You are given that cos(A)=−35, with A in Quadrant II, and cos(B)=817, with B in Quadrant I. Find cos(A−B). Give your answer as a fraction.

Answers

Answer 1

Expand cos(A - B) with the identity

cos(A - B) = cos(A) cos(B) + sin(A) sin(B)

A is in quadrant II, so sin(A) > 0, and B is in quadrant I, so sin(B) > 0. Using the Pythagorean identity, we get

cos²(A) + sin²(A) = 1   ⇒   sin(A) = + √(1 - (-3/5)²) = 4/5

cos²(B) + sin²(B) = 1   ⇒   sin(A) = + √(1 - (8/17)²) = 15/17

Then

cos(A - B) = (-3/5) × 8/17 + 4/5 × 15/17 = 36/85

Answer 2

cos (A - B) is 36/85

How to simply the identity

Expand cos(A - B) with the identity

You get, cos(A - B) = cos(A) cos(B) + sin(A) sin(B)

Since A is in quadrant II, so sin(A) > 0,

B is in quadrant I, so sin(B) > 0.

Using the Pythagorean identity, we get

cos²(A) + sin²(A) = 1  

Make sin A the subject of formula

[tex]sin(A)^{2}[/tex] =  ([tex]\sqrt{(1 - (-3/5}[/tex])²)

Find the square root of both sides, square root cancels square

[tex]sin A[/tex] = 4/5

Repeat the same for the second value

[tex]sin A^{2} = \sqrt{(1- 8/17)^2}[/tex]

[tex]sin A[/tex] = 15/17

Substitute values into cos(A - B)

cos(A - B) =  cos(A) cos(B) + sin(A) sin(B) = (-3/5) * 8/17 + 4/5 * 15/17

cos (A - B) = 36/85

Therefore, cos (A - B) is 36/85

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Related Questions

Determine the number of crawlers and rovers to make,that will maximize the company profit in a given week

Answers

Answer:

jjjijijijiiijijijijijijij no pliss inglés. ;D.

Let (-7,3) be a point of terminal side of 0
Find Cos Sec Cot

Answers

The trigonometry ratios are cos(θ) = -7/√58, sec(θ) = -√58/7 and cot(θ) = -7/3

How to determine the trigonometry ratios?

The point on the terminal side is given as:

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

Start by calculating the hypotenuse using:

[tex]h= \sqrt{x^2 + y^2[/tex]

So, we have:

[tex]h= \sqrt{(-7)^2 + 3^2[/tex]

Evaluate

[tex]h= \sqrt{58[/tex]

The cosine is then calculated using:

cos(θ) = x/h

This gives

cos(θ) = -7/√58

The secant is then calculated using:

sec(θ) = 1/cos(θ)

This gives

sec(θ) = -√58/7

The cotangent is then calculated using:

cot(θ) = cos(θ)/sin(θ)

Where

sin(θ) = y/h

So, we have:

sin(θ) = 3/√58

So, we have:

cot(θ) = (-7/√58)/(3/√58)

This gives

cot(θ) = -7/3

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25. Which of the following expresses 374,274
in scientific notation?
(1)
(2)
(3)
3.74274 x 105
3.74274 x 106
37.4274 X 106
374.274
x 105
× 103
(4)
(5) 3742.74
Ite

Answers

Answer:

3

Step-by-step explanation:

374274 =3.74274 x 100000=3.74272x 10^5

Students were asked to prove the identity (sec x)(csc x) = cot x + tan x. ​

Answers

Let's prove that (sec x)(csc x) is equal to cot x + tan x

[tex]\Longrightarrow \sf (sec(x) )(csc(x))[/tex]

[tex]\Longrightarrow \sf \dfrac{1}{\cos \left(x\right)\sin \left(x\right)}[/tex]

[tex]\Longrightarrow \sf \dfrac{\cos ^2\left(x\right)+\sin ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)}[/tex]

[tex]\Longrightarrow \sf \dfrac{\cos ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)} + \dfrac{\sin ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)}[/tex]

[tex]\Longrightarrow \sf \dfrac{\cos\left(x\right)}{\sin \left(x\right)} + \dfrac{\sin \left(x\right)}{\cos \left(x\right)}[/tex]

[tex]\Longrightarrow \sf cot(x) + tan(x)[/tex]

Hence student A did correctly prove the identity properly.

