Sketch a right triangle corresponding to the trigonometric function of the acute angle 8. Then find the exact values of the other five trigonometric functions of
Answers
Solution:
Given:
[tex]cot(\theta)=2[/tex]Using the trig ratio of cot;
[tex]\begin{gathered} cot\theta=\frac{1}{tan\theta} \\ tan\theta=\frac{opposite}{adjacent} \\ Hence, \\ cot\theta=\frac{adjacent}{opposite} \\ cot\theta=\frac{2}{1} \\ adjacent=2 \\ opposite=1 \end{gathered}[/tex]The hypotenuse is gotten using the Pythagoras theorem;
[tex]\begin{gathered} h^2=2^2+1^2 \\ h^2=4+1 \\ h^2=5 \\ h=\sqrt{5} \end{gathered}[/tex]Thus, the sketch of the right triangle is;
[tex]\begin{gathered} Thus, \\ opposite=1 \\ adjacent=2 \\ hypotenuse=\sqrt{5} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} sin\theta=\frac{opposite}{hypotenuse} \\ sin\theta=\frac{1}{\sqrt{5}} \\ sin\theta=\frac{1}{\sqrt{5}}\times\frac{\sqrt{5}}{\sqrt{5}}=\frac{\sqrt{5}}{5} \\ sin\theta=\frac{\sqrt{5}}{5} \end{gathered}[/tex][tex]\begin{gathered} cos\theta=\frac{adjacent}{hypotenuse} \\ cos\theta=\frac{2}{\sqrt{5}} \\ cos\theta=\frac{2\sqrt{5}}{5} \end{gathered}[/tex][tex]\begin{gathered} tan\theta=\frac{opposite}{adjacent} \\ tan\theta=\frac{1}{2} \end{gathered}[/tex][tex]\begin{gathered} csc\theta=\frac{1}{sin\theta} \\ csc\theta=\frac{1}{\frac{\sqrt{5}}{5}} \\ csc\theta=\sqrt{5} \end{gathered}[/tex][tex]\begin{gathered} sec\theta=\frac{1}{cos\theta} \\ sec\theta=\frac{1}{\frac{2\sqrt{5}}{5}} \\ sec\theta=\frac{\sqrt{5}}{2} \end{gathered}[/tex]
Related Questions
he table shows the gallons of water in a pool over time. A two column table with six rows. The first column, Time in minutes, has the entries, 0, 1, 2, 3, 4, 5. The second column, Water in Pool in gallons, has the entries, 50, 44, 38, 32, 26, 20. Choose the term that describes the slope of the line of a graph representing the data in the table. The slope of a line graphed to represent the volume of water in a pool over time would be described as .
Answers
The slope of the line to represent the volume of water in a pool over time would described as -10
From the given table we have to choose points to find the slope of the line
The domain is defined as the set of possible inputs of the function.
The range is defined as the set of all possible outputs of the function.
The slope of the line is the change in y coordinate with respect to the change in y coordinates
Slope of the line m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Where m is the slope of the line
[tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] are the coordinates of the two points
We have to choose two points
The two points (2,44) and (4,26)
m = [tex]\frac{26-46}{4-2}[/tex]
m = -20/2
m = -10
Hence, the slope of the line to represent the volume of water in a pool over time would described as -10
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Part 3: Solve a real-world problem using a cube root function.
Once Isabel rented the warehouse space, she decided to post ads on several social media sites to advertise her online bookstore. Let x represent the number of months the ads have been posted. Isabel finds that the function below describes the number of books sold as a function of the number of months her ads have been posted.
f(x) = 1000 + 1000
⦁ How many books were sold after 8 months? (3 points)
⦁ Graph the function. (10 points)
Answers
Considering the given function, it is found that 3000 books were sold after eight months.
FunctionThe function in this problem is defined as follows:
f(x) = 1000(∛x) + 1000
In which f(x) represents the number of books sold after x months.
After eight months, we have that x = 8, hence the number of books is calculated as follows:
f(8) = 1000(∛8) + 1000
The lone instance of x in the function was replaced by eight to find the numeric value.
The cube root of eight is calculated as follows:
8 = 2 x 2 x 2 = 2³
Hence:
∛8 = 2
Thus the numeric value of the expression is:
f(8) = 1000(∛8) + 1000 = 1000 x 2 + 1000 = 2000 + 1000 = 3000 books.
The graph of the situation is given by the image at the end of the answer, at a domain of x >= 0, as the number of months cannot assume negative values.
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.5t + .1 < 10t + .05
Answers
Answer: t> -4/95
Step-by-step explanation: times both sides by 10(just make the calculation easier, no need to do that)
5t+1<100t+5
-95t<4
t > -4/95
Find the slope of the line passing through the pair of points or state that the slope is
undefined. Then indicate whether the line through the points rises, falls, is horizontal, or
is vertical.
