if secx+cosecy = 2, and sinx+cosy=k evaluate 3k/4.

Need help ASAP!

Answers

Answer 1

The equations secx+cosecy = 2, and sinx+cosy=k are trigonometry equations

The result of [tex]\frac {3k}4[/tex] is [tex]\frac{3\sin(y)\cos(x)\sin(x) + 3\sin(y)\cos(x)\cos(y)}{2[\cos(x) + \sin(y)]}[/tex]

How to evaluate 3k/4

The equations are given as:

secx+cosecy = 2, and sinx+cosy=k

Divide both equations

[tex]\frac{\sin(x) + \cos(y)}{\sec(x) + \csc(y)} = \frac k2[/tex]

Divide through by 2

[tex]\frac{\sin(x) + \cos(y)}{2[\sec(x) + \csc(y)]} = \frac k4[/tex]

Express sec and cosec as inverse ratios

[tex]\frac{\sin(x) + \cos(y)}{2[1/\cos(x) + 1/\sin(y)]} = \frac k4[/tex]

Take the LCM

[tex]\frac{\sin(y)\cos(x)[\sin(x) + \cos(y)]}{2[\cos(x) + \sin(y)]} = \frac k4[/tex]

Expand

[tex]\frac{\sin(y)\cos(x)\sin(x) + \sin(y)\cos(x)\cos(y)}{2[\cos(x) + \sin(y)]} = \frac k4[/tex]

Multiply through by 3

[tex]\frac{3\sin(y)\cos(x)\sin(x) + 3\sin(y)\cos(x)\cos(y)}{2[\cos(x) + \sin(y)]} = \frac {3k}4[/tex]

Rewrite as:

[tex]\frac {3k}4 =\frac{3\sin(y)\cos(x)\sin(x) + 3\sin(y)\cos(x)\cos(y)}{2[\cos(x) + \sin(y)]}[/tex]

Hence, the result of [tex]\frac {3k}4[/tex] is [tex]\frac{3\sin(y)\cos(x)\sin(x) + 3\sin(y)\cos(x)\cos(y)}{2[\cos(x) + \sin(y)]}[/tex]

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Related Questions

combine like terms 4(p+3)-8 i need the answer quick

Answers

Answer:

4p + 4

Step-by-step explanation:

Original expression:

4(p + 3) - 8

Apply the distributive law:  a(b + c) = ab + ac

⇒ 4p + 12 - 8

Subtract 8 from 12:

⇒ 4p + 4

The store buys a vase for $25. The vase sells for $55. What is the markup on the vase?

Answers

Answer:

The answer is $30

Step-by-step explanation:

Markup refers to the amount added to the cost price of goods to cover overhead and profit.

The vase was bought for $25, then is now selling for $55

$55-$25=$30

hope this helps please mark brainliest :)

55 - 25 =30 its pretty easy

Can anyone please help me with this ASAP

Answers

Yeah what is it ? I can help you

Estimate 26 % of 160.

Answers

Answer:

about 42 the not rounded is 41.6

Answer:

60

Step-by-step explanation:

Multiply to find that the answer is: 41.6

To estimate, simply round the numbers before multiplying. That would be thirty percent of 200. The answer is 60. This is close to 41.6 and is a reasonable estimate.

Find the value of x if mean of the given data is 4.5
5, 7, 7, 8, x, 5, 4, 3,1 and 2

Answers

Answer:

Step-by-step explanation:

First add what you have.

Sum = 5 + 7 +7+8 + x + 5 + 4 +3 + 1 +2

Sum =  x + 42

Now when you divide this by the number of terms, you get

(x + 42) / 10

The answer is 4.5

(x + 42) / 10 = 4.5                 Multiply by 10

x + 42 = 4.5 * 10

x + 42 = 45                           Subtract 42

x = 45  - 42

x = 3

good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.

Answers

Answer:

C

Step-by-step explanation:

Causation is when one thing causes another.

Correlation means one thing is related to another but doesn't cause it.

A - we know more rain means more rainfall which means more water in a river.

B - We know hotter temperature means things melt or evaporate faster.

C - This does not work. How does vision loss cause people to have hearing aids? There might be a correlation but it can't cause it.

D - We know fewer mistakes mean higher grades.

Which situation best demonstrates the phrase "correlation is not causation"?

O As rainfall increases, so does the water level in the river.

