Write the six trigonometric functions for a right triangle with legs of length 21 and 28, o is adjacent to the leg of length 28.
Answers
First, we need to find the length of the hypotenuse. The Pythagorean theorem states:
\(c^2=a^2+b^2\)where a and b are the legs and c is the hypotenuse of a right triangle.
Substituting with a = 21 and b = 28, we get:
\(\begin{gathered} c^2=21^2+28^2 \\ c^2=441+784 \\ c^2=1225 \\ c=\sqrt[]{1225} \\ c=35 \end{gathered}\)The length of the hypotenuse is 35.
Sine formula
\(\sin (angle)=\frac{\text{opposite}}{\text{hypotenuse}}\)Considering angle θ, the opposite leg is 21. Therefore:
\(\begin{gathered} \sin (\theta)=\frac{21}{35} \\ \text{ Simplifying:} \\ \sin (\theta)=\frac{3}{5} \end{gathered}\)Cosine formula
\(\cos (angle)=\frac{\text{adjacent}}{\text{hypotenuse}}\)Considering angle θ, the adjacent leg is 28. Therefore:
\(\begin{gathered} \cos (\theta)=\frac{28}{35} \\ \text{ Simplifying:} \\ \cos (\theta)=\frac{4}{5} \end{gathered}\)Tangent formula
\(\tan (angle)=\frac{opposite}{adjacent}\)Considering angle θ, the adjacent leg is 28 and the opposite leg is 21. Therefore:
\(\begin{gathered} \tan (\theta)=\frac{21}{28} \\ \text{ Simplifying:} \\ \tan (\theta)=\frac{3}{4} \end{gathered}\)Secant formula
\(\begin{gathered} \sec (angle)=\frac{hypotenuse}{adjacent} \\ \text{ }alternatively\colon \\ \sec (angle)=\frac{1}{\cos (angle)} \end{gathered}\)Substituting with the cosine value previously found:
\(\begin{gathered} \sec (\theta)=\frac{1}{\cos (\theta)} \\ \sec (\theta)=\frac{1}{\frac{4}{5}} \\ \sec (\theta)=\frac{5}{4} \end{gathered}\)Cosecant formula
\(\begin{gathered} csc(angle)=\frac{hypotenuse}{opposite} \\ \text{ }alternatively\colon \\ \csc (angle)=\frac{1}{\sin (angle)} \end{gathered}\)Substituting with the sine value previously found:
\(\begin{gathered} \csc (\theta)=\frac{1}{\sin (\theta)} \\ \csc (\theta)=\frac{1}{\frac{3}{5}} \\ \csc (\theta)=\frac{5}{3} \end{gathered}\)Cotangent formula
\(\begin{gathered} cot(angle)=\frac{adjacent}{opposite} \\ \text{ }alternatively\colon \\ \cot (angle)=\frac{1}{\tan (angle)} \end{gathered}\)Substituting with the tangent value previously found:
\(\begin{gathered} \cot (\theta)=\frac{1}{\tan (\theta)} \\ \cot (\theta)=\frac{1}{\frac{3}{4}} \\ \cot (\theta)=\frac{4}{3} \end{gathered}\)Related Questions
Autumn found a wallet containing $ 900 in the street. She returned the wallet to its owner, who gave her a $ 180 reward. What percentage of the $ 900 was the reward?
Answers
Answer:
\(\frac{180}{900} = 0.2\) × \(100 =20\)
Autumn got a 20% reward of the $900 she found.
What is the allusion:
"I don't know if this store carries shoes in your size, Sasquatch," my dad joked when we went shopping for another new pair of shoes, my second pair in two
months.
Shoes
Dad
Sasquatch
Two Months
Answers
The allusion in this statement is "Sasquatch," referencing a legendary creature known for its large size and used humorously to imply the person's abnormally large shoe size.
The allusion in the given statement is "Sasquatch." Sasquatch, also known as Bigfoot, is a legendary creature often depicted as a large, hairy, and elusive humanoid. In this context, the reference to Sasquatch is used metaphorically to humorously imply that the person's shoe size is abnormally large.
The mention of Sasquatch adds a playful and exaggerated tone to the conversation about shopping for shoes. It serves as a lighthearted way for the dad to comment on the frequency of buying new shoes, suggesting that the person's feet grow rapidly or that they have a high shoe consumption rate.