(3,-5) and (-7,-5)
...
Select the correct choice below and, if necessary, fill in the answer box within your
choice.
Answers
Answer:
The slope is o. The line will be vertical and the equation of the line is y = -5
Step-by-step explanation:
Determine the solutions of the equation [x - 30 = 11. 1. Rewrite for two solutions: (x – 3) = 11, -(x - 3) = 11 Solve for x in each equation. What are the solutions to the equation? O x= -14, -8 O x= -14,8 O X=-8, 14 O x= 8,14
Answers
First solution
(x-3)=11
x=11+3
x=14Second solution
-(x-3)-11
multiply by -1 both sides
x-3=-11
x=-11+3
x=-8therefore
answer is
-8,14
For the following, find f(2.1) and f(4).
Answers
Answer:
option A
Step-by-step explanation:
put x= 4 in condition 4<=x<8
as it satisfied condition
and put x= 2.1 in condition 2<x<4
)) Sonoma bikes 5 miles to Paige's house. On a map, 5 they measure that distance as 7 cm. The same map shows that the mall is 3 cm from Paige's house. What is the actual distance between Paige's house and the mall?
Answers
Find the scale factor by dividing the real length by the map length. Since Sonoma's house is 5 miles away from Paige's house but they appear 7cm appart in the map, then the scale factor is:
[tex]undefined[/tex]Multiply and combine like terms to degerming the product of these polynomials.
(2 n-3)(5 n+6)
Enter your results in the response box.
Answers
Answer:
7n-18
Step-by-step explanation:
The working out is attached. Hope it helps!
this is the last one i need help with. please & thank you asap
Answers
Answer:
slope = 3/7
Step-by-step explanation:
Locations of points: (-4 , 1) and (3 , 4)
slope = rise / run
between two plotted points this means that:
slope = change in y / change in x
slope = (4 - 1) / (3 - (-4))
slope = (4 - 1) / (3 + 4)
slope = 3/7
what is ST? I've included a photo of the problem
Answers
Answer
ST = 14
According to the diagram
UV = VW
ST = UT
UT = VT - UV
UV = 14 and VT = 29
UT = 29 - 14
UT = 15
SInce UT = ST, Therefore, ST = 14
I need help with this practice problem The subject is trigonometry It asks to graph the function If you can ❗️ use Desmos to graph
Answers
We will have the following:
3² +4² + 12² is equal to n² for some positive number n . Find n.
Answers
Answer:
n = 13
Step-by-step explanation:
For this, you need to square all of the numbers and then add them together. Most of the time, you can put them into a calculator but I will work it out below.
Squaring means multiplying a number by itself, so we get:
3² + 4² +12² =n²
Turns into:
(3*3) + (4*4) +(12*12) = n²
Then work out the multiplication:
9 + 16 + 144 = n²
Add everything together
169 = n²
Now take the square root of each side:
[tex]\sqrt{169} =\sqrt{n^{2}}[/tex]
This comes out to be:
± 13 = n
The question asks for the positive number, so you answer is:
n = 13
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Tobin's friend Rose claims that she can read minds. To test
Rose's abilities, Tobin draws 3 cards without replacement
from a standard deck of 52 playing cards. Tobin asks Rose
to identify each of the 3 cards she drew in order.
Assume that Rose has no special abilities and is randomly
guessing the cards.
What is the probability that Rose identifies all 3 cards in
the correct order?
Answers
The probability that rose identifies all 3 cards in the correct order is 1/132,600 by the concept of permutation.
What is permutation?It is the separate arrangements of a given number of associates taken all at once, or some of them, or just a few of them. There are two possible meanings, AB and BA, for instance, if we have the two elements A and B.
Following the arrangement of 'r' items from a total of 'n' elements, the number of permutations is,
nPr = n! / (n – r)!
Here to obtain the probability in correct order use permutation formula
Recall that, Probability is calculated as favorable outcomes divided by all possible outcomes.
Favorable number of outcomes = 1 (as only one order is correct)
Total outcomes = 52p3 (since 3 cards to be arranged from pack of 52)
So, the probability of rose identifies all 3 cards in correct order =1/52p3
Probability = [tex]\frac{1}{52!/(52-3)!}[/tex]
Probability = 49! /52!
Probability = 49! /52*51*50*49!
Probability = 1/52*51*50
Probability = 1/132,600
Therefore, the probability that rose identifies all 3 cards in the correct order is 1/132,600.
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Please help if you can!!!