Also Looking at student B's work, he verified the identity properly.

So, Both are correct in their own way.

Part B

Identities used:

[tex]\rightarrow \sf sin^2 (x) + cos^2 (x) = 1[/tex]       (appeared in step 3)

[tex]\sf \rightarrow \dfrac{cos(x) }{sin(x) } = cot(x)[/tex]               (appeared in step 6)

[tex]\rightarrow \sf \dfrac{sin(x )}{cos(x) } = tan(x)[/tex]               (appeared in step 6)

One number is 2 more than another number. The product of the numbers is 440. Find the numbers.​

Answers

Answer:

219,221

Step-by-step explanation:

the second number can be represented by the equation n1+2=n2

adding these expressions together you get

(n+2)+n=440

youre going to think of n now as just your first number because the equation solves for n1

with that you will get a number valued at 219

you then solve the first equation n1+2=n2 because we now know the value of n1

219+2=221

so the second numbers value is 221

A horse was galloping at average speed of 50km/hr for the first 12 minutes. For the next x minutes, the horse slowed down and it’s average speed decreases to 30km/hr. The average speed of the horse for the whole journey is 45km/h. Find its total distance travelled in kilometres

Answers

The total distance travelled is 1075.91 km.

What is average speed?

The average speed is the total distance traveled by the object in a particular time interval. The average speed is a scalar quantity.

45 * (x +12)= 50* 1/5 + 1/2 *x

45x + 540= 10+ 0.5 x

44.5 x = 530

x= 11.91 (neglect the negative sign cause time can't be negative)

So, distance= 45* 23.91 = 1075.91 Km

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Translate this sentence into an equation. Craig's savings decreased by 23 is .55

Answers

Answer:

x-23=.55

Step-by-step explanation:

Answer: 0.55 = x - 23

Step-by-step explanation:

let his savings = x

Javier is going to a water park with his little brother, Caden. Since Caden is only 4 feet tall, they check to see if he is tall enough to ride the Super Slide. Sadly, the park's website says that he needs to be at least 52 inches tall. How many more inches does Caden need to grow before he is tall enough to ride the Super Slide?

Answers

Caden needs to grow 4 inches tall enough to ride the Super Slide.

What is unit conversion?

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

Given that:-

Javier is going to a water park with his little brother, Caden. Since Caden is only 4 feet tall, they check to see if he is tall enough to ride the Super Slide. Sadly, the park's website says that he needs to be at least 52 inches tall.

Caden's height = 4 feet

Min height to ride the Super slide is = 52 inches

Caden's height in inches will be:-

1 feet = 12 inches

4 feet = 12 x 4 = 48 inches.

The difference between the height will be given as:-

D = 50 - 48 = 4 inches

So Caden should grow his height by 4 inches to ride the super slide.

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A tank weighs 5.6kg when it 1/4 filled with water.If it weighs 10.4kg when it is full ,what will be it's weight when it is empty.​

Answers

Answer:

4 kg

Step-by-step explanation:

........................

Answer:

4 kg

Explanation:

Let the mass of tank be 't' and water 'w'

First equation :              (when it is 1/4 filled with water)

[tex]\sf t + \frac{1}{4} w = 5.6[/tex]

Second equation :        (when it is filled fully with water)

[tex]\sf t +w = 10.4[/tex][tex]\sf w = 10.4 - t[/tex]

Insert second equation into first equation :

[tex]\rightarrow \sf t + \dfrac{1}{4} (10.4 - t) = 5.6[/tex]

[tex]\rightarrow \sf t - \dfrac{1}{4} t + 2.6 = 5.6[/tex]

[tex]\rightarrow \sf \dfrac{3}{4} t = 5.6 - 2.6[/tex]

[tex]\rightarrow \sf \dfrac{3}{4} t = 3[/tex]

[tex]\rightarrow \sf t = 4[/tex]

The tank weights 4 kg when it is empty.

