Answers
If we want to solve this problem we first need to list a few properties of trigonometric functions:
[tex]\begin{gathered} \text{cot }\theta=\frac{\cos\theta}{\sin\theta} \\ \sin^2\theta+\cos^2\theta=1 \end{gathered}[/tex]We are told that cot(θ)=1/2. Using the first equation and this data we obtain the following:
[tex]\frac{1}{2}=\frac{\cos\theta}{\sin\theta}[/tex]We multiply both sides and we get an expression for the cosine of θ:
[tex]\begin{gathered} \frac{1}{2}\sin\theta=\frac{\cos\theta}{\sin\theta}\cdot\sin\theta \\ \cos\theta=\frac{1}{2}\sin\theta \end{gathered}[/tex]Now we are going to take the second property I wrote in the begining and replace the cosine of θ with this new expression that we found:
[tex]\begin{gathered} \sin^2\theta+\cos^2\theta=\sin^2\theta+(\frac{1}{2}\sin\theta)^2=1 \\ \sin^2\theta+\frac{1}{4}\sin^2\theta=1 \\ \frac{5}{4}\sin^2\theta=1 \end{gathered}[/tex]We must solve this equation for the sine of θ. We can multiply both sides by 4/5:
[tex]\begin{gathered} \frac{4}{5}\cdot\frac{5}{4}\sin^2\theta=1\cdot\frac{4}{5} \\ \sin^2\theta=\frac{4}{5} \end{gathered}[/tex]And we apply a square root to both sides:
[tex]\begin{gathered} \sqrt{\sin^2\theta}=\sqrt{\frac{4}{5}} \\ |\sin\theta|=\frac{2}{\sqrt{5}} \end{gathered}[/tex]We are told that θ is located in quadrant I which means that its sine is positive. Therefore we get:
[tex]\sin\theta=\frac{2}{\sqrt{5}}[/tex]AnswerThen the answer is 2/√5
Related Questions
In a painting of the Mona Lisa, the length of the painting is 4 - inches, Milo scales the drawing up by 2 What is the length of the scaled copy?
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Wee, it he is scalaing the painting by two the new length must be twice the original length.
length = 2 x 4 = 8 in
New length = 8 in
A regular hexagon has perimeter 72m. Find the area
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A regular hexagon has six equal sides:
If you notice, a regular hexagon has exactly six equilateral triangles inside of it.
So, to find the area we could find the area of a triangle and then multiply this result by 6. This seems to be a little bit complicated to do, so, there's a formula to find the area of a regular hexagon, which is:
[tex]\begin{gathered} A=\frac{3\sqrt{3}s^2}{2} \\ Where: \\ s:Measure\text{ of a side of the regular hexagon} \end{gathered}[/tex]We know that the measure of any side of our regular hexagon equals 12m, so, we could just replace in the equation:
[tex]A=\frac{3\sqrt{3}(12m)^2}{2}\rightarrow A=\frac{3\sqrt{3}(144m^2)}{2}\rightarrow A=216\sqrt{3}m^2[/tex]Simplified, that's about 374.1 m2.
Geometry- Need help` brainly logged me out w my other tutor who explained it so if u see this miss tutor my bad
Answers
"Reason" means a mathematical justification for the assert on the left. "Given" means something that doesn't need justification; it's an assumption.
The first statement,
[tex]\bar{FG}\cong\bar{FJ},[/tex]is given.
The second reason is Base Angles Theorem. Note the word angles in the middle. Its corresponding statement on the left must involve angles. There is only one option involving angles:
[tex]\measuredangle G\cong\measuredangle J.[/tex]Finally, statement 3 is also in the assumptions made above (tagged by Given:). It's also Given.
AnswerThe reason #1 is Given.
The statement 2 is
[tex]\measuredangle G\cong\measuredangle J.[/tex]The reason #3 is Given.
Is (2,7) a solution to the system of equations: y= x + 5 y= 4x + 1 Part 1 (circle 1) Yes No Part 2 Shows a proof of your answer
Answers
Answer
(2, 7) is not a solution to this system of equations.
The ordered pair doesn't fit into the second equation
Explanation
To check if the given ordered pair is a solution to this, we will insert the values into the two equations and if they fit into rach equation, then, the ordered pair is a solution for this.
y = x + 5
y = 4x + 1
(2, 7) means x = 2, y = 7
y = x + 5
7 = 2 + 5
7 = 7
y = 4x + 1
7 = 4(2) + 1
7 = 8 + 1
7 ≠ 9
The ordered pair doesn't fit into the second equation, hence, (2, 7) is not a solution to this system of equations.
