[tex]\tan(2\alpha)=\dfrac{2\tan \alpha }{1-\tan^2 \alpha}\\\\\\\dfrac{\sin(2\alpha)}{\cos(2\alpha)}=\dfrac{\dfrac{2\sin\alpha}{\cos\alpha}}{1-\dfrac{\sin ^2\alpha}{\cos^2\alpha}}\\\\\\\dfrac{\sin(2\alpha)}{\cos(2\alpha)}=\dfrac{\dfrac{2\sin\alpha}{\cos\alpha} }{\dfrac{\cos^2\alpha}{\cos^2\alpha}-\dfrac{\sin ^2\alpha}{\cos^2\alpha}}\\\\\\\dfrac{\sin(2\alpha)}{\cos(2\alpha)}=\dfrac{\dfrac{2\sin\alpha}{\cos\alpha} }{\dfrac{\cos^2\alpha-\sin^2 \alpha}{\cos^2\alpha}}[/tex]
[tex]\dfrac{\sin(2\alpha)}{\cos(2\alpha)}=\dfrac{2\sin\alpha}{\cos\alpha} \cdot\dfrac{\cos^2\alpha}{\cos^2\alpha-\sin^2 \alpha}\\\\\\\dfrac{\sin(2\alpha)}{\cos(2\alpha)}=\dfrac{2\sin\alpha\cos\alpha}{\cos^2\alpha-\sin^2 \alpha} \\\\\\\dfrac{\sin(2\alpha)}{\cos(2\alpha)}=\dfrac{\sin(2\alpha)}{\cos(2\alpha)}[/tex]
Answer:
See below.
Step-by-step explanation:
tan 2A = sin 2A / cos 2A
= 2 sinA cosA / (cos^2A - sin^2A)
Now divide top and bottom of the fraction by cos^2 A:
2 sinA cosA cos^2A sin^2 A
------------------- / ----------- - -------------
cos^2A cos^2 A cos^2 A
= 2 tan A / 1 - tan^2A).
If f(x)=x^4-x^3+x^2 and g(x)=-x^2, where x =/= 0, what is (f/g)(x)?
Answer:
- x² + x - 1
Step-by-step explanation:
(f / g)(x)
= [tex]\frac{x^4-x^3+x^2}{- x^2}[/tex]
divide each term on the numerator by - x²
= [tex]\frac{x^4}{- x^2}[/tex] - [tex]\frac{x^3}{-x^2}[/tex] + [tex]\frac{x^2}{-x^2}[/tex]
= - [tex]x^{4-2}[/tex] + [tex]x^{3-2}[/tex] - [tex]x^{2-2}[/tex]
= - x² + x - [tex]x^{0}[/tex] = - x² + x - 1
What is this functie
f(x) = 2x + 5
Which of the following is the correct equation for this function?
A. y= (x+4)(x+2)
B. y=x^2+ 3x – 2
C. y+ 2 = – 2(x+3)^2
D. y+ 2 = 2(x+3)^2
The equation which is correct for the given function is:
D. [tex]y+2=2(x+3)^2[/tex]
Step-by-step explanation:By looking at the graph we observe that the graph of the function passes through the point (-4,0) , (-2,0) , (-3,-2)
A)
[tex]y=(x+4)(x+2)[/tex]
when x= -3 we have:
[tex]y=(-3+4)(-3+2)\\\\y=1\times (-1)\\\\y=-1\neq -2[/tex]
Hence, option: A is incorrect.
B)
[tex]y=x^2+3x-2[/tex]
when x= -2 we have:
[tex]y=(-2)^2+3\times (-2)-2\\\\y=4-6-2\\\\y=-4\neq 0[/tex]
Hence, option: B is incorrect.
C)
[tex]y+2=-2(x+3)^2[/tex]
when x= -2 we have:
[tex]y+2=-2(-2+3)^2\\\\y+2=-2[/tex]
[tex]y=-4\neq 0[/tex]
Hence, option: C is incorrect.
D)
[tex]y+2=2(x+3)^2[/tex]
We see that the graph of this equation matches the given graph of the function.