Complete the following table using the equation: y = -2x²

Answers

The parabola is a downward parabola which is passing through origin and leading coefficient of the negative 2.

What is the parabola?

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

The equation of a quadratic function, of vertex (h, k), is given by:

y = a(x – h)² + k

where a is the leading coefficient.

The equation of the parabola will be

y = -x²

The given parabola is a downward parabola which is passing through origin and leading coefficient of the negative 2.

The graph of the function is given below.

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I need someone to do this for me please!
Thank you so much in advance :D

Answers

Answer:

[tex] \cfrac{61}{24} [/tex]

Step-by-step explanation:

Given expression:

[tex] \cfrac{2}{3} + \bigg(\cfrac{5}{2} \bigg) {} ^{ 2} \times \cfrac{3}{10} [/tex]

Solution:

Simplify using PEMDAS.

[tex] = \sf \cfrac{2}{3} + \cfrac{25}{4} \times \cfrac{3}{10} \\ \\ = \cfrac{2}{3} + \cfrac{15}{8} \\ \\ = \cfrac{16 +45 }{24} \\ \\ = \boxed{\cfrac{61}{24} }[/tex]

Done!

Answer:

[tex]\frac{61}{24}[/tex]

Step-by-step explanation:

[tex]\frac{2}{3}[/tex] + ( [tex]\frac{5}{2}[/tex] )² × [tex]\frac{3}{10}[/tex] ← evaluate exponent

= [tex]\frac{2}{3}[/tex] + [tex]\frac{25}{4}[/tex] × [tex]\frac{3}{10}[/tex] ← evaluate multiplication ( cancel 25 and 10 by 5 )

= [tex]\frac{2}{3}[/tex] + [tex]\frac{5}{4}[/tex] × [tex]\frac{3}{2}[/tex]

= [tex]\frac{2}{3}[/tex] + [tex]\frac{15}{8}[/tex] ← evaluate addition

= [tex]\frac{2(8)}{3(8)}[/tex] + [tex]\frac{15(3)}{8(3)}[/tex]

= [tex]\frac{16}{24}[/tex] + [tex]\frac{45}{24}[/tex]

= [tex]\frac{61}{24}[/tex]

Which is the best description for the graph below?

Answers

Uh, there’s no graph.

PLEASE ITS DUE TODAY

Complete the table for the given rule

Rule: Y = 4x

X | Y
5
3
4

Answers

Answer:

Answers are 20, 12 and 16

Step-by-step explanation:

Y=4x

for x = 5

y=4(5)

y=20

for x = 3

y=4(3)

y=12

for x = 4

y=4(4)

y=16

Answer:

X I Y

5 20

3 12

4 16

Step-by-step explanation:

since y=4 multiplied by x

so, 5x4=20

3x4=12

4x4=16

I need this whole page solved please

Answers

Answer:

5. 540°

Step-by-step explanation:

m<a + m<c = 180°

m<h + m<f = 180°

m<k + m<m = 180°

Then m<a + m<c + m<h + m<f + m<k + m<m = 180° x 3 = 540°

Assume the domain of the function is {1,2,3,...}. Determine the theta notation for the function f(n)=7n^2+4n+2

Answers

We have that O(n²) is the theta notation for 7n² + 4n + 2.

Let's give big-Oh a formal definition:

O(g(n)) = {the set of all f such that 0 [tex]\leq[/tex] f(n) [tex]\leq[/tex] cg(n) for any n >= n₀ fulfilling positive constants c and n₀}

To show this

We need to find c and n₀ such that:

7n² + 4n + 2 <= cn² for all n >= n₀ .

Divide both sides by n², getting:

7 + 4/n + 2/(n²) <= c for all n >= n₀ .