Hope this Helps!!!
two numbers have a sum of -10 and a difference of -2 what is the product of numbers
Answers
let 'x' and 'y' be two numbers that have a sum of -10 and a difference of -2, then, we have the following system of equations:
[tex]\begin{gathered} x+y=-10 \\ x-y=-2 \end{gathered}[/tex]notice that if we add both equations at the same time, we get:
[tex]\begin{gathered} x+y=-10 \\ x-y=-2 \\ --------- \\ 2x=-12 \\ \Rightarrow x=\frac{-12}{2}=-6 \\ x=-6 \end{gathered}[/tex]now that we have that x = -6, we can find the value of y substituting x = -6 on any equation:
[tex]\begin{gathered} -6+y=-10 \\ \Rightarrow y=-10+6=-4 \\ y=-4 \end{gathered}[/tex]therefore, x = -6 and y = -4. Next, we have that the product is (-6)(-4) = 24
The solutions to a quadratic equation are -2 and 6. What is the equation of its axisof symmetry?
Answers
General form of a quadratic equation is
[tex]ax^2+bx+c=0[/tex]another form is
[tex](x+h)(x+k_{})=0[/tex]where h and k are the number opposite by the sign of the solutions, then on this case the values of h and k are 2 and -6
[tex](x+2)(x-6)=0[/tex]Our equatio is a parabola then if we find the vertex we are finding the axis of simmetry
to find the vertex we trasnforme ou equation to the general form of a quadratic equation multipliying parenthesis
[tex]\begin{gathered} (x\times x)+(x\times-6)+(2\times x)+(2\times-6)=0 \\ x^2-6x+2x-12=0 \\ x^2-4x-12=0 \end{gathered}[/tex]now take the equation and derivate
[tex]\begin{gathered} 2x-4-0=0 \\ 2x-4=0 \end{gathered}[/tex]if we solve x we find the coordinate x of the vertex and the axis of simmetry
then
[tex]\begin{gathered} 2x-4=0 \\ 2x=4 \\ x=\frac{4}{2} \\ \\ x=2 \end{gathered}[/tex]axis of Symmetry is x=2
Jim stocks shelves at a grocery store. He aerns $8.60 per hour for 37.5 hours each week. One week a large shipment arrives late and Jim is asked to work overtime at 1.5 times his regular rate. He works 4.5 hours for overtime. What are his total earnings for the week?
Answers
Explanation
Since Jim earns 8.60 per hour for 37.5 hours each week. His normal earnings for a week becomes,
[tex]earnings=8.60\times37.5=322.5\text{ dollars}[/tex]During the late shipment period, Jim had to earned an overtime payment at 1.5 times his regular rate. This means per overtime hour he would earn
[tex]1.5\times8.60=12.9[/tex]Therefore, for 4.5 hours for overtime, we will have;
[tex]12.9\times4.5=58.05\text{ dollars}[/tex]Hence, altogether, he would make;
[tex]322.5dollars+58.05dollars=380.55\text{ dollars}[/tex]Answer: 380.55 dollars
Three cards are drawn from an ordinary deck and not replaced find the probability of the following P(getting 3 queens)P(getting an ace and king and queen)P(getting club and spade and heart)P(getting 3 diamonds)Answer the following problems using multiplication rule make sure to reduce your fraction
Answers
a) P(3 queens) ) = 4/52*3/51*2/50 = 1/5525
b) P(ace,king, queen) = 4/52*4/51*4/50 = 8/16575
c) P( ) = 10/52 * 10/51*10/50 = 5/663
d) P(3 diamonds) = 10/52 * 9/51* 8/50 = 6/1105
f(2)=1/xsolve both go 2)=3x
Answers
The functions are:
[tex]\begin{gathered} f(x)=\frac{1}{x} \\ g(x)=3x \end{gathered}[/tex]We need to evaluate f(x) in x=-2 and g(x) in x=2, so:
[tex]\begin{gathered} f(-2)=\frac{1}{(-2)}=-\frac{1}{2}=-0.5 \\ g(2)=3\cdot2=6 \end{gathered}[/tex]Question: What is the solution to this system of linear equations? 8x + 2y = 2 and x + 3y 2 = 14 I NEED The claim, evidence and reasoning. Please I need help
Answers
What is the value of y in the equation 2(2y − 16) = 0? (5 points)4689
Answers
Given the following equation,
[tex]\text{ 2\lparen2y - 16\rparen = 0}[/tex]Let's determine the value of y.