O The hotter the temperature, the faster ice will melt

O As the number of people with vision loss increases, the sale of hearing aids increases. ✓

In this case ,the correlation isn't causation because the sale of hearing aids hasn't increased because of increasement in vission loss cases but hearing aids cases but perhaps there's a correction of the sales of hearing aids and vision loss

O The fewer mistakes a student makes on a math test, the better their grade is on the math test.

Deon runs each lap in 4 minutes. He will run at most 32 minutes today. What are the possible numbers of laps he will run today? Use n for the number of laps he will run today.
Write your answer as an inequality solved for n.

Answers

Answer:

4n ≤ 32

/4      /4

n ≤ 8, he could run less than 8 or just 8 laps,

so possible laps:

1, 2, 3, 4, 5, 6, 7, or 8 laps he could've ran.

I don't understand this​

Answers

Answer:

Given that measure 2 is 79 degrees, we know it'll be supplementary to angle 1 meaning that that both angle measures 1 and 2 will equal 180 degrees:

79 + x = 180

-79        -79

x = 101, ∠1 = 101°

Angles 2 and 4 are vertical, so they are congruent meaning they measure the same degrees:

if ∠2 = 79, then ∠4 is also equal to 79°

Now that we found the measure of angle 1, we can determine the measure of angle 3 since they are vertical as well, (vertical angles are congruent, meaning they measure the same degrees):

if ∠1 = 101, then ∠3 is also equal to 101°

02.
39
za
Diagram NOT
accurately drawn
63
D
E
G
ABC is parallel to DEFG
BCBF
Angle ABE = 39"
Angle CFG = 63
Work out the size of angle x
Give a reason for each stage in your working.
HELP

Answers

The measure of angle x from the diagram is 102 degrees

Lines and angles

From the given diagram, we can see that the measure of angle "x" lies on the same line with 39 degrees. Since the sum of angles on a straight line is 180 degrees, hence;

39 + x + 39 = 180

78 + x = 180

Subtract 78 from both sides

78 + x - 78 = 180 - 78

x = 180 - 78

x = 102 degrees

Hence the measure of angle x from the diagram is 102 degrees

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Who was alan turing and what were his contributions to the field of mathematics?.

Answers

Moder computer science his work on computation theory

Answer:

Alan Mathison Turing OBE FRS was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist.

Born: June 23, 1912, Maida Vale, London, United Kingdom

Died: June 7, 1954, Wilmslow, United Kingdom

Turing's main contribution to mathematics, however, was his work on computation theory. Presaging the invention of the modern computer, Turing designed an abstract computing device known as the Turing machine — an entirely virtual construct which could perform calculations and follow instructions.

please solve!!!!!!!!!!!!!!!!!!!!!!!

Answers

Solution:

We know that:

[tex]\bullet \ \ \tex\text{Area of triangle:} = \frac{1}{2} \times \tex\text{Base} \times \tex\text{Height}[/tex]

Let the base of the triangle be 11 yd. If we extend the base, it will allow us to find the height of the triangle, which is 8 yd.

Using the formula:

[tex]\bullet \ \ \tex\text{Area of triangle:} = \frac{1}{2} \times 11 \times 8[/tex]

Now, let's simplify.

[tex]\bullet \ \ \tex\text{Area of triangle:} = \frac{1}{2} \times 11 \times 8[/tex]

[tex]\bullet \ \ \tex\text{Area of triangle:} = 11 \times 4[/tex]

[tex]\boxed{\bold{\tex\text{Area of triangle:} = 44 \ \tex\text{yd}^{2}}}[/tex]

I NEED HELP! I WILL GIVE BRAINLIEST

Answers

Answer:

As time increases, grams decrease

To describe the relationship between the two quantities, we first have to identify what those two quantities are.

Well, it says it right on the graph.

Our two quantities are time (the x value) and grams (the y value)

So, what is the relationship between the two quantities?

Well, let's first look at what each one is doing.

Well, time is increasing

Grams, however, are decreasing

So, the relationship is as follows:

As time increases, grams decrease

the perimeter of rectangular lawn is 300 m. if the length and breadth are in ratio of 8:7, find the area of the lawn​

Answers

Answer:

5600 m²

Step-by-step explanation:

The perimeter of a rectangle is 2x + 2y = 300

If we have a ratio of length to breadth, we can just assign variables to simplify the problem. It doesn't matter if x is breadth or length and the same goes for y. But in this case, I just choose x as length and y as breadth.

x = 8n

y = 7n

2(8n) + 2(7n) = 300

30n = 300

n = 10

so, plugging n into x and y

x = 8(10) = 80

y = 7(10) = 70

Area of a rectangle

A = xy

A = (80)(70) = 5600 m²

HELPPP FOR BRIANLEST!!!!