If we choose n₀ equal to 1, then we need a value of c such that:

7 + 4 + 2 <= c

We can set c equal to 13. Now we have:

7n² + 4n + 2 <= 13n² for all n >= 1 .

Hence, 7n² + 4n + 2=O(n²)

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How do you round 56.053 to the nearest whole number

Answers

Answer:

56

Step-by-step explanation:

all your doing is removing the .053 to get your whole number

What is the domain of the function shown on the graph?

Answers

The asnwer is C

for finding domain look at just x-axis from left to right , because there are arrows , so domain is all real numbers or from negative infinity to positive infinity

Please give brainliest

Somebody please assist me solve

(2) The number of incoming calls reaching the switchboard of a computer per minute is thought to be a Poisson random variable with rate 6.5. Compute
i)The probability that during any given minute, the switchboard will
receive between 4 and 6 calls inclusive.
ii)The probability that the operator will have a breathing spell of at least
30 seconds between successive calls.
iii)The mean time lag between two calls.

Answers

P(n) = (e^-λ . λ^n)/n! where λ = 6.5
P(4) = (e^-6.5 x 6.5^4) / 4! = 0.111822…
P(5) = (e^-6.5 x 6.5^5) / 5! = 0.145368…
P(6) = (e^-6.5 x 6.5^6) / 6! = 0.157829…
P(between 4 and 6 inclusive) = 0.111822… + 0.145368… + 0.157829… = 0.4150 (4sf)

In a 30 second interval λ = 6.5 / 2 = 3.25
P(0) = (e^-3.25 x 3.25^0) / 0! = 0.03877
The probability of getting no calls in a 30 second interval is 0.03877 (ie less than 4%)

If the average number of calls in a minute is 6.5 then the average interval between calls will be 60/6.5 = 9.23 seconds.

Please help with this difficult one...

Answers

The composite function is given as follows:

[tex](f \circ g)(x) = \frac{2x + 6}{3x + 22}[/tex]

The domain of the composite function is: [tex]\mathbb{R} - \left\{-\frac{22}{3}, 3\right\}[/tex]

What is the composite function of f(x) and g(x)?

The composite function is given by:

[tex](f \circ g)(x) = f(g(x))[/tex]

In this problem, the functions are:

[tex]f(x) = \frac{2}{x + 3}[/tex].[tex]g(x) = \frac{13}{x + 3}[/tex].

Hence the composite function is:

[tex](f \circ g)(x) = f\left(\frac{13}{x + 3}\right) = \frac{2}{\frac{13}{x + 3} + 3} = \frac{2(x + 3)}{13 + 3(x + 3)} = \frac{2x + 6}{3x + 22}[/tex]

For the domain, we have to remove the points outside the domain of both the primitive and the composite functions, that is, the zeroes of the denominators, hence:

[tex]x + 3 \neq 0 \rightarrow x \neq 3[/tex]

[tex]3x + 22 \neq 0 \rightarrow x \neq -\frac{22}{3}[/tex]

Hence the domain is:

[tex]\mathbb{R} - \left\{-\frac{22}{3}, 3\right\}[/tex]

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what is the name of the shape graphed by the function theta=-4pie/3

Answers

Step-by-step explanation:

On a polar plane, the shape will be a line that goes through the pi/2- pi quadrant , and 3pi/2- 2pi quadrant

On a Cartesian or rectangular plane, the shape will be a line as well passing through 2nd and 4th quadrant

Help pls ???????????

Answers

The second derivative of the first function is s"(x) = = -[8e^(x/5) - 2]e^(x/5)/25(e^(x/5) + 2)³.

The second derivative of the second function is; k''(t) = (36t² - 6)e^(-3t²)

How to find the second derivative?