Answer:
D. y + 2 = 2(x+3)^2
Step-by-step explanation:
f(x) = x5 – 8x4 + 16x3?
The graph touches, but does not cross, the x–axis at x =
The graph of the function crosses the x–axis at x =
.
URGENT
The true statement is the graph of the function crosses the x-axis at x = x = 0, 1.34 and 7.97
The function is given as:
[tex]\mathbf{f(x) = x^5 - 8x^4 + 16x^3}[/tex]
See attachment for the graph of [tex]\mathbf{f(x) = x^5 - 8x^4 + 16x^3}[/tex]
From the attachment, we have the following highlights
The graph crosses the x-axis at all points it touches the x-axis,The graph of the function crosses the x-axis at x = x = 0, 1.34 and 7.97Hence, the true statement is (b) above
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Find Percent increase or Percent Decrease
Question
The price of a share of one stock rose from $12.50 to $50. Find the percent increase
Provide your answer below:
The increase in price of the stock is $37.50. To find the percent increase, divide the increase (37.50) by the original price (12.50) and multiply by 100, giving a percent increase of 300%.
Explanation:The question requires us to find the percent increase in the price of a stock. First, to find the increase, we subtract the initial price from the final price. We get $50 - $12.50 = $37.50. This is the increase in price. To find the percentage increase, we divide this increase by the initial price and multiply by 100 to convert it into percent. Therefore, the percentage increase = ($37.50 / $12.50) x 100 = 300%. Therefore, there is a 300% increase in the stock price.
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PLEASE HELP ME!! THIS IS FOR MY MATH FINALS! RESPOND ASAP!!
While Raj was in Italy he heard the weather forecaster say it was going to be 14C that day. Raj wasn’t sure if that was hot or cold, so he converted the temperature to degrees Fahrenheit. What is the temperature in degrees Fahrenheit?
Use the formula, F=9/5C+32, where F is the number of degrees in Fahrenheit and C is the number of degrees in Celsius. Round your answer to the nearest whole number.
A) 25C
B) 40C
C) 57C
D) 83C
Answer:
The answer is 57 degrees Fahrenheit
Step-by-step explanation:
The temperature in degrees Fahrenheit is 57.2°F
What is formula for temperature in Fahrenheit?The Fahrenheit temperature scale is used in the United States; the Celsius, or centigrade, scale is employed in most other countries and for scientific purposes worldwide.
The conversion formula for a temperature that is expressed on the Celsius (°C) scale to its Fahrenheit (°F) representation is:
°F = (9/5 × °C) + 32.
Given:
temperature= 14 C
using formula,
F=9/5C+32,
F= 9/5 * 14+32
F= 126/5+32
F= 25.2+32
F= 57.2
Hence, the temperature in degrees Fahrenheit is 57.2°F.
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What is the slope of a line perpendicular to the line represented by the equation y=-2/5x+4/5
Answer:
[tex]\large\boxed{m=\dfrac{5}{2}}[/tex]
Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===================================\\\\\text{We have the equation of a line:}\ y=-\dfrac{2}{5}x+\dfrac{4}{5}\to m_1=-\dfrac{2}{5}.\\\\m_2=-\dfrac{1}{m_1}\to m_2=-\dfrac{1}{-\frac{2}{5}}=\dfrac{5}{2}[/tex]
Which of the following functions will produce the graph shown below?
ANSWER
The answer is B.
[tex]y = \frac{ {x}^{2} - 1}{ {x}^{2} + 2x - 3 } [/tex]
EXPLANATION
The graph represents a rational function.
This rational function has a hole at x=1 and a vertical asymptote at x=-3.
This implies that the denominator of the rational function in factored form is
[tex](x + 3)(x - 1)[/tex]
When we expand this, we get:
[tex] {x}^{2} + 2x - 3[/tex]
This tells us that the answer must be option B.
This graph also has a horizontal asymptote at y=1.
The numerator must therefore have leading term that is quadratic with the coefficient being unity or 1.