Answers

Answer:

12/17

Step-by-step explanation:

total that are NOT Toe Knows shoe (7) plus total that are NOT pleased (10) and subtract total that are not toe knows and not pleased (5)

7 + 10 - 5 = 12

over total (17)

12/17 doesn't simplify

14, 9, 7, 13, 15, 9, 10
What is the mode of this data?

Answers

Answer: 9

Step-by-step explanation: To find the mode, you order the numbers from lowest to highest and see which number appears the most often.

Help me please!!!!!!!!!!!!!!!

Answers

Answer:

[tex] \frac{5}{6} \: - \frac{5}{6} [/tex]

Step-by-step explanation:

[tex] \sqrt{ \frac{25}{36} } = \frac{ \sqrt{25} }{ \sqrt{36} } = \frac{5}{6} [/tex]

$4000 is divided between three children in the ratio 2:3:5.
How much does each child receive?​

Answers

Okay so here is how it works:

Because 2:3:5 is the ratio 10 is the total because 2+3+5 is 10 right?

You therefore equate 10 to 4000

10=4000

so if 10 is equal to 4000 what about 2,3 or 5?

2/10×4000=800

3/10×4000=1200

5/10×4000=2000

Hope this anwered your question

Help………dndjrjrjrjrjrrhrhd

Answers

Not a math wizard, but this is what you get when completed on a calculator

please hellllllp i need to get these done

Answers

Answer:

56

Step-by-step explanation:

180 = Triangle total angle amount

180 - 68 = 112

112/2= 56

Have an amazing day!!

PLEASE RATE AND MARK BRAINLIEST!!!

Your answer is y = 56.

The New Horizons is an interplanetary space probe that approached the dwart planet Pluto in 2015. How many arc degrees of Pluto are visible to the New Horizons space probe while approaching the dwarf planet?

Answers

The value of angle x which is substended in the circle will be D. 342.6°.

How to calculate the circle?

From the information given, it has been depicted that the value of the angle that's facing x is 17.4°.

Therefore, the value of x which is inscribed in the circle will be:

= 360° - 17.4°

= 342.6°

In conclusion, the correct option is 342.6°.

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write equation from 2 points. I need help with 12 and 11.

Answers

12)

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{4}}}\implies \cfrac{-2}{-8}\implies \cfrac{1}{4}[/tex]

now, I used y₂ - y₁  and x₂ - x₁, is pretty much the same slope the other way.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{\cfrac{1}{4}}(x-\stackrel{x_1}{4}) \\\\\\ y-5=\cfrac{1}{4}x-1\implies y=\cfrac{1}{4}x+4[/tex]

13)

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{0}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{(-2)}}}\implies \cfrac{-2}{-4+2}\implies \cfrac{-2}{-2}\implies 1[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_2=m(x-x_2) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{1}(x-\stackrel{x_1}{(-4)}) \\\\\\ y=1(x+4)\implies y=x+4[/tex]

notice, for the point-slope form, we can use either x₁ , y₁  or x₂ , y₂ , doesn't quite matter, so long we use the corresponding coordinates.

Answer number 8 and 10 please

Answers

Answer:

Q8 It is because the data collected are too scattered and cannot show an obvious trend.

if it's correct pls mark brainliest tks

A radio station is giving away a total of Rs 124,000 in August on promotion. If they increase the amount given away each day by Rs 100.

(i) How much should they give away the first day?
(ii) How much have they give away on the 15th day ?​

Answers

On the first day the company is giving Rs124, 000.

On the fifteenth day the company will give Rs 125400

The amount they wanted to give in august for promotion is Rs 124,000. They increased the amount each day by Rs 100.

Therefore, the sequence will be as follows;

124,000, 124,100, 124,200 .......

i.

The amount they will give on the first day is Rs124, 000

Arithmetic progression formulaaₙ = a + (n - 1)d

ii

The sequence is increasing by 100. Therefore,

common difference = 100

first term = 124, 000

Therefore,

a₁₅ = 124000 + (15 - 1)100

a₁₅ = 124000 + 1400

a₁₅ = 125400

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I will give brainliest
Find Volume of cone

Answers

half of 4 is 2

22 * 2 44

what is the answer to 35r−21<−35r+19

Answers

Answer:

r < 4/7

Step-by-step explanation:

35r−21<−35r+19

35r + 35r < 19 + 21

70r < 40

r < 40/70 or r < 4/7

The epicenter of an earthquake is the point on Earth’s surface directly above the earthquake’s origin. A seismograph can be used to determine the distance to the epicenter of an earthquake. Seismographs are needed in three different places to locate an earthquake’s epicenter. Find the location of the earthquake’s epicenter if it is 3 miles away from (2,1) , 4 miles away from (5,-3) , and 5 miles away from (10,1)

Answers

Based on the calculations, the location of the earthquake’s epicenter is at (-1, 1).

