Find the values of the six trigonometric functions of an angle in standard position if the point with coordinates (40, 9) lies on its terminal side.
 


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We can set up and solve a proportion to determine the actual distance between two cities using a scale of distance on a map. The setup would be 1/15 = 9.8/x and by solving this proportion we find the two cities are 147 miles apart.

The topic at hand involves understanding a proportion, an important part of mathematical concepts. More specifically, we are dealing with a proportion that involves distances on a map and the equivalent distances in real life.

For part a) of your question, the proportion can be expressed as '1 inch on the map is to 15 miles in real life as 9.8 inches on the map is to x miles in real life'. In mathematical terms, this can be written as:

1/15 = 9.8/x

For part b) of your question, we can determine the actual distance between Pittsburgh, Pennsylvania and State College, Pennsylvania by solving the proportion for x:

To do this, you can cross multiply (1 * x = 15 * 9.8), getting you x = 147 miles. This means Pittsburgh and State College are 147 miles apart in real life.

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In mathematics, you can use proportions to solve map reading and scale problems. The relationship between the map distance and real distance is given as a proportion 1/15 = 9.8/x. Using cross-multiplication, we find that Pittsburgh and State College are 147 miles apart in real life.

The relationship between the distance on the map and the actual distance can be represented as a proportion. This is a Mathematical concept often used in map reading and scale problems.

Given in the problem, we know that 1 inch on the map is equivalent to 15 miles in real life. Thus, a) the proportion can be set up like this: 1/15 = 9.8/x. Here x represents the actual distance between Pittsburgh and State College in miles.

To find the actual distance (b), we cross-multiply and solve for x: x = 9.8 * 15, which equals 147 miles. Therefore, Pittsburgh and State College are 147 miles apart in real life.

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Final answer:

To solve the proportion 0.75:n = 5:8, set the two ratios equal to each other and solve for n.

Explanation:

To solve the proportion 0.75:n = 5:8, we can set the two ratios equal to each other:

0.75/n = 5/8

Next, we can cross-multiply to solve for n:

0.75 * 8 = 5 * n

6 = 5n

Lastly, we can divide both sides of the equation by 5 to find the value of n:

n = 6/5

Therefore, n is equal to 1.2.

Answer:

Number of cakes decorated = 1.4 in a minute

Step-by-step explanation:

A baker decorates 42 cupcakes in 30 minutes. If she decorates cupcakes at the constant rate then we have to find the number of cakes the baker can decorate in 1 minute.

We should always use the unitary method to calculate the outcome.

∵ A baker can decorate in 30 minutes = 42 cakes

∴ baker can decorate in 1 minute = [tex]\frac{42}{30}=1.4[/tex] cupcakes.

Therefore, 1.4 cakes per minute will be the answer.

Answer:

y + 2 = - [tex]\frac{4}{5}[/tex](x - 3)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = - [tex]\frac{4}{5}[/tex] and (a, b) = (3, - 2), hence

y - (- 2) = - [tex]\frac{4}{5}[/tex](x - 3), that is

y + 2 = - [tex]\frac{4}{5}[/tex](x - 3)

Answer:

One point greater than the last grade

Step-by-step explanation:

1. First off, N is the variable, so that means it can be any number, and when it uses the word greater, it means to ADD another number, which means one point greater.

Hello There!

n+1 could represent one point greater than the last test grade.

In this case, n could be the last grade so if we put this in words, the last test grade + 1 point so 1 would represent adding from the previous test.

Answer:

x=21

Step-by-step explanation:

x-7=14

add  7 to both sides

x=21

The expression x - 7 for x = 14 is equal to 7.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To evaluate x - 7 for x = 14,

We substitute 14 for x and simplify:

x - 7 = 14 - 7 = 7

Therefore,

The expression x - 7 for x = 14 is equal to 7.

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By using FOIL method and multiplying two parenthesis, we get the value of y as x² + 2x + 1

What is FOIL method?

To multiply binomials, utilize the FOIL Method. First, Outside, Inside, and Last are represented by the letters, denoting the sequence of multiplying terms. For your answer, multiply the first word, the outside term, the inside term, the last term, and then combine like terms. The foil approach is a useful strategy since it allows us to manipulate numbers regardless of how ugly they may appear when mixed with fractions and negative signs.