[tex]\text{ 2\lparen2y - 16\rparen = 0}[/tex][tex]\text{ }\frac{2(2y\text{ - 16\rparen}}{2}\text{ = 2}[/tex][tex]\text{ 2y - 16 = 0}[/tex][tex]\text{ 2y = 16}[/tex][tex]\text{ }\frac{2y}{2}\text{ = }\frac{16}{2}[/tex][tex]\text{ y = 8}[/tex]Therefore, y = 8
The answer is 8.
I got the first one right but I can’t figure out the rest. College Calculus 1. Please help :)
Answers
SOLUTION
Consider the image given
In other to evaluate the value of
[tex]g(f(0))[/tex]We first evaluate
[tex]f(0)[/tex]From the graph,
[tex]f(0)=0[/tex]Then, we obtain the value of g(0) by tracing the value of zero on the blue curve, we have
[tex]g(0)=3[/tex]Therefore
g(f(0) = 3
help my brother the other one I tried was a scam
Answers
1. Given the integers a and b, a common multiple is a positive integer that is divisible by both a and b.
2. The Least Common Multiple (LCM ) is the smallest positive integer that is divisible by both a and b.
3. Multiples of 6: 6 (= 6x1), 12 (= 6x2), 18 (= 6x3), 24 (= 6x4), ...
Multiples of 4: 4 (= 4x1), 8 (= 4x2), 12 (= 4x3), 16 (= 4x4), ...
The smallest number of these two lists is 12, then the LCM between 6 and 4 is 12.
P(A)=0.35P(B)=0.40P(A and B)=0.13Find P(A or B).Round your answer to two decimal places.
Answers
Given:
[tex]\begin{gathered} P\left(A\right)=0.35 \\ P\left(B\right)=0.40 \\ P\left(A\text{ }and\text{ }B\right)=0.13 \end{gathered}[/tex]To find:
[tex]P(A\text{ or }B)[/tex]Explanation:
Using the formula,
[tex]\begin{gathered} P(A\text{ or}B)=P(A)+P(B)-P(A\text{ and }B) \\ =0.35+0.40-0.13 \\ =0.62 \end{gathered}[/tex]Therefore, the value is,
[tex]P(A\text{ or }B)=0.62[/tex]Final answer:
The value is,
[tex]P(A\text{ or }B)=0.62[/tex]PLEASE HELP 15 POINTS I'M GIVING BRAINLIEST
Answers
Answer:
below
Step-by-step explanation:
In a RIGHT triangle such as this, cos = adjacent leg / hypotenuse
cos (beta) = 22/24 = 11/12
GEOMETRY: Express the volume of each cube below as a monomialNeeded fast!
Answers
Remember that
The volume of a cube is equal to
[tex]V=b^3[/tex]where b is the long side of the cube
so
Part 19
we have that
[tex]b=7c^6d^2[/tex]substitute in the formula
[tex]V=(7c^6d^2)^3[/tex]Applying property of exponents
[tex]\begin{gathered} V=(7^3)(c^{(6\cdot3)})(d^{(2\cdot3)}) \\ V=342c^{(18)}d^6 \end{gathered}[/tex]Part 20
we have
[tex]b=6r^7s^8[/tex]substitute in the formula
[tex]\begin{gathered} V=(6r^7s^8)^3 \\ V=216r^{(21)}s^{(24)} \end{gathered}[/tex]Flying against the wind, an airplane travels 2010 kilometers in 3 hours. Flying with the wind, the same plane travels 10,530 kilometers in 9 hours. What is the rate of the plane in still air and what is the rate of the wind?
Answers
it is given that,
the distance travel against wind = 2010
time = 3 hrs
so, the relative speed is = distance/ time = 2010/3 = 670 km/hr
the distance travel with wind is 10,530
time 9 hrs
so,the relative speed is,= 10 530/9 = 1170 km/hr
let a = speed of plane ,
b = speed of wind
so, when plane travel with wind the the relative speed is ,
a + b = 1170
when travel against wind then the relative speed,
a - b = 670
sum the equation
a + b + a - b = 1170 + 670
2a = 1840
a = 920
put a = 920 in equation a + b = 1170
920 + b = 1170
b = 1170 - 920
b = 250
thus, the rate of plane is 920
rate of wind is 250
I have been stuck on this for a while, your help would be most appreciated!