What is an epicenter?

An epicenter can be defined as the point on the surface of planet Earth, which is perpendicular to the hypocenter (focus) and directly above the earthquake’s origin. Also, it indicates where the seismic waves from an earthquake are most intense.

For this exercise, we would set the epicenter at x and y. Using the equation of a circle, we have the following:

At A (2, 1) and 3 miles away;

[tex](y-1)^2+(x-2)^2=3^2[/tex]   ......equation 1.

At B (-5, 3) and 4 miles away;

[tex](y-3)^2+(x-(-5))^2=4^2\\\\(y-3)^2+(x+5)^2=4^2[/tex]   ......equation 2.

At C (10, 1) and 5 miles away;

[tex](y-1)^2+(x-10)^2=5^2[/tex]   ......equation 3.

Subtracting eqn. 2 from eqn. 1, we have:

[tex](x-2)^2-[(x+5)^2]=3^2-4^2\\\\x^2-2x-2x+4-[(x^2+5x+5x+25)]=9-16\\\\x^2-4x+4-x^2-10x-25=-7\\\\-14x-21=-7\\\\-14x=-7+21\\\\-14x=14\\\\x=\frac{-14}{14}[/tex]

x = -1 when y = 1.

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Answer: i used desmos to graph the circles and from the graph, you can tell that the point of intersection (epicenter) is (5, 1)

Step-by-step explanation:

Helppppppppppppppppppppppppppp

Answers

Answer:

Answer B
z = 15

Step-by-step explanation:

The question is asking you what the value of each triangle would be if the total was 45 (The square). A equation for this would be:
45 = 3z

divide 3 on both sides to get:

15 = z

Find the measure of each angle

m∠A =

m∠B =

m∠BCA =

Answers

Solution:Finding the bottom left angle of the triangle:

Before we solve for each angle, let's find the bottom left angle of the triangle.

We know that:

Straight line = 106 + xStraight line = 180

This means that:

⇒ 106 + x = 180

Step-by step calculations:

⇒ 106 + x = 180

⇒ 106 - 106 + x = 180 - 106

x = ∠BCA = 74°

Solving for y:

We know that:

⇒ Sum of the interior angles of the triangle: 180°

This means that:

⇒ (74) + (3y + 22) + (4y) = 180

Step-by step calculations:

⇒ (74) + (3y + 22) + (4y) = 180

⇒ 96 + 7y = 180

⇒ 96 - 96 + 7y = 180 - 96

⇒ 7y = 84

⇒ 7y/7 = 84/7

⇒ y = 12

Finding the measure of each angle:

Step-by step calculations:

⇒ ∠B = 3y + 22

⇒ ∠B = 3(12) + 22

⇒ ∠B = 36 + 22

∠B = 58°

-------------------------------------

⇒ ∠A = 4y

⇒ ∠A = 4(12)

∠A = 48°

(87 POINTS I NEED ANSWER TODAY!!!) A right trapezoidal prism is sliced parallel to its base.

What is the shape of the resulting two-dimensional cross section?


trapezoid

parallelogram

rectangle

square

Answers

Answer:

trapezoid

Step-by-step explanation:

A right trapezoid has 2 parallel sides and 2 adjacent right angles.

In geometry, the base of a prism is the actual shape.

So the base of a triangular prism is the triangle, similarly the base of a pentagonal prism is the pentagon, etc.

Therefore, the base of a trapezoidal prism is the trapezoid itself.

If the prism is cut parallel to the base, then the cross section will be the same shape as the base.  So in this case, it will be a trapezoid.

Answer:

sQUARW

Step-by-step explanation:

A car travels 480 miles in 12 hours. What is the rate in miles per​ hour? In hours per​ mile

Answers

Answer: 40 miles per hour

Explanation: Divide the 480 by 12 hours and you get 40 mph

Answer:

40 miles per hour and .025 hours per mile

Step-by-step explanation:

480/12=40

12/480 = .025

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