Look at the triangle show on the right. The Pythagorean Theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse. Margaret uses this theorem to simplify and rewrite the expression (b/r)^2 + (a/r)^2 using the triangle shown. Which trigonometric identity can she prove with her expression? *

Answers

Answer 1

Answer:

[tex]cos^2\theta + sin^2\theta = 1[/tex]

Step-by-step explanation:

Given

[tex](\frac{b}{r})^2 + (\frac{a}{r})^2[/tex]

Required

Use the expression to prove a trigonometry identity

The given expression is not complete until it is written as:

[tex](\frac{b}{r})^2 + (\frac{a}{r})^2 = (\frac{r}{r})^2[/tex]

Going by the Pythagoras theorem, we can assume the following.

a = Oppositeb = Adjacentr = Hypothenuse

So, we have:

[tex]Sin\theta = \frac{a}{r}[/tex]

[tex]Cos\theta = \frac{b}{r}[/tex]

Having said that:

The expression can be further simplified as:

[tex](\frac{b}{r})^2 + (\frac{a}{r})^2 = 1[/tex]

Substitute values for sin and cos

[tex](\frac{b}{r})^2 + (\frac{a}{r})^2 = 1[/tex] becomes

[tex]cos^2\theta + sin^2\theta = 1[/tex]


Related Questions

6. What would a+c< 100 mean in this situation?|

Answers

Answer:

Sum of a and c is less than 100.

Step-by-step explanation:

^

The following numbers are arranged in ascending order. Their median and mean are same .Find the value of x: 4, 7 ,x + 1, x+ 3 ,x + 4, 14, 16​

Answers

Answer:

x=7

Step-by-step explanation:

(4+7+x+1+x+3+x+4+14+16)/7​=x+3

(11+x+1+x+3+x+4+14+16)/7​=x+3

(49+3x)/7​=x+3

49+3x/7​=x+3

49+3x​=7x+21

49=4x+21

28=4x

x=7

SOMEONE PLEASE HELP ME I NEED IT

Answers

Answer: m=-5/11

Step-by-step explanation:

To find the slope of two points use the formula m=y2-y1/x2-x1

Answer:

-5/11

Step-by-step explanation:

(21,-4) & (10, 1)

x1, y1 x2,y2

Slope = (y2 - y1)/(x2 - x1)

= (1 - (-4))/(10 - 21)

= -5/11

You work in a grocery store warehouse recording shipments. A driver delivers 25 crates of strawberries for distribution. A store calls needing seven crates of strawberries. After you fill this order, how many crates of strawberries are available for other stores?

Answers

Answer:

18 crates

Step-by-step explanation:

Data provided in the question

The Number of  strawberries for distribution delivered is 25 crated

Now he seven crates is required

So the remaining crates left is

= 25 - 7

= 18 crates

hence, after filling the order the number of order crates of strawberries is 18 crates and the same is to be considered

3.f(-4)-3.g(-2) please ​

Answers

Step-by-step explanation:

3.f(-4)-3.g(-2)

3 [f(-4) - g(-2)]

need help with a question ​

Answers

Answer:

You need to put the Question to get us to answer it sorry

Step-by-step explanation:

What is the constant RATIO (how do you you multiply ) of the exponential curve that passes through the points (0, 3) and (5, 96) ?

Answers

Answer:

The answer is 1.788

Step-by-step explanation:

A 2-pound bag of sugar contains 227 one-teaspoon servings and costs $2.49. A batch of muffins uses 1 2 cup of sugar. How many whole batches can you make if you use as much of the sugar as possible? What is the cost of sugar for each batch? (1 cup = 48 teaspoons; do not consider leftover sugar in the cost calculation.) You can make a total of batches at $ per batch.

Answers

Answer:

a) 9 whole batches can be made

b) The cost of sugar for each batch = $0.26

Step-by-step explanation:

A 2-pound bag of sugar contains 227 one-teaspoon servings and costs $2.49.

This means:

2 pound bag of sugar = 227 teaspoon servings

2 pounds bag of sugar cost $2.49

We are told that:

A batch of muffins uses 1/2 cup of sugar.

a).How many whole batches can you make if you use as much of the sugar as possible?