The above question says," y = (x + 1)²

We can look it as ( x + 1) ( x+ 1)

Use concept of FOIL here,

So, y = (x+1)(x+1)

multiplying x with x and then with 1 and then multiplying 1 with x and then with 1.

y = x² + x + x +1

By combining the like term , we will get

x² +2x+1

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Final answer:

To simplify the expression y = (x + 1)² - 2, we need to expand the square and combine like terms.

Explanation:

To simplify the expression y = (x + 1)² - 2, we need to expand the square and combine like terms.

Square the binomial (x + 1)² using the formula for the square of a binomial:

(x + 1)² = x² + 2x + 1

Now substitute this expression back into the original equation:

y = x² + 2x + 1 - 2

Combine like terms:

y = x² + 2x - 1

Answer:

He did not test it against anyone who did not drink milk before bed and he tested it on a relatively small number of people. In order to have more accurate results he should include more people in the study and should test it against the same number of people who haven't drank milk before bed. He should also take into account the amount of milk that they drank before going to bed.

Answer:

No comparision and repeatibility

Step-by-step explanation:

Firstly, this total number of hours each friend sleeps is not specified and therefore can vary each night. What is constant is that they drank milk before they slept and for one month the analysis was made. Secondly, he never made a comparison between milk drinkers and non-milk drinkers and therefore the analysis is just one sided and open to other effects such as exercise, eating habits etc. Furthermore, no repeatability was conducted to determine if the same results would be obtained. Lastly, the ages of the friends are unknown so making a conclusion of teenagers is inaccurate.

Answer:

The factors of x^3+2x^2+5x+10 are (x^2+5)(x+2)

Step-by-step explanation:

x^3+2x^2+5x+10

Group the expression by two:

=(x^3+2x^2)+(5x+10)

Factor out GCF in each group.

=x^2(x+2)+5(x+2)

Note:(The binomials in parentheses should be the same, if not the same... there is an error in the factoring or the expression can not be factored.)

Now factoring out the GCF which basically has you rewrite what is in parentheses and place other terms left together:

=(x^2+5)(x+2)

Thus the factors of x^3+2x^2+5x+10 are (x^2+5)(x+2)....

Answer:

Length [tex]14\ cm[/tex]

Width [tex]3\ cm[/tex]

Step-by-step explanation:

Let

x-----> the length of rectangle

y ----> the width of rectangle

we know that

The area of rectangle is equal to

[tex]A=xy[/tex]

[tex]A=42\ cm^{2}[/tex]

so

[tex]42=xy[/tex] ----> equation A

[tex]x=2y+8[/tex] ---> equation B

substitute equation B in equation A and solve for y

[tex]42=(2y+8)y\\ \\2y^{2}+8y-42=0[/tex]

Solve the quadratic equation by graphing

The solution is [tex]y=3\ cm[/tex]

see the attached figure

Find the value of x

[tex]x=2(3)+8=14\ cm[/tex]

therefore

Length [tex]14\ cm[/tex]

Width [tex]3\ cm[/tex]

The dimensions of the rectangle are: Width ( W = 3 ) cm and  Length ( L = 14 ) cm

We are given that the length L is 8 cm greater than twice its width W. This can be expressed as:

[tex]\[ L = 2W + 8 \][/tex]

The area  of the rectangle is given by the formula:

[tex]\[ A = L \times W \][/tex]

Given that the area is 42 cm², we can write:

[tex]\[ 42 = (2W + 8) \times W \][/tex]

Expanding the equation:

[tex]\[ 42 = 2W^2 + 8W \][/tex]

Rearranging the equation in standard quadratic form:

[tex]\[ 2W^2 + 8W - 42 = 0 \][/tex]

Now, let's solve this quadratic equation for ( W ). We can use the quadratic formula:

[tex]\[ W = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]

Where:

-  a = 2

-  b = 8

-  c = -42

Now, let's substitute the values into the quadratic formula:

[tex]\[ W = \frac{{-8 \pm \sqrt{{8^2 - 4 \times 2 \times (-42)}}}}{{2 \times 2}} \]\[ W = \frac{{-8 \pm \sqrt{{64 + 336}}}}{{4}} \]\[ W = \frac{{-8 \pm \sqrt{{400}}}}{{4}} \]\[ W = \frac{{-8 \pm 20}}{{4}} \][/tex]

Now, we have two possible values for \( W \):

[tex]\[ W_1 = \frac{{-8 + 20}}{{4}} = \frac{{12}}{{4}} = 3 \]\[ W_2 = \frac{{-8 - 20}}{{4}} = \frac{{-28}}{{4}} = -7 \][/tex]

Since the width cannot be negative, we discard [tex]\( W_2 = -7 \)[/tex]. Thus, the width of the rectangle is ( W = 3 ) cm.