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GUESS THE ANGLE.
two angles whose sum is 180 degrees.
Answers
Answer:
There is an insane amount of possibilities for this, asking me to guess is legitimately unfair. Still, you deserve an answer.
90 + 90
45 + 135
120 + 60
150 + 30
10 + 170
20 + 160
140 + 40
130 + 50
120 + 60
And so on
Hey can someone help?
Answers
Answer:
V = 144
Step-by-step explanation:
Formula for volume of a rectangular prism:
V = whl
Given:
w = 3
h = 8
l = 6
Work:
V = whl
V = 3(8)(6)
V = 144
two planes take off from the same airstrip. the first plane flies west for 150 miles and then flies 30 degrees south of west for 220 miles. the second plane flies east for 220 miles and then flies x degrees south of east for 150 miles. if x < 30, which plane is farther from the airstrip after the second leg? justify your answer.
Answers
The first plane is farther from the airstrip after the second leg
Which plane is farther from the airstrip after the second leg?The first plane
Initial distance = 150 miles west
Additional distance = 220 miles 30 degrees SW
This means that
Additional distance = 220 * cos(30) miles SW
Additional distance = 190.53 miles
Total distance = 150 + 190.53 = 340.53
The second plane
Initial distance = 220 miles east
Additional distance = 150 miles x degrees SE
This means that
Additional distance = 150 * cos(x) miles SW
Total distance = 220 + 150 cos(x)
Given that
x < 30
We have
Second plane < First plane
220 + 150 cos(x) < 340.53
Evaluate
cos(x) < 0.8035
Take the arc cos of both sides
x < 36
x < 36 is not the same as x < 30
Hence, the first plane is farther
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The Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, . . . (where F0 0).
(a) Give the recursive definition for the sequence.
(b) Write out the first few terms of the sequence of partial sums: 0, 0 + 1, 0 + 1 + 1,. . .
(c) Give a closed formula for the sequence of partial sums in terms of Fn (for example, you might say F0 + F1 + · · · + Fn 3F 2 n−1 + n, although that is definitely not correct).
(Discrete Mathematics)
Answers
The Fibonacci sequence is the sequence in which the numbers are written such that each succeeding number is sum of two preceding numbers.
The Fibonacci sequence is defined recursively as follows:
F0 = 0
F1 = 1
For n > 1, Fn = Fn-1 + Fn-2
(b) The sequence of partial sums is:
S0 = 0
S1 = 0 + 1 = 1
S2 = 0 + 1 + 1 = 2
S3 = 0 + 1 + 1 + 2 = 4
S4 = 0 + 1 + 1 + 2 + 3 = 7
S5 = 0 + 1 + 1 + 2 + 3 + 5 = 12
(c) A closed formula for the sequence of partial sums in terms of Fn is not possible, since the sequence of partial sums depends on the values of all previous terms in the Fibonacci sequence. However, it is possible to express the nth term of the sequence of partial sums, Sn, in terms of the nth term of the Fibonacci sequence, Fn, using the following formula:
Sn = F0 + F1 + ... + Fn = (F0 + F1) + (F1 + F2) + ... + (Fn-1 + Fn) = F1 + F2 + ... + Fn + F0 + F1 + ... + Fn-1 = 2Sn-1 - Fn + F0
This formula can be derived by considering the previous term in the sequence of partial sums and adding the current term of the Fibonacci sequence to it.
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The radioactive substance uranium-240 has a half-life of
14 hours. The amount A(t) of a sample of uranium-240 remaining (in grams) after t
hours is given by the following exponential function.
A(t)=3200 (1/2)t/14
Answers
Answer:
Just pUt t=40 then answer come
How many 1/2 foot unit cubes can be added to fill a 388 1/4 rectangular prism
PLEASE HELP WILL MARK BRAINLIEST!!!
Answers
Answer:
The volume of the cube is 1/2 x 1/2 x 1/2 = 1/8
Step-by-step explanation:
I DONT KNOW IF THIS IS THE RIGHT ANSWER
3×/5 2×/3 + 1/5 = 0
Answers
Answer:
what is the question. the equation is invalid.