Therefore the function is actually
[tex]y = \frac{ {x}^{2} - 1}{ {x}^{2} + 2x - 3 } [/tex]
If AC = 15 centimeters, and BC = 12 centimeters, which does AB equal?
a. 6
b. 8
c. 9
d. 10
Which of the following are reciprocal functions? sin x and cos x tan x and cot x cot x and csc x csc x and sec x
Answer:
1). sin x and csc x
2). cos x and sec x
3).tan x and cot x
Step-by-step explanation:
Points to remember
Trigonometric ratios
Sin θ = Opposite side/Hypotenuse
Cos θ = Adjacent side/Hypotenuse
Tan θ = Opposite side/Adjacent side
Csc θ = Hypotenuse /Opposite side
Sec θ = Hypotenuse /Adjacent side
Cot θ = Adjacent side/Opposite side
To find the correct answers
From the above points we get reciprocal of functions are,
1). sin x and csc x
2). cos x and sec x
3).tan x and cotx
HELP ASAP PLEASE
14. The first term of a geometric series is 2 and the common ratio is 4. Write a rule to find the nth term. Find the 14th term of the sequence.
The rule for nth term will be [tex]\rm a_n = 2\times 4^{n-1}[/tex] and the 14th term of the sequence is 134217728.
What is Geometric series ?The series which can be written in the form of
[tex]\rm a_n = a_1 \times r^{n-1}[/tex]
nth term, a₁ is the first term, and r is the common ratio.
is called geometric series/
It is given in the question that
The first term of a geometric series is 2 and the common ratio is 4.
The rule for nth term will be
[tex]\rm a_n = 2\times 4^{n-1}[/tex]
To find the 14th term of the sequence.
[tex]\rm a_{14} = 2\times 4^{14-1}\\\\\rm a_{14} = 2\times 4^{13}\\\\a_{14}= 2 \times67108864 \\\\\\a_{14}= 134217728[/tex]
Therefore the 14th term of the sequence is 134217728.
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To find the nth term of a geometric series with first term 2 and common ratio 4, the formula [tex]a * r^(n-1)[/tex] is used.
For the 14th term, apply 2 * [tex]4^(13)[/tex] to get 134,217,728.
The student has asked for the rule to find the nth term of a geometric series and for the 14th term specifically. The first term is given as 2, and the common ratio is 4.
In a geometric series, the nth term is found using the formula[tex]a * r^(n-1)[/tex], where a is the first term and r is the common ratio. To find the 14th term, we would use the formula [tex]2 * 4^(14-1)[/tex].
Let's calculate the 14th term:
Substitute the given values into the formula: 2 * [tex]4^(13)[/tex].Calculate 4 raised to the 13th power, which is 67,108,864.Multiply this result by the first term, which is 2, to get the 14th term: 134,217,728.Therefore, the 14th term of the sequence is 134,217,728.
Which graph represents a line with a siope of
and a y-intercept equal to that of the line y= 2x-22
Answers are on the picture.
Please Help Me On This
Answer:
last choice
Step-by-step explanation:
So the y-intercept is -2 and the slope is -2/3
The only choices I'm going to look at is first and last because they go through -2 on y-axis.
Now -2/3 is the slope that means the graph should be going down reading it left to right so the last choice,
What is the result of the following division?
For this case we must indicate the result of the following expression:
[tex]\frac {2x ^ 3-3x + 5} {x + 3}[/tex]
We must build a quotient that, when multiplied by the divisor, eliminates the terms of the dividend until it reaches the remainder.
It must be fulfilled that:
Dividend = Quotient * Divider + Remainder
Answer:
See the attached image
Option A
Answer: Choice A
Step-by-step explanation:
Justin and Desiree each wrote a ratio comparing the numbers of students and tables in their classroom. There are 6 tables in the room with 4 students at each table.
Justin states that the ratio is 4:1.
Desiree insists the ratio is 24:6.
They both ask Luke to tell them which ratio is correct. Which statement below would be the best answer for Luke?
Answer:
Desiree and Justin have the same ratio, Justin's is just simplified.
Step-by-step explanation:
Take Desiree's ratio and divide both sides by 5
24:6
24/6 : 6/6
4:1
This is the same ratio as Justin
Both ratio's are the same
Answer:
Both are correct
Step-by-step explanation:
2x^2+7x=15 write in standard then factor the left side of the equation.