Now, let's find the length using the equation ( L = 2W + 8 ):

[tex]\[ L = 2 \times 3 + 8 \]\[ L = 6 + 8 \]\[ L = 14 \][/tex]

Answer:

35.8333 (3 repeated) in^3

Step-by-step explanation:

Just Multiply 2, 5 1/3, and 10 3/4 all together (you'll get 107.5) and divide it by 3 to get your answer.

Answer:

AC = 29.9

AB = 30.9

Step-by-step explanation:

for edg 2020

Answer:

I think this is right  483/100000

Sorry if i'm wrong

Answer:

5x² - 13x - 6

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor, that is

5x(x - 3) + 2(x - 3) ← distribute both parenthesis

= 5x² - 15x + 2x - 6 ← collect like terms

= 5x² - 13x - 6

For this case we have that by definition, the volume of a cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where:

r: It's the radio

h: It's the height

We have as data that:

[tex]r = 7\\h = 16[/tex]

Substituting the data we have:

[tex]V = \pi * (7) ^ 2 * 16\\V = \pi * 49 * 16\\V = 784 \pi[/tex]

So, the cylinder volume is[tex]784 \pi[/tex]

Answer:

[tex]784 \pi[/tex]

Answer:

r= C over 2π

Step-by-step explanation:

C =  2πr

To solve for r, divide each side by  2π

C/  2π =  2πr/  2π

C/  2π =  r

Answer: r= C over 2π or [tex]r=\dfrac{C}{2\pi}[/tex]

Step-by-step explanation:

Formula to find the circumference of a circle is given by :-

[tex]C=2\pi r[/tex], where r is the radius of the circle .

To find the formula for r , we need to divide both sides by [tex]2\pi[/tex], we get

[tex]r=\dfrac{C}{2\pi}[/tex]

Hence, an equivalent equation solved for r will be :-

[tex]r=\dfrac{C}{2\pi}[/tex] i.e. r= C over 2π

This question requires us to use the cosine rule:

a^2 = b^2 + c^2 - 2bc*cos(A),

where A is the included angle between sides b and c, and a is the side of the triangle opposite to the angle.

In the context of the question, a is the length of the tunnel (let's call this t), b is 6 km, c is 7 km and A is 29°.

Given the values in the question and those we defined, we can rewrite the equation for the cosine rule as:

t^2 = 6^2 + 7^2 - 2(6)(7)cos(29)

Now, evaluating this we get:

t^2 = 36 + 49 - 84cos(29)

t^2 = 85 - 84cos(29)

t = sq.root (85 - 84cos(29))

= 3.40 km (rounded to two decimal places)

Answer:

3.40

Step-by-step explanation:

I checked the answer and it was right!!

Answer:

1386 ft^3.

Step-by-step explanation:

Volume = width * length * height

= 9 * 11 * 14

= 1386 ft^3.

Answer:

√52

Step-by-step explanation:

D=√(3+3)²+(1-5)²

=√36+16

=√52

Answer:

52

Step-by-step explanation:

Answer:

9.50x+12y<=60

Step-by-step explanation:

For this case we have that by definition, the mechanical power is given by:

[tex]P = \frac {W} {t}[/tex]

Where:

W: It is the work done

t: It's time

For its part:

[tex]W = F * d[/tex]

Where:

F: It is the applied force

d: It is the distance traveled

According to the data we have that the drag force of the tractor is [tex]F = 300lb[/tex], while the distance traveled is [tex]d = 80ft.[/tex]

Substituting:

[tex]P = \frac {300 * 80} {120}\\P = \frac {24000} {120}\\P = 200[/tex]

Finally, the power is:

[tex]\frac {200lb-ft} {s}[/tex]

Answer:

Option C

The correct option is 200 ft-lb/sec. The power output is 200 ft-lb/sec.