Using the income statement below, calculate the following profitability ratios for Western Bookkeeping and Tax Service. Assume that stockholder's equity equals $441,600 and total assets equal $640,000.
Profit margin ratio
Return on equity ratio
Asset turnover ratio
Write the profit margin and return on equity ratios as a percent, rounded to the nearest percent. Write the asset turnover ratio as a decimal, rounded to two decimal places.
Answers
The computation of the profitability ratios for Western Bookkeeping and Tax Service is as follows:
Profit margin ratio = 8%Return on equity ratio = 8%Asset turnover ratio = 0.75.What are profitability ratios?Profitability ratios are the financial ratios that evaluate an entity's ability to convert its earnings (revenue) into profit versus different criteria.
Some of the common profitability ratios include:
Gross Profit MarginOperating Income RatioNet Income RatioReturn on Investment (ROI)Return on EquityReturn on Total AssetsAsset turnover RatioEarnings per share.Stockholders' equity = $442,600
Total assets = $640,000
Net sales = $480,000
Net income = $36,000
Profit margin ratio = Net income/Net Sales x 100
= $36,000/$480,000 x 100
= 7.5%
= 8%
Return on equity ratio = Net income/Shareholders' Equity x 100
= $36,000/$442,600 x 100
= 8.13%
= 8%
Asset turnover ratio = Net Sales/Total Assets
= $480,000/$640,000
= 0.75
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\(3a-5=-23\)
Thank you!! :)
Answers
\( \boxed{ \mathfrak{here \: \: is \: \: the \: \: solution \: \: for \: \: teeny : }}\)
\(3a - 5 = - 23\)\(3a = - 18\)\(a = - 6\)Thanks for brainliest Anny !!
Answer:
a = -6
Step-by-step explanation:
\(3a - 5 = - 23\)
\(3a - 5 + 5 = - 23 + 5\)
\(3a = - 23 + 5\)
\( - (23 - 5) = - 18\)
\(a = - 18 \div 3 = - 6\)
\(\boxed{\green{a = - 6}}\)
Find first derivative of f(x)=(x+1)(2x-1)
Answers
Answer:
\(4x-1\)
Step-by-step explanation:
129 is decreased to 32.
??????
Answers
Answer:
that means 129 went down to 32, so you have to find the the difference or what number made 129 down to 32. 129-97=32
Find two prime numbers whose sum and difference are prime numbers. Pls help.
Answers
Answer:
2 and 3
2+3 = 5
3-2 = 1
is the number
2+3=5
3-2=1
is the number
PLEASE HELP!!!!! which answer correctly shows how to use a number line? -3/4 + 1 1/4
Answers
Answer:
C
Step-by-step explanation:
The answer would be C because the bottom line hits the -3/4 and the top line adds on 1 1/4, which would give you the answer of 1/2.
What is the image point of (2,-5) after a translation right 4 units and up 3 units?
Answers
Answer:
(6,-2)
Step-by-step explanation:
You have the shape on your graph and move it up how ever many spaces it tells you and to the left or right however many times it tells you
Answer:
(6,-2)
Step-by-step explanation:
i hope this helps
what is the ratio of hearts to suns write your answer in simplest form for example 8:6 is equivalent to to 4:3
Answers
Step-by-step explanation:
this is the answer
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Find the average
rate of change for the given
function from x = -1 to x = 4. (5 points)
Answers
What is the range of the function? f(x)=3^x−1−2
Answers
The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is y > -2
Calculating the range of the equation?From the question, we have the following parameters that can be used in our computation:
f(x) = 3ˣ ⁻ ¹ - 2
The above equation is an exponential function
The rule of an exponential function is that
The domain is the set of all real numbersHowever, the range is always greater than the constant termIn this case, it is -2
So, the range is y > -2
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13.
Graph f(x)=4x(1/2)^x
Answers
start by plugging values for x into the function
a) f(1) = 4 (1/2)^1
f(1) = 2
the first coordinate point is (1,2)
b) f(0) = 4(1/2)^0
f(0) = 4
(0,4)
this method will help you find the coordinate points and where to plot.
