Solve the equation. 2cos2(x+30°)=1 for 0°≤x≤360°​

Answer:

ok

Step-by-step explanation:

I think

Given:

The point P = (3,2) is rotated 270° counterclockwise about the origin.

To find:

The image of the given point after rotation.

Solution:

If a point rotated 270° counterclockwise about the origin, then the rule of rotation is:

[tex](x,y)\to (y,-x)[/tex]

Using this rule, we get

[tex]P(3,2)\to P'(2,-3)[/tex]

Therefore, the image of given point P = (3,2) after the rotation of 270° counterclockwise about the origin, is P'(2,-3).

Answer:

17.27

Step-by-step explanation:

so we do 5.5/2=2.75

2x3.14= 6.28

6.28x2.75=17.27

Answer:

Step-by-step explanation:

Given

f(x) = 4x + 7

so

f(a + h) = 4(a + h) + h

          = 4a + 4h +h

          = 4a + 5h

f(a) = 4a + 7

now by the question

[tex]\frac{f(a+h) - f(a)}{h}\\=\frac{4a + 5h - 4a + 7}{h}\\=\frac{ 5h + 7}{h} \\= \frac{5h}{h} + \frac{7}{h} \\= 5 +\frac{7}{h}[/tex]

hope it helps :)

The angle of elevation of a kite is 53.13°

"It is the angle formed by the line of sight and the horizontal plane for an object above the horizontal surface."

"For a right triangle, the sine of acute angle [tex]\theta[/tex] is,

[tex]sin(\theta)=\frac{opposite ~side}{hypotenuse}[/tex]"

For given question,

Consider the following diagram for given question.

The length of the string (AC) = 50m

The kite is flying 40m vertically above the ground.

⇒AB = 40m

We need to find the angle of elevation [tex]\theta[/tex]

Consider the sine of angle  [tex]\theta[/tex]

[tex]\Rightarrow sin(\theta)=\frac{AB}{AC} \\\\\Rightarrow sin(\theta)=\frac{40}{50}\\\\\Rightarrow sin(\theta)=0.8\\\\\Rightarrow \theta=sin^{-1}(0.8)\\\\\Rightarrow \theta=53.13^{\circ}[/tex]

Therefore, the angle of elevation of a kite is 53.13°

Learn more about the angle of elevation here:

https://brainly.com/question/21137209

#SPJ3

Answer:

Step-by-step explanation:600

Answer:

58.9

Step-by-step explanation:

y²=x²+z²-2×z cos(y)

20²=22²+18²-2(22)(18) cos (y)

400=484+324-792 cos(y)

-408=-772 cos (y)

408/792=cos y

y=cos⁻¹(408/792)=58.9

hope it helps...

have a great day!!

Answer:

Nine to thirty-six equals ten to forty.

Step-by-step explanation:

The word ‘to’ can be substituted in for the colon (:). This is to denote the mathematical concept of ratios.

The word ‘equals’ can be used in place of the equal sign (=).

Answer:

The athlete jogged at 4 miles per hour for 30 minutes, and jogged at 6 miles per hour for 1 hour.

Step-by-step explanation:

Given that at first an athlete jogs at 4 miles per hour and then jogs at 6 miles per hour, traveling 8 miles in 1.5 hours, to determine how long does the athlete jogs at each speed the following calculation must be performed:

4 x 1.5 + 6 x 0 = 6

4 x 1 + 6 x 0.5 = 7

4 x 0.75 + 6 x 0.75 = 7.5

4 x 0.5 + 6 x 1 = 8

Therefore, the athlete jogged at 4 miles per hour for 30 minutes, and jogged at 6 miles per hour for 1 hour.

Answer:

6.99 rounded up to 7 :))

Step-by-step explanation:

1/3 = 0.33

2.33 * 3 = 6.99 ft

Answer:

77.43% decrease

Step-by-step explanation:

A decrease of 11% = (100 - 11)% = 89% = [tex]\frac{89}{100}[/tex] = 0.89

A decrease of 13% = (100 - 13)% = 87% = [tex]\frac{87}{100}[/tex] = 0.87

A 11% decrease followed by a 13% decrease has an overall change of

0.89 × 0.87 = 0.7743 × 100% = 77.43%

Answer:

82+2>34

84>34

True

I hope this helps :)

Answer:

A- point A

Step-by-step explanation:

Absolute value doesnt care about the sign so a negative is a positive.

PLease Brainliest

Answer:

$320

Step-by-step explanation:

400*0.8(decimal form of 80%) = 320

Answer:$80

Step-by-step explanation:

$400x0.80=$320 off

400-320=$80

Or

$400 x 0.20= $80 sale price

Answer:

The answer is C

Step-by-step explanation:

If you plot them carefully.