Determining the Power Output of a Tractor

To find the power output of the tractor dragging a 300 lb. concrete block over a distance of 80 ft. in 120 seconds, we need to use the formula for power:

Power = Work / Time

Step-by-step explanation:

 1. Calculate the Work Done: Work is calculated as the force applied times the distance moved by the force. Here, the force is the weight of the block (300 lb), and the distance is 80 ft.

   Work = Force x Distance

   Work = 300 lb x 80 ft = 24,000 ft-lb.

 2. Calculate the Time: The time given is 120 seconds.

 3.  Calculate the Power: Power is the rate at which work is done, given by dividing the work by the time.

Power = Work / Time

Power = 24,000 ft-lb / 120 sec = 200 ft-lb/sec.

Therefore, the power output of the tractor is 200 ft-lb/sec.

Answer:

y + 13 = 5(x + 2)

Step-by-step explanation:

The point-slope form of the equation for a line with slope m and passing through a point (a, b) is given as;

[tex]y-b=m(x-a)[/tex]

The slope of the line is 5; the coefficient of x in the given equation. The point given is (–2, –13). We plug in these values into the above equation and simplify;

[tex]y-(-13)=5(x-(-2))\\\\y+13=5(x+2)[/tex]

Which is the equation of the line in point-slope form

Answer:

b

Step-by-step explanation:

Answer:

C. 3

Step-by-step explanation:

Given expression is:

[tex]({3^{\frac{1}{7}})^7[/tex]

We know that the rules of exponents are used to solve these kind of questions.

When there is exponent on exponent like in this question 1/7 has an exponent of 7 , the exponents are multiplied.

So,

[tex]=3^{(7*\frac{1}{7} )}[/tex]

The 7's will be cancelled out and remaining power will be 1

[tex]=3^1\\=3[/tex]

Hence, option C is correct ..

Answer:

The correct answer is option C

3

Step-by-step explanation:

Points to remember

Identities

(xᵃ)ᵇ = xᵃᵇ

(x¹/ᵃ)ᵇ = xᵃ/ᵇ

To find the correct answer

It is given that, (3¹/⁷)⁷

By using above identities we can write,

(3¹/⁷)⁷ = 3⁽¹/⁷ *⁷⁾

= 3¹

 = 3

Therefore the simplified form of  (3¹/⁷)⁷ = 3

The correct answer is option C

(3¹/⁷)⁷ = 3

The equation equivalent to r = 1 + 2 is mathematically given as

(x^2+y^2-2y)^{2}=x^2+y^2

Question Parameter(s):

r = 1 + 2

Generally, the equation for the polar cordinates  is mathematically given as

[tex]x=rsin\theta\\\\y=rcos\theta[/tex]

Therefore

[tex](sin^{2}\theta + cos^{2}\theta) = 1[/tex]

Hence

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

In conclusion

[tex]\sqrt{x^2+y^2} = 1+2\frac{y}{\sqrt{x^2+y^2}}\\\\x^2+y^2-2y= \sqrt{x^2+y^2}[/tex]

(x^2+y^2-2y)^{2}=x^2+y^2

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[tex]

L(x)=-2377+3\Longrightarrow L(x)=-2374 \\

V(x)=x

[/tex]

Both of the functions are linear. [tex]L(x)[/tex] is constant.

However we are required to determine the range of [tex](L\circ V)(x)[/tex]

[tex](L\circ V)(x)=L(V(x))=L(x)=-2374[/tex]

So the only possible solution that such notation gives is -2374 so therefore the answer in terms of range is [tex]x\in\{-2374\}[/tex]

Hope this helps.

r3t40

Answer:

D

Step-by-step explanation:

The Line goes from 0 to -4 and then -(-1) makes +1 so -4 goes to -3

Answer:

D. I did an pre-exam with this question and got it right

Answer:

both answers are inside

Step-by-step explanation:

70 is greater then 23 which explains why it's hotter. Absolute value is the distance from a number to 0. being 70 slots away from 0 is greater than 23 slots.

Your answer would be 48.

Just multiply.

2 x 8 = 16

16 x 3 = 48

Hope helps!-Aparri

Answer:

3 cups of strawberries, 1 1/2 cups of grapes

Step-by-step explanation:

Basically you need 1 C of strawberries and 1/2 C of grapes for 2 people. Multiply those amounts by 3, for 6 people