The net of a triangle prism is shown.what is the surface area of the prism
Answers
The total surface area of the triangular prism using the net is 640 square meters
Calculating the total surface area using the net.From the question, we have the following parameters that can be used in our computation:
The net of a triangular prism (see attachment)
The surface area of the triangular prism from the net is calculated as
Surface area = sum of areas of individual shapes that make up the net of the triangular prism
Using the above as a guide, we have the following:
Area = 2 * 8 * 17 + 8 * 16 + 2 * 1/2 * 15 * 16
Evaluate
Area = 640
Hence, the surface area is 640 square meters
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A pie chart shows the number of rabbits 900, sheep 700, cattle 300 and pigs 500 What angle represent the number of sheep on the farm
Answers
Step-by-step explanation:
total number of animals on the farm is
900+700+500+300=2,400
angle for sheep will be
(700/2,400)*360=105°
can some one help me its all the points i have :(
Answers
Answer:
-2
Step-by-step explanation:
Convert the rectangular coordinates (-√√2, -√2) into polar form.
Express the angle using radians in terms of 7 over the interval
0 ≤0 < 27, with a positive value of r.
Answers
The polar form of the rectangular coordinates (-√√2, -√2) is (2√(1 + √2), 15π/28)
Converting into polar formTo convert the rectangular coordinates (-√√2, -√2) into polar form, we first need to find the value of r (the radius) and θ (the angle).
r = √((-√√2)^2 + (-√2)^2) = √(2 + 2√2) = 2√(1 + √2)
To find the value of θ, we can use the following formula:
θ = atan(y/x)
where atan is the inverse tangent function, and (x, y) are the rectangular coordinates.
θ = atan(-√2/(-√√2)) = atan(√2) = π/4 radians
However, we need to express the angle in terms of 7 over the interval 0 ≤ θ < 2π/7, with a positive value of r.
To do this, we can add a multiple of 2π/7 to the value of θ until we get an angle in the desired interval.
θ = π/4 + 2π/7 = (7π + 8π)/28 = 15π/28 radians
So the polar form of the rectangular coordinates (-√√2, -√2) is:
(2√(1 + √2), 15π/28)
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Please help find length
Answers
Answer:
180
Step-by-step explanation:
to find the side of the smaller triangle you do \(5^{2}\) x \(12^{2}\) and get 3600. Then do\(\sqrt{} 3600\) and get 60. Since the larger triangle is 3 times that size you do 3 x 60 and get 180.
HELLLP FAST
Mathamatics
Answers
Answer:
512 ft and 1,232 ft
Step-by-step explanation:
area is length x width
the pool's area can be calculated doing 32ft x 16ft
the area of the pool is 512 ft
the deck's area can be calculated doing 28ft x 44ft
the area of the deck is 1,232 ft
you're welcome<3
WILL MARK BRAINLIST!!!!!
10 is 5% of what number?
What percent of 90 is 36?
4 is what percent of 20?
Answers
Answer:
1: 50
2: 2.5
3: 5
1: multiply 10 by 100 and then divide the total by 5
as follows:
(10 x 100) / 5multiply 10 by 100 and then divide the total by 5 as follows:
(10 x 100) ÷5
equals 200
2: 90 is 250% of 36
3: 4: 20*100 =
(4*100): 20 =
400: 20 = 20
Please help me with this, its due today
Answers
180-135=45
(x+2)=45
x=43
Answer:
43 is answer
Step-by-step explanation:
65+x+2+70=180
137+x=180
x=43
Multiplying StartFraction 3 Over StartRoot 17 EndRoot minus StartRoot 2 EndRoot EndFraction by which fraction will produce an equivalent fraction with a rational denominator?
Answers
Answer:
(√17 + √2)/(√17 + √2)Step-by-step explanation:
You need to determine the conjugate of the denominator.
√17 - √2 has conjugate of √17 + √2, when multiplied the product is going to be a rational number:
(√17 - √2)/(√17 + √2) = 17 - 2 = 15Therefore correct choice is B or second from the top:
(√17 + √2)/(√17 + √2)Answer:
B
Step-by-step explanation:
Because trust is a good thing in this world
two-thirds of the quantity 63 less than y
Answers
Answer:
y - 2/3 * 63 or y - 42
Step-by-step explanation:
two-thirds of the quantity 63: 2/3 * 63
two-thirds of the quantity 63 less than y: y - 2/3 * 63 = y - 42