Answer:

parallel y=7x+26

perpendicular y=1/7x+32/7

Step-by-step explanation:

parallel line have the same slope

y-5=7(x-(-3))

y-5=7(x+3)

y-5=7x+21

y=7x+21+5

y=7x+26

perpendicular slope  is the opposite of the original slope of 7

y-5=-1/7(x-(-3))

y-5=-1/7(x+3)

y-5=-1/7x-3/7

y=-1/7x-3/7+5

y=-1/7x+32/7

Answer:

Verified below

Step-by-step explanation:

We want to show that (Cos2θ)/(1 + sin2θ) = (cot θ - 1)/(cot θ + 1)

In trigonometric identities;

Cot θ = cos θ/sin θ

Thus;

(cot θ - 1)/(cot θ + 1) gives;

((cos θ/sin θ) - 1)/((cos θ/sin θ) + 1)

Simplifying numerator and denominator gives;

((cos θ - sin θ)/sin θ)/((cos θ + sin θ)/sin θ)

This reduces to;

>> (cos θ - sin θ)/(cos θ + sin θ)

Multiply top and bottom by ((cos θ + sin θ) to get;

>> (cos² θ - sin²θ)/(cos²θ + sin²θ + 2sinθcosθ)

In trigonometric identities, we know that;

cos 2θ = (cos² θ - sin²θ)

cos²θ + sin²θ = 1

sin 2θ = 2sinθcosθ

Thus;

(cos² θ - sin²θ)/(cos²θ + sin²θ + 2sinθcosθ) gives us:

>> cos 2θ/(1 + sin 2θ)

This is equal to the left hand side.

Thus, it is verified.

Answer:

pretty sure its twenty

Step-by-step explanation:

you have to subtract the maximum from the minimum values

so 25-5=20

have a nice day!!!!!!!!

Answer:

If you think numbers with fractions are annoying, consider transforming the number into fractions!

Step-by-step explanation:

7 1/2 is (14+1)/2, and 3 1/8 is (24+1)/3. Not you have 15/2 miles for 25/3 days and by dividing them you get 0.9 miles a day

Answer:

Reflected OVER Y makes A

A (-7,3) -> (7,3)

Translated makes

A (7,3) -> (7-5, 3-5) = (2,-2)

B)

Step-by-step explanation:

Answer: B rational

Step-by-step explanation:

Answer:

-6, 10

Step-by-step explanation:

When you reflect of the y-axis the x will be negative if the original point was positive and the y will stay the same

Answer:

(a): Marginal pmf of x

[tex]P(0) = 0.72[/tex]

[tex]P(1) = 0.28[/tex]

(b): Marginal pmf of y

[tex]P(0) = 0.81[/tex]

[tex]P(1) = 0.19[/tex]

(c): Mean and Variance of x

[tex]E(x) = 0.28[/tex]

[tex]Var(x) = 0.2016[/tex]

(d): Mean and Variance of y

[tex]E(y) = 0.19[/tex]

[tex]Var(y) = 0.1539[/tex]

(e): The covariance and the coefficient of correlation

[tex]Cov(x,y) = 0.0468[/tex]

[tex]r \approx 0.2657[/tex]

Step-by-step explanation:

Given

x = bottles

y = carton

See attachment for complete question

Solving (a): Marginal pmf of x

This is calculated as:

[tex]P(x) = \sum\limits^{}_y\ P(x,y)[/tex]

So:

[tex]P(0) = P(0,0) + P(0,1)[/tex]

[tex]P(0) = 0.63 + 0.09[/tex]

[tex]P(0) = 0.72[/tex]

[tex]P(1) = P(1,0) + P(1,1)[/tex]

[tex]P(1) = 0.18 + 0.10[/tex]

[tex]P(1) = 0.28[/tex]

Solving (b): Marginal pmf of y

This is calculated as:

[tex]P(y) = \sum\limits^{}_x\ P(x,y)[/tex]

So:

[tex]P(0) = P(0,0) + P(1,0)[/tex]

[tex]P(0) = 0.63 + 0.18[/tex]

[tex]P(0) = 0.81[/tex]

[tex]P(1) = P(0,1) + P(1,1)[/tex]

[tex]P(1) = 0.09 + 0.10[/tex]

[tex]P(1) = 0.19[/tex]

Solving (c): Mean and Variance of x

Mean is calculated as:

[tex]E(x) = \sum( x * P(x))[/tex]

So, we have:

[tex]E(x) = 0 * P(0) + 1 * P(1)[/tex]