Answers
Sue traveled 96 miles in 12 hours. A unit rate to describe Sue's travel is 8 miles per hour. What is another unit rate in this situation?
Answers
Answer:
Sue travels 8 miles per hour.
Step-by-step explanation:
A farmer sows 100 seeds of a new type of corn and wants to quickly determine the yield, or total number of ears of corn, for the crop when it has matured. He decides to take a simple random sample of 10 corn plants. He labels the 100 plants 00–99. Refer to the given line from a random number table. Which numbers represent the sample of 10 corn plants?
58160 09695 38399 40400 32662 46254
58, 16, 00, 96, 95, 38, 39, 94, 04, 00
58, 16, 00, 96, 95, 38, 39, 94, 04, 32
58, 16, 96, 95, 38, 39, 94, 04, 32, 66
58, 16, 09, 69, 38, 39, 40, 32, 66, 46
Answers
Answer: Here the correct option is 2) 58, 16, 00, 96, 95, 38, 39, 94, 04, 32
Step-by-step explanation:
!!PLEASE HELP!!
Stefan is baking taquitos for a school fundraiser. The recipe calls for 2 1/2 cups of beans and 3 1/4 cups of rice. What is the ratio between cups of beans and cups of rice?
Answers
The ratio between cups of beans and cups of rice is 10/13 . Option C
What is ratio?
A ratio can described as an ordered pair of numbers, like y and z, that is written mathematically in the form y / z where the denominator of the fraction is not equal to zero.
It is known to describe the number of times an element or number contains another number proportionally.
It is also seen as the comparison of two quantities, elements or numbers that has the same units and likewise, explains how much one of the elements or quantity is found in the another one.
This is done based on their sizes or magnitudes.
A proportion is a mathematical equation with two ratios set equivalent or equal to each other.
Given that;
Beans = 2 1/ 2 cups
Rice = 3 1/4 cups
Convert to mixed fractions;
Beans = 5/2
Rice = 13/4
Now, divide the cups of beans by that of rice;
= 5/ 2 ÷ 13/4
= 5/2 × 4/13
= 10/13
Hence, the ratio is 10/13
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The total bill for dinner was $43.75 (including tax and a tip). paid a 22.9% tip, what was his bill before adding the tip?
Answers
Answer:
$33.75
Step-by-step explanation:
22.9% of $43.75 = $10.0
43.75 - 10.0 = $33.75
Hope that helps
Answer:
$35.60
Step-by-step explanation:
I cross multiplied related numbers:
[tex]\frac{43.75}{x}[/tex]=[tex]\frac{122.9}{100}[/tex] cross multiply
4375=122.9x, divide both sides by 122.9
35.598=x round to hundredths
35.60
What what solid is generated when the semi circle is rotated about the line
Answers
Sphere solid is generated when the semicircle is rotated about the line.
Given,
The semi circle is rotated about the line.
To find the what solid is generated?
Now, According to the question:
We know that when a semicircle is rotated about any line then the three dimensional figure or a solid that is formed on this rotation transformation is Sphere.
Hence, Sphere solid is generated when the semicircle is rotated about the line.
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help meeeeeeeeeee pleaseeeeeeeeeeeeeeeeeee
Answers
Step-by-step explanation:
I just answered this. how often did you post this basic question ?
−2 4/5×(−3 1/2)
I really need help.
Answers
Explanation: First make the mixed numbers improper fractions.
-2 4/5 would be -14/7 because -2 x 5 + (-4) is -14. -3 1/2 is -7/2 because -3 x 2 + (-1).
Now times both the denominators and numerators. -14 x -7 is 98 and 5 x 2 is 10. The improper fraction is 98/10
Now make the improper fraction a mixed number which would be 9 4/5. 10 goes into 98 9 times and there is 8 left, keep the denominator 10.
8/10 isn’t simplified as you divide both by 2 which is 4/5
Don’t forget your mixed number and the answer is 9 4/5
Barnaby decided to count the number of ducks and geese flying south for the winter. Thefirst day he counted 175 ducks and 63 geese. What is the ratio of ducks to the total num-ber of birds flying overhead in simplest terms?
Answers
So, here we have that there are 175+63 = 238 birds in total.
We want to know the ratio of ducks to the total number of birds flying overhead. There are 175 ducks for a total of 238, so the ratio is:
175:238
The amount of water a bag of salt can treat is known in cubic feet.