(1 cup = 48 teaspoons)

Hence, A batch of muffins = 1/2 cups of sugar = 48 teaspoons of sugar ÷ 2

= 24 teaspoons of sugar

Hence:

24 teaspoons of sugar = 1 batch of muffins

227 teaspoons of sugar = x

Cross Multiply

24 × x = 1 × 227

x = 227/24

x = 9.4583333333 batches of muffins

We are asked to name the number of whole batches that can be made.

Therefore, 9 whole batches of muffins can be made

b) What is the cost of sugar for each batch? (do not consider leftover sugar in the cost calculation.) You can make a total of batches at $ per batch.

Since we are not to consider the leftover sugar in the cost calculation,

1 batch = 24 teaspoons of sugar

9 whole batches =

9 × 24 teaspoons = 216 teaspoons of sugar was used

The left over = 227 - 216 = 11 teaspoons of sugar is left

We know that:

227 teaspoons of sugar = $2.49

216 teaspoons of sugar = x

Cross Multiply

= 216 × $2.49/227

= $2.369339207

24 teaspoons of sugar = 1 batch of muffins

Therefore,

216 teaspoons of sugar =

$2.369339207

24 teaspoons of sugar =

24 × $2.369339207/ 216

= $0.2632599119

Approximately = $0.26

Therefore, the cost of sugar for each batch = $0.26

A music app charges $2 to download the app plus $1.29 per song download, Identify the rate of change.

Answers

Answer: 1.29

Step-by-step explanation: y=1.29x+2

1.29 is the coefficient of X, slope, and the rate of change.

what is the relationship between the radius and diameter of a circle?

Answers

The Radius is the distance from the center outwards. The Diameter goes straight across the circle, through the center.

The relationship between the radius and diameter of a circle is that the diameter is twice the length of the radius.

In other words, the diameter of a circle is equal to 2 times the radius. Mathematically, this relationship can be expressed as:

Diameter (D) = 2 * Radius (r)

This relationship is consistent for all circles. No matter the size of the circle, the diameter will always be exactly twice the length of the radius. The radius is the distance from the center of the circle to any point on the circle's circumference, while the diameter is the distance from one point on the circumference to another, passing through the center. Understanding this relationship is essential in various geometrical calculations and formulas involving circles.

To know more about diameter:

https://brainly.com/question/32968193


#SPJ6

To win a contest, the number of beans in a jar has to be guessed within 20 of the actual number. If the number of beans in the jar is 645, which equation can be used to find the minimum and maximum number of beans that will win the contest, and what is the maximum guess that could win?

|x – 645| = 20; maximum guess: 635 beans
|x – 645| = 20; maximum guess: 665 beans
|x – 20| = 645; maximum guess: 635 beans
|x – 20| = 645; maximum guess: 665 beans

Answers

Answer:

B

Step-by-step explanation:

Just took the test on edge 2020

The maximum guess that could win is,

⇒ |x - 645| = 20; the maximum guess is 665.

Therefore, Option b is correct.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Since, We have given the information that the jar has to be guessed within 20

So, the total has to be equal to 20.

Hence, the equation which is the required equation to calculate the minimum and maximum number of beans that will win the contest is,

|x - 645| = 20

When we will remove the modulus we will get two values + and -

So, x = 20 + 645 = 665

And x = 20 - 645 = -625

Hence, the maximum guess is 665.

Therefore, Option b is correct.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ7

Three ice cream cones cost $8.40. At this rate, how much do two ice cream cones cost?​

Answers

Answer:

two cost 5.6 dollars

Step-by-step explanation:

8.4 / 3=2.8$

2.8*2=5.6$

Answer:

$5.60

Step-by-step explanation:

You first take 8.40 and divide it by 3. Which makes you get 2.8. 2.8 is the cost per ice cream cone. Do 2.8 times 2 to get 5.6.

Estimate the sum 78.5+51.4

Answers

The answer to that question is 129.9. Hope this helps and if you could can you mark as brainliest? I’m trying to rank up and I just need 2 more!