Answer:
see explanation
Step-by-step explanation:
Given
2x² + 7x = 15 ( subtract 15 from both sides )
2x² + 7x - 15 = 0 ← in standard form
To factorise the left side
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 2 × - 15 = - 30 and sum = + 7
The factors are + 10 and - 3
Use these factors to split the x- term
2x² + 10x - 3x - 15 ( factor the first/second and third/fourth terms )
2x(x + 5) - 3(x + 5) ← factor out (x + 5) from each term
(x + 5)(2x - 3) ← in factored form
Which equation is equivalent to y - 6 = -12(x+4)?
Answer:
The answer is y = -12x - 42
Step-by-step explanation:
First distribute -12 into the paranthesis.
y - 6 = -12x - 48
Then add 6 to both sides.
y = -12x - 42
That's your final answer. I hope this helps love! :)
Answer:
[tex]x = \frac{ - 1}{12} y + \frac{ - 7}{2} \\ c. \: y = - 12x - 42[/tex]
Step-by-step explanation:
[tex] 1. \: - 12x - 48 = y - 6 \\ 2. \: - 12x = y + 42 \\ 3. \: \frac{12x}{ - 12} = \frac{y + 42}{ - 12} \\ x = \frac{ - 1}{12} y + \frac{ - 7}{2} [/tex]
Please answer ASAP. You begin with 1/2 scoop of ice cream. Since you're hungry, you ask the vendor for 2/7 more scoops of ice cream. Then, you eat 5/8 scoops. How many scoops of ice cream are left on your cone? I will mark Brainliest for first correct answer.
Answer:
9/56
Step-by-step explanation:
[tex] \frac{1}{2} + \frac{2 }{7} - \frac{5}{8 } = \frac{9}{56} [/tex]
You invested $5000 between two accounts paying 4% and 9% annual interest, respectively. If the total interest earned for the
year was $350, how much was invested at each rate?
$
was invested at 4% and
was invested at 9%.
Answer:
Part 1) The amount invested at 4% was $2,000
Part 2) The amount invested at 9% was $3,000
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]I=P(rt)[/tex]
where
I is the Final Interest Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
Let
x------> the amount invested at 4%
5,000-x ----> the amount invested at 9%
in this problem we have
[tex]t=1\ year\\ P=\$5,000\\I=\$350\\r1=0.04\\r2=0.09[/tex]
substitute in the formula above
[tex]350=x(0.04*1)+(5,000-x)(0.09*1)[/tex]
[tex]350=0.04x+450-0.09x[/tex]
[tex]0.05x=450-350[/tex]
[tex]0.05x=100[/tex]
[tex]x=2,000[/tex]
so
[tex]5,000-x=5,000-2,000=3,000[/tex]
therefore
The amount invested at 4% was $2,000
The amount invested at 9% was $3,000
The value of one of Kevin's baseball cards was $6.00 when he first got it. The value of this card now is $15.00. What is the percent increase in the value of the card?
Answer: %150
Step-by-step explanation:
Percent increase = New Value - original value/ original value * 100
15 - 6/6 * 100
9/6 * 100
1.5 * 100
150
A walking path across a park is represented by the equation y= -4x - 6 . A new path will be built perpendicular to this path. The path will intersect at the point (-4 , 10) . Identify the equation that represents the new path .
Answer:
y=1/4 x +11
Step-by-step explanation:
So this is a word problem but it isn't too bad to figure what they want: They are looking for a line that is perpendicular to y=-4x-6 and goes through (-4,10).
So we are looking for an equation whose slope is the opposite reciprocal of the given equation's slope.
The given equation has a slope of -4
The opposite reciprocal of -4 is 1/4 so that is the slope of our new line.
So we know our equation is in the form of y=1/4 x+b
Now we are given that this line should go through (-4,10) so plug it in to find b.