Answers
Answer:I Don't Know What She Said
Step-by-step explanation:
If f(x)=x²-20 and g(x) = 4+3x, then f(g(-3)) =
Answers
The value of function f(g(-3)= 5.
What is composite function?
A composite function is generally a function that is written inside another function. Composition of a function is done by substituting one function into another function. For example, f [g (x)] is the composite function of f (x) and g (x).
Given, f(x)=x²-20 and g(x) = 4+3x
first we will find
f(g(x)) = f(4+3x)^2-20
=9x^2+16+24x-20
=9x^2+24x-4
Now to find, f(g(-3)), substitute x=-3,
= 9(9)+24(-3)-4
=81-72-4
=5
To know more about composite function, visit:
https://brainly.com/question/4075277
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The sum of two numbers is30. The sum of4 times the larger and6 times the smaller is128. Find the numbers.
Answers
let
the smaller number = x
the larger number = y
x + y = 30
4y + 6x = 128
[tex]\begin{gathered} x+y=30 \\ 4y+6x=128 \\ x=30-y \\ 4y+6(30-y)=128 \\ 4y+180-6y=128 \\ -2y=128-180 \\ -2y=-52 \\ y=\frac{52}{2} \\ y=26 \\ x+y=30 \\ x+26=30 \\ x=30-26 \\ x=4 \end{gathered}[/tex]
The numbers are 4 and 26.
How do I know if 6.209 is greater or lesser than 6.29
Answers
Since,
[tex]6.29-6.209=0.081[/tex]The difference gives us a positive value.
So, 6.29 is grater than 6.209
Answer: Add a 0 to 6.29 and compare the numbers to see which one is greater
6.29 (or 6.290) is greater than 6.209 since the hundrenth in 6.29 is 9 and the other hundrenth for 6.209 is 0.
Blair purchases the T-shirts from Company B. She needs to add a 75markup to her total cost to make a profit when she sells the shirts at thcarnival. How should Blair determine the selling price of each T-shirt athe carnival?Drag a number into each box to make the statements true.She canThe total cost Blair paid for one T-shirt is $calculate the markup by multiplying her total cost byBlair will sell each T-shirt at the carnival for $
Answers
Isolating selling price,
[tex]\begin{gathered} \frac{\text{ markup \% }}{100}\text{= }\frac{\text{ selling price - cost}}{\text{ cost}} \\ \frac{\text{ markup \% }}{100}\cdot\cos t=\text{selling price - cost} \\ \frac{\text{ markup \% }}{100}\cdot\cos t+cost=\text{selling price} \\ \cos t(\frac{\text{ markup \% }}{100}+1)=\text{ selling price} \end{gathered}[/tex]The markup is 75 %. Supposing that the cost of a T-shirt is $6.00, then the selling price will be:
[tex]\begin{gathered} \text{selling price = 6.00}\cdot(\frac{75}{100}+1) \\ \text{selling price = 6.00}\cdot(0.75+1) \\ \text{selling price = 6.00}\cdot1.75 \\ \text{selling price = \$}10.5 \end{gathered}[/tex]What type of number is 3 - 77iChoose all answers that apply:A. RealB. ImaginaryC. Complex
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What is the value of X?
Answers
Check the picture below.
Make sure your calculator is in Degree mode.
At the start of a research study, a colony of penguins had a population of 20,000. One year later, it had a population of 21,200.Assuming the population of the colony has grown exponentially, which expression best models thepopulation? Let t represent the time in years from the start of the research study.1,200(1.015)^t20,000 (1.06)^4t21,200 (1.012)^t20,000 (1.06)^tAssuming the colony continues to grow at the same rate, what will the population of the colony be 4 years after the start of the research study?Round your answer to the nearest whole number.
Answers
Solution:
An exponential function is generally expressed as
[tex]\begin{gathered} y=a(b)^t\text{ ----- equation 1} \\ \end{gathered}[/tex]Given that in a research study, a colony of penguins had a population of 20,000.
This implies that
[tex]\begin{gathered} when\text{ t=0,} \\ 20,000=ab^0 \\ \Rightarrow20000=a\times1\text{ \lparen where b}^0=1) \\ thus, \\ a=20000 \end{gathered}[/tex]Substitute the value of a into equation 1.
Thus,
[tex]y=20000(b)^t\text{ ----- equation 2}[/tex]One year later, it had a population of 21,200. This implies that when t equals 1, we substitute the values of 21200 and 1 for y and t respectively into equation 2.