Answer:

129.9

Step-by-step explanation:

78.5

+ 51.4

129.9

Hope this helps! (:

Which graph shows the solution to the inequality −2(2x+3)≤26?
pls help

Answers

Answer:

the answer is c

Step-by-step explanation:

Please help quickly!

Answers

Answer:

A

Step-by-step explanation:

You are subtracting 2 from y every step.

Arron can join a gym for $19.99 per month plus an annual fee of $12.80 or he can pay $21.59 per month. He thinks the second option is better because he plans to use the gym for 10 months. Is Aaron correct ? Set up an equation (with variables on both sides) to describe the situation.

Answers

Answer: Aaron is wrong. The first option is better as it costs less than the second option.

Step-by-step explanation:

Arron can join a gym for $19.99 per month plus an annual fee of $12.80.

Since Aaron wants to spend 10 months at the gym, this will cost him:

= $12.80 + ($19.99 × 10)

= $12.80 + $199.9

= $212.7

Paying $21.59 for 10 months will be:

= $21.59 × 10

= $215.9

The first option is better as it costs less than the second option.

can someone please help me with this question

Answers

Answer:

60 in^3

Step-by-step explanation:

You just multiply the base by the height.

Answer:600

Step-by-step explanation: hope this helps you

The perimeter of a rectangle is 70cm. If the length of the rectangle is 5cm more than its breadth, find the dimensions of the rectangle.

Plsss help I put 15 points

Answers

Hope it helps man .....

What is the value of x?

Answers

Answer:

As x is the exterior angle

Step-by-step explanation:

therefore

let name the angle exterior angle be ACE

interior angleABC=76°and angleBAC=55°

sum of 2 interior angle is equal to exterior angle

=76+55=x

=131=x

A function f(x) is graphed.
What is the slope of the function?
ma
What is the y-intercept of the function?
b.
Which equatich represents the graph of the function?

Answers

The slope is 2. The y-intercept is 1. The equation is y=2x +1

Answer:

slope:1/2

y intercept:-1/2

equation of the line: y=1/2x-1/2

Step-by-step explanation:

choose two points from the line( I chose (3,1) and (-1,-1)) and then using y1-y2/x1-x2, do 1 - -1/3 - -1 which is 2/4 simplified to 1/2. the slope is 1/2.

now to find the y intercept, you just have to plug in the numbers from one of the sets of points you chose and your slope using y = mx +b(I will be using the point (-1,-1)). equational look like this: -1=1/2•-1+b

since b is the y intercept, solve for b and you get b= -1/2.

so nowsince you know the slope and the y intercept you just plug it in to the equation

y = mx + b and you get y=1/2x-1/2.

pls respond ,.... 25 points

Answers

The answer is B, hope this helped you!

Which of the following equations has a solution of x = 5
10x/2=1


2 (x – 3) + 8 = 6x – 18
2x – 5 + 3x = 8 + 14
O 4(1 - 2) + 3 = -2 (2 + 2) + 1

Answers

Answer:

equals 345762819

Step-by-step explanation:

i dont know for short i just want a points

The ocean exploration institute has a submarine that is used to study patterns of fish moment the submarine started at the surface of the water and collected data at three different depths each time the submarine dove 40 feet down write an integer equation to model the situation and determine the lowest depth of the submarine

Answers

Answer:

120 feet

Step-by-step explanation:

Given that the submarine started at the surface of the water and collected data at three different depths.

As each time the submarine dove 40 feet down, so,

the depth covered in one dive = 40 feet.

From the surface, the depth covered in 1 drive, [tex]d_1= 40[/tex] feet

Similarly, the total depth covered in 2 drive, [tex]d_2 = 2\times 40= 80[/tex] feet.

So, for any integer [tex]n[/tex], the depth covered in [tex]n[/tex] drive,

[tex]d_n=40n[/tex]

This is the required integer equation to model the situation.

Since, for three different depths, there must be 3 drive and the submarine will be at the lowest depth after 3rd dive.