[tex]E(x) = 0 * 0.72 + 1 * 0.28[/tex]

[tex]E(x) = 0 + 0.28[/tex]

[tex]E(x) = 0.28[/tex]

Variance is calculated as:

[tex]Var(x) = E(x^2) - (E(x))^2[/tex]

Calculate [tex]E(x^2)[/tex]

[tex]E(x^2) = \sum( x^2 * P(x))[/tex]

[tex]E(x^2) = 0^2 * 0.72 + 1^2 * 0.28[/tex]

[tex]E(x^2) = 0 + 0.28[/tex]

[tex]E(x^2) = 0.28[/tex]

So:

[tex]Var(x) = E(x^2) - (E(x))^2[/tex]

[tex]Var(x) = 0.28 - 0.28^2[/tex]

[tex]Var(x) = 0.28 - 0.0784[/tex]

[tex]Var(x) = 0.2016[/tex]

Solving (d): Mean and Variance of y

Mean is calculated as:

[tex]E(y) = \sum(y * P(y))[/tex]

So, we have:

[tex]E(y) = 0 * P(0) + 1 * P(1)[/tex]

[tex]E(y) = 0 * 0.81 + 1 * 0.19[/tex]

[tex]E(y) = 0+0.19[/tex]

[tex]E(y) = 0.19[/tex]

Variance is calculated as:

[tex]Var(y) = E(y^2) - (E(y))^2[/tex]

Calculate [tex]E(y^2)[/tex]

[tex]E(y^2) = \sum(y^2 * P(y))[/tex]

[tex]E(y^2) = 0^2 * 0.81 + 1^2 * 0.19[/tex]

[tex]E(y^2) = 0 + 0.19[/tex]

[tex]E(y^2) = 0.19[/tex]

So:

[tex]Var(y) = E(y^2) - (E(y))^2[/tex]

[tex]Var(y) = 0.19 - 0.19^2[/tex]

[tex]Var(y) = 0.19 - 0.0361[/tex]

[tex]Var(y) = 0.1539[/tex]

Solving (e): The covariance and the coefficient of correlation

Covariance is calculated as:

[tex]COV(x,y) = E(xy) - E(x) * E(y)[/tex]

Calculate E(xy)

[tex]E(xy) = \sum (xy * P(xy))[/tex]

This gives:

[tex]E(xy) = x_0y_0 * P(0,0) + x_1y_0 * P(1,0) +x_0y_1 * P(0,1) + x_1y_1 * P(1,1)[/tex]

[tex]E(xy) = 0*0 * 0.63 + 1*0 * 0.18 +0*1 * 0.09 + 1*1 * 0.1[/tex]

[tex]E(xy) = 0+0+0 + 0.1[/tex]

[tex]E(xy) = 0.1[/tex]

So:

[tex]COV(x,y) = E(xy) - E(x) * E(y)[/tex]

[tex]Cov(x,y) = 0.1 - 0.28 * 0.19[/tex]

[tex]Cov(x,y) = 0.1 - 0.0532[/tex]

[tex]Cov(x,y) = 0.0468[/tex]

The coefficient of correlation is then calculated as:

[tex]r = \frac{Cov(x,y)}{\sqrt{Var(x) * Var(y)}}[/tex]

[tex]r = \frac{0.0468}{\sqrt{0.2016 * 0.1539}}[/tex]

[tex]r = \frac{0.0468}{\sqrt{0.03102624}}[/tex]

[tex]r = \frac{0.0468}{0.17614266944}[/tex]

[tex]r = 0.26569371378[/tex]

[tex]r \approx 0.2657[/tex] --- approximated

Answer:

He drinks 6 cups a day.

Step-by-step explanation:

1 pint - 2 cups

3 x 2 = 6

Hey, so I really put a lot of time and effort in my answers, so if you can, could you please give me a "Brainliest" because I really want to rank up! Thank you so much for the points, and I hope the answer helped you!!! :)

Answer:

6 cups.

Step-by-step Explanation:

1 pint is equal to 2 cups.

Therefore, 3 pints of milk is equal to 2 cups of milk.

Answer:

1/4 of 0.25

Step-by-step explanation:

2/4 x 2/4 = 1/4

Answer:

18 because of its addition

Step-by-step explanation:

πr²=3+2+7+2+2+2

=5+9+4

=18

Answer:

40

explanation:

The range is the difference between the smallest and highest numbers in a list or set. To find the range, first put all the numbers in order. Then subtract the lowest number from the highest. The answer gives you the range of the list.

Step-by-step explanation:

sorry I don't know the answer I want some points so because I do this I really really sorry. and thanks for point