I hope I helped you ^_^

Please help solve 1, and 2

Answers

Answer:

Step-by-step explanation:

1). WXYZ is a rectangle,

  Properties of a rectangle,

  i). Opposite sides are equal and parallel.

  ii). All interior angles measure 90°.

  iii). Diagonals are equal in measure.

a). WY = ZX = 30

 Therefore, ZT = [tex]\frac{1}{2}(ZX)[/tex]

                    [tex]ZT=15[/tex]

b). WY = ZX = 45

c). Since, WY = ZX,

    (4b - 16) = (3b + 5)

    4b - 3b = 16 + 5

     b = 21

2). GOAT is a rhombus and m∠OGA = 35°,

    a). m∠TGA = m∠OGA = 35°

    b). m∠GXO = 90°

    c). m∠GXT = 90°

    d). Since adjacent angles of a rhombus are supplementary,

         m∠OGT + m∠GTA = 180°

         70° + m∠GTA = 180°

         m∠GTA = 110°

         m∠GTO = [tex]\frac{1}{2}(m\angle GTA)[/tex]

                        = [tex]\frac{1}{2}(110^{\circ})[/tex]

                        = 55°

     e). Since, opposite angles of a rhombus are equal,

          m∠OGT = m∠OAT = 70°

     f). m∠GOA = m∠GTA = 110°

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