Answers
Given:
There is a rectangular prism shape water tank given with 23yd 15yd anf 4yd measurements
Required:
A) We need to find the volume of tank in cubic ft
B) 18.8 cubic ft need 1 salt bag then we need to find to total needed salt bag
C) $4.65 per bag then find total cost
Explanation:
first pf all we need to convert given measures in feet from yd
[tex]\begin{gathered} 1yd=3ft \\ 23yd=69ft \\ 15yd=45ft \\ 4yd=12ft \end{gathered}[/tex]A)
Volume
[tex]V=lwh=69*45*15=37260ft^3[/tex]B)
18.8 cubic ft need 1 bag
then
37260 cubic ft need x
[tex]x=\frac{37260}{18.8}=1981.9\approx1982\text{ bags}[/tex]C)
Cost for 1 bag is $4.65
then
cost for 1982 bags is y
[tex]y=1982*4.65=9216.3[/tex]Final answer:
A) volume of tank in cubic ft is 37260
B) 18.8 cubic ft need 1 salt bag then we need total 1982 needed salt bags
C) $4.65 per bag then total cost is $9216.3
Need help answering the following polynomial
Answers
The expression represents a quadratic polynomial with two terms. The constant term is [tex]-\frac{1}{6}[/tex], the leading term is [tex]x^{2}[/tex], and the leading coefficient is [tex]-1[/tex].
The given expression is [tex]-x^{2}-\frac{1}{6}[/tex].
We have to complete the given sentence;
The expression represents a ........... polynomial with ........terms. The constant term is .........., the leading term is..........., and the leading coefficient is .................... .
we first complete the given sentence then we explain the sentence.
The expression represents a quadratic polynomial with two terms. The constant term is [tex]-\frac{1}{6}[/tex], the leading term is [tex]x^{2}[/tex], and the leading coefficient is [tex]-1[/tex].
Firstly about Quadratic Polynomial
When the highest degree term in a second-degree polynomial equals to 2, the polynomial is said to be quadratic.
Now about Constant Term
A number that is constant and does not have any variables in an algebraic expression is a constant term.
Now about Leading Coefficient
The numbers placed in front of the variable with the biggest exponent are known as leading coefficients.
Hence, the expression represents a quadratic polynomial with two terms. The constant term is [tex]-\frac{1}{6}[/tex], the leading term is [tex]x^{2}[/tex], and the leading coefficient is [tex]-1[/tex].
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Find the distance between the points P (3, 5) and Q (8,7).
Answers
Answer:
The distance between two points (x₁,y₁) and (x₂,y₂) on the coordinate plane is d=√((x₂-x₁)²+(y₂-y₁)²)
√(8 - 3)² + (7 - 5)² = √29 ≈ 5.3851648071345
The graph depicts the growth in costs using a line segment. Use the midpoint formula to approximate the cost during the year 1987.The approximate cost during the year 1987 was $ ____.
Answers
Answer:
The approximate cost during the years 1987 was $7527
Explanation:
The midpoint formula is:
[tex]M(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]For two given points.
In this case, we can see in the graph the points (1983, 5021) and (1991, 10033)
Then, using the midpoint formula:
[tex]M(\frac{1983+1991}{2},\frac{5021+10033}{2})=M(1987,7527)[/tex]Thus, the approximation for the year 1987 is $7527
A map of a park has no scale. The distance between the campground and the entrance station on the map is 2 inches. The actual distance between them is 8 miles. On the map, the distance between the campground and the lake is 12 inch.
What is the actual distance in miles between the campground and the lake?
Answers
The distance between the lake and campground is 48 miles.
Given
The distance between the campground and the entrance is 2
The actual distance between them is 8 miles
Hence the scale is 2 for 8 miles
Also, Distance on the map between campground and lake is 12 inch.
Let us say actual distance is x
There fore we can form equation as
2x = 12x18
2x = 216
x=48
Hence the actual distance between campground and lake is 48 miles.
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Write an equation. Let X represent the number described in the exercise. Then solve the equation & find the number. Four subtracted from the product of 5 and a number is 51.Write an equation.
Answers
We have to write an equation from the word problem,
Four subtracted from the product of 5 and a number is 51
Let's break it down:
--- product of 5 and a number can be written as,
[tex]\begin{gathered} 5\times x \\ =5x \end{gathered}[/tex]--- four subtracted from "product of 5 and a number" can be written as,
[tex]5x-4[/tex]^^ All this is equal to 51, so we can write,
[tex]5x-4=51[/tex]To find the unknown number, we solve the above equation. The steps are shown below:
[tex]undefined[/tex]Use the function below to find f(-2).
f(x) = 3x
A. -6
B. -9
O C.
O D.
996
610
9
Answers
Answer:
option d is the correct answer
Michael has a twelve gallon gas tank. When he filled
his tank up, he pumped nine gallons of gas. What
fraction of his tank had been empty?
Answers
Answer:
3/4
Step-by-step explanation:
9/12 Divide the top and bottom by 3
3/4