This gives
[tex]\begin{gathered} 21200=20000(b)^1 \\ \Rightarrow21200=20000b \\ divide\text{ both sides by the coefficient of b, which is b.} \\ thus, \\ \frac{21200}{20000}=\frac{20000b}{20000} \\ \Rightarrow b=1.06 \end{gathered}[/tex]Substitute the obtained value of b into equation 2.
Thus, the expression that best models the population is
[tex]20,000(1.06)^t[/tex]Assuming the colony grows at the same rate, the population of the colony after 4 years is evaluated by solving for y when the value of t is 4.
Thus,
[tex]\begin{gathered} y=20,000(1.06)^t \\ when\text{ t=4, we have} \\ y=20,000(1.06)^4 \\ =20000\times(1.06)^4 \\ =20000\times1.26247696 \\ \Rightarrow y=25249.5392 \\ \therefore y=25250\text{ \lparen nearest whole number\rparen} \end{gathered}[/tex]Hence, after 4 years the population of the colony will be 25250 penguins (nearest whole number).
in a particular hospital, newborn babies were delivered yesterday. here are their weights (in ounces). 121 ,101 ,97 121,124 ,112 assuming that these weights constitute an entire population, find the standard deviation of the population. round your answer to two decimal places.
Answers
The standard population formula is:
[tex]\sigma=\sqrt[]{\frac{\sum ^{}_{}(x_{}-\mu)^2}{n}}[/tex]where
x is the data points
μ is the mean of the data
and n is the number of data points
The mean is computed as follows:
[tex]\mu=\frac{\Sigma x}{n}[/tex]In this case, the mean is:
[tex]\mu=\frac{121+101+97+121+124+112}{6}=\frac{676}{6}=112.67[/tex]Then, the standard deviation of the population is:
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{(121-112.67)^2+(101-112.67)^2+(97-112.67)^2+(121-112.67)^2+(124-112.67)^2+(112-112.67)^2}{6}} \\ \sigma=\sqrt[]{\frac{69.39+136.19+245.55+69.39+128.37+0.045}{6}} \\ \sigma=\sqrt[]{108.22} \\ \sigma=10.4 \end{gathered}[/tex]Which of the following is a solution to the quadratic equation below?x²-3x-54-0A. 9B. -57C. 2D. 27
Answers
A. 9
Explanationto solve for x we can use the quadratic formula
it says
[tex]\begin{gathered} for \\ ax^2+bc+c=0 \\ the\text{ solution for x is} \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \end{gathered}[/tex]hence
Step 1
a) let
[tex]\begin{gathered} x^2-3x-54=0\Rightarrow ax^2+bx+c=0 \\ so \\ a=1 \\ b=-3 \\ c=-54 \end{gathered}[/tex]b) now, replace in the formula and evaluate
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ x=\frac{-(-3)\pm\sqrt{(-3)^2-4(1)(-54)}}{2(1)} \\ x=\frac{-(-3)\pm\sqrt{9+216}}{2}=\frac{3\pm\sqrt{225}}{2} \\ x=\frac{3\pm15}{2} \end{gathered}[/tex]so
[tex]\begin{gathered} x_1=\frac{3+15}{2}=9 \\ x_2=\frac{3-15}{2}=-6 \end{gathered}[/tex]therefore, the answer is
A. 9
I hope this helps you
find the slope of the line
Answers
Solution
We can use the following points from the graph:
(0,-2) and (2,1)
And we can find the slope on this way:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{1+2}{2-0}=\frac{3}{2}[/tex]Then we can find the intercept on this way:
1= 3/2 (2)+b
b= 1-3= -2
Then the equation would be:
y= 3/2 x -2
5 times 5 I need help solving that one
Answers
5 times 5 = 5 x 5
= 25
Answer : 25
(MP Reason An internet company spends half their yearly profits on advertising for the next year. Of the remaining half, they spend 1/5 on new computers. What fraction of the total profits does the company spend on new computers? Use the number line to show how you can to make his bowl? Write an equati Harcourt Pub 4 find the fraction. 1 o Module 8. Lesson 3
Answers
Let the total profit be represented by 1
The internet company spends half their yearly profits on advertising for the next year. The amount of the profit spent on advertising is 1/2 = 0.5
The amount left is 1 - 0.5 = 0.5
Of the remaining half, they spend 1/5 on new computers. It means that the amount spent on new computers is
1/5 * 0.5 = 0.1 = 1/10
Therefore, the fraction of the total profits does the company spend on new computers is
0.1/1 = 0.1 = 1/10
The number line is shown below