1)  We are given the function;

s(x) = 4/(1 + 2e^(-0.2x)

First derivative is;

ds/dx = [8e^(x/5)]/5(e^(x/5) + 2)²

Second Derivative is;

d²s/dx² = -[8e^(x/5) - 2]e^(x/5)/25(e^(x/5) + 2)³

At x = 0;

d²s/dx² = -[8e^(0/5) - 2]e^(0/5)/25(e^(0/5) + 2)³

d²s/dx² = 8/675

B) We are given the function;

k(t) = e^(-3t²)

The first derivative is;

dk/dt = -6te^(-3t²)

The second derivative is;

k''(t) = (36t² - 6)e^(-3t²)

At t = 1, we have;

k''(t) = (36(1)² - 6)e^(-3(1²))

k"(t) = 1.494

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hey
can someone solve this 4 me​

Answers

Answer:

∠a = 50°

∠b = 130°

∠c = 130°

Explanation:

Following Vertical Angles Theorem:

∠(2a - 50)  =  ∠a2a - 50 = a2a - a = 50a = 50

A straight line has 180° angle measure, ∠c and ∠a lies on a straight line

∠c + ∠a = 180°∠c + 50° = 180°∠c = 180° - 50°∠c = 130°

Also, following vertical angle theorem:

∠b = ∠c∠b = 130°

Circle G is shown. Line segment F G is a radius with length 3.
In circle G, r = 3 units. Maria draws a circle with double the area of circle G.

What is the area of Maria’s circle?

6Pi units squared
9Pi units squared
12Pi units squared
18Pi units squared

Answers

The area of Maria’s circle is 18π square units option fourth is correct.

What is a circle?

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

The figure is missing.

Please refer to the attached picture for the figure.

We have given the radius of the circle as 3 units

r = 3 units

Area of circle = πr² = π(3)² = 9π square units

The area of Maria’s circle = 2(9π) = 18π square units

Thus, the area of Maria’s circle is 18π square units option fourth is correct.

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I need the answer to this equation

Answers

What’s the question ?

Given the data set (4,85),(7,92),(14,110), which of the following equation best represents a line of best fit

Answers

Gggggghhhgghgggghhhjjhh

given: f(x)=2x^2 and g(x)=x-8. Find f(g(x))

Answers

The value of the composite function f(g(x)) is 2(x-8)^2

Composite functions

Composite functions are functions in another function. Given the following functions

f(x)=2x^2 and

g(x)=x-8

Determine f(g(x))

f(g(x)) = f(x-8)

f(x-8) = 2(x-8)^2

f(g(x)) = 2(x-8)^2

Hence the value of the composite function f(g(x)) is 2(x-8)^2

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Evaluate the expression.
-2(12 - 2 (-4))²
What is the value of the expression?
Enter your answer in the box.

Answers

Answer:

-2(10(-4))²

-2(-40)²

-2 × 1600

= -3200

Answer: = -3200

Step-by-step explanation:

took the test

Read the following two statements. Then, if possible, use the Law of Detachment to draw a conclusion. The doctor recommends rest if the patient has the flu. The doctor recommends rest. not possible The patient does not have the flu. If the doctor recommends rest, the patient has the flu. The patient has the flu.

Answers

The doctor recommends rest if the patient has the flu. Then the correct option is A.

What is decision-making?

Determining the proper option, acquiring evidence, and exploring various options are all steps in the decision-making process.

Read the following two statements.

Then, if possible, use the Law of Detachment to draw a conclusion.

Then the correct option is A.

The doctor recommends rest if the patient has the flu.

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helpp me please
Find the missing term.
The roots of x2 − ( ) + 34 are 5 ± 3i.

Answers

Answer: 10

Step-by-step explanation:

The sum of the roots is [tex](5+3i)+(5-3i)=10[/tex], so the answer is 10

. Solve for the missing value (x).
Include the correct unit of measure in your answer.

12.5mg : 5mL = 24mg : x mL

Answers

The missing value of x will be 9.6 mL.

What are ratio and proportion?

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

The equation is given below.

12.5 mg : 5 mL = 24 mg : x mL

Then the value of x will be

12.5 / 5 = 24 / x

          x = (24 × 5) / 12.5

          x = 9.6 mL

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