So, for the lowest depth, n=3

Hence, the lowest depth = 40x3= 120 feet.

A girl’s club held a fundraiser last year and raised $600 for the local soup kitchen. This year they raised $960. What is the percent change in the total amount raised by the girl’s club?
The percent change is 0.38%.
The percent change is 0.6%.
The percent change is 38%.
The percent change is 60%.

Answers

Answer: option D

Step-by-step explanation:

Answer:

D.) The percent change is 60%

Step-by-step explanation:

I know this because 960-600= 360

360÷600= .6

.6= .60

.60= 60%

Hope this helped!!! :)

Which of the following is equivalent to 5(7 - p)?
5p - 35
-5p + 35
35 + 5p
-35 + 5p

Answers

the answer is 35 - 5x :)

Answer:

-5p+35

Step-by-step explanation:

=(5)(7+−p)

=(5)(7)+(5)(−p)

=35−5p

=−5p+35

Which number line shows the solution to the inequality –2(3x – 1) < 8? A. Number lines from minus five to five by increament of one from left to right and each tick mark is labeled. Shaded part from minus infinity to open circle at minus one B. Number lines from minus five by increament of one from left to right and each tick mark is labeled. Shaded part from open circle at minus one to infinity C. Number lines from minus five by increament of one from left to right and each tick mark is labeled. Shaded part from minus infinity to open circle at two D. Number lines from minus five to five by increament of one from left to right and each tick mark is labeled. Shaded part from open circle at two to infinity

Answers

Answer:

The correct option is B.

Step-by-step explanation:

The inequality is: -2(3x - 1) < 8.

Solve for x as follows:

-2(3x - 1) < 8

-6x + 2 < 8

-6x < 6

-x < 1

x > -1

The solution for x is in the interval (-1, ∞].

The number line will be:

B. Number lines from minus five by increment of one from left to right and each tick mark is labeled. Shaded part from open circle at minus one to infinity

​can someone help me solve this system. thanks
2y = 6
3(x + y) = 12

Answers

Answer

y=3   x=1

Step-by-step explanation:

3(x+3)=12

3x+9=12

subtract 9 from both sides to get...

3x=3

divide 3 from both sides to get...

x=1

Step-by-step explanation:

this is very easy

2y=6

y=2/6=3

so ,

3(x+y)=12

3x+3y=12

3x+3+3=12

3x+9=12

3x=12-9

3x=3

x=3/3

x=1

What value is equivalent to (3^6)^3?

Answers

Answer:

1/2 is the simplified fraction for 3/6.

Step-by-step explanation:

im not sure but i think thats it

Answer:

387,420,489

Step-by-step explanation:

First, evaluate what is in the parentheses. This is equivalent to 729. Now take this number, and cube it (or do 729^3). This is equivalent to 387420489.

The ^ symbol means 'to the power of'.

For example, if you want to raise the number 5 to the power of 4, then you would do 5 ^ (to the power of) 4. Also looks like this:  [tex]5^{4}[/tex]

Which of these items is the better buy? A. An 8-pack of glue sticks for $3.99 or 1 glue stick for $0.54? B. A 12-pack of tape for $2.50 or 1 roll of tape for $0.19 c. A 100-pack of pencils for $4.88 or 1 pencil for $0.05 d. A 50-pack of paper clips for $0.89 or a 25-pack of paper clips for $0.45

Answers

Answer: A is the 8-pack, B is the single roll, C is the 100 pack, D is the 50 pack.

Step-by-step explanation:

For each of these, multiply the smaller number by a number that has a product of the bigger number, example D. multiply 25 by 2 to get 50, then compare the totals.

Answer:

the first one is an 8 pack of glue sticks

the second one is 1 tape roll for .19

the third one is 100 pack of pencils for 4.88

the fourth one is a 25 pack of paper clips

Step-by-step explanation:

ITS SUPER EASY PLEASE HELP ITS DUE IN AN HOUR PLEASEEEEEEEEEEEEEEEEEE

Answers

I’m almost positive that the anwser is -20.

Answer:

4*(-5) = -20

Step-by-step explanation:

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