10=1/4 * (-4)+b
10=-1+b
11=b
So the equation is y=1/4 x+11
Answer: [tex]y=\frac{1}{4}x+11[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
Given the equation of the line [tex]y= -4x - 6[/tex], you can identify that the slope is:
[tex]m=-4[/tex]
By definition, the slopes of perpendicular lines are negative reciprocals, then the slope of equation of the line that represents the new path which will be built perpendicular to other path, is:
[tex]m=\frac{1}{4}[/tex]
Knowing that the path will intersect at the point (-4 ,10), you need to substitute the slope and this point into [tex]y=mx+b[/tex] and solve for "b":
[tex]10=\frac{1}{4}(-4)+b\\\\10+1=b\\\\b=11[/tex]
Therefore, the equation that represents the new path is:
[tex]y=\frac{1}{4}x+11[/tex]
There are 36 squares in the model.What is the result of 36 divided by 3
Answer:
The result of 36 divided by 3 is 12
Answer:
12 is the answer
Step-by-step explanation:
The formula W = Fd shows the relationship between work, force, and distance. Solve this formula for distance.
Answer:
[tex]d = \frac{W}{F}[/tex]
Step-by-step explanation:
To do this, we must isolate the variable d.
W = Fd
To isolate d, we must divide the variable F from both sides.
W ÷ F = Fd ÷ F
W ÷ F = d
Now that we have isolated the variable d, we have successfully solved this formula for distance.
[tex]d = \frac{W}{F}[/tex]
Answer:
d = W/F.
Step-by-step explanation:
You simply divide both sides by F:
W / F = Fd / F
W/F = d.
each machine ch the bottling plant can fill several gallons of milk every 15 seconds . this sequence describes the number of gallons of milk each machine at the bottling plant can fill over time 12,24,36,48,80
Answer:
A-B-D-B
Step-by-step explanation:
Type in the correct answer. What is the slope of line m?
Answer:
[tex]-\dfrac{1}{2}[/tex]
Step-by-step explanation:
In the given graph of straight line to find the slope of the line.
First we choose two points on line and then using formula to find the slope.
Formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Point on line from graph: (2,-1) and (-2,1)
[tex]x_1\rightarrow 2[/tex]
[tex]y_1\rightarrow -1[/tex]
[tex]x_2\rightarrow -2[/tex]
[tex]y_2\rightarrow 1[/tex]
Substitute the points into formula
[tex]m=\dfrac{1+1}{-2-2}[/tex]
[tex]m=-\dfrac{1}{2}[/tex]
Hence, The slope of the line is [tex]-\dfrac{1}{2}[/tex]
The slope (m) of the line passing through the points (-2, 1) and (2, -1) is -1/2.
The slope of a line is a measure of its steepness or incline. It determines how much the line rises or falls for each unit of horizontal change. Mathematically, the slope is defined as the ratio of the vertical change (the difference in y-coordinates) to the horizontal change (the difference in x-coordinates) between any two points on the line.
The slope is typically denoted by the letter "m" and can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are any two distinct points on the line.
The slope can be positive, negative, zero, or undefined. A positive slope indicates that the line is upward-sloping from left to right, a negative slope indicates a downward-sloping line, a zero slope indicates a horizontal line and an undefined slope indicates a vertical line. The magnitude of the slope represents the steepness of the line.
To find the slope (m) of a line passing through two points (x1, y1) and (x2, y2), you can use the formula:
m = (y2 - y1) / (x2 - x1)
In this case, the points are (-2, 1) and (2, -1). Let's substitute the values into the formula:
m = (-1 - 1) / (2 - (-2))
= (-2) / (2 + 2)
= (-2) / 4
= -1/2
Therefore, the slope (m) of the line passing through the points (-2, 1) and (2, -1) is -1/2.
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PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! WILL MARK BRAINLIEST TO BEST DETAILED ANSWER
Minnie is doing a survey to find the time her classmates spend playing musical instruments. She asks the following question: Which student spends the most time playing musical instruments? Part A: Describe the data you would expect her to collect from this question. (5 points) Part B: Explain whether this is a statistical question. If this is not a statistical question, then modify the question to make it statistical. (5 points)
A. You would just get a lot of names back from people, thinking they have the most time playing instruments.
B. This question is not a statistically accurate question if you would like statistical answers back.
Statistical question definition:
A statistical question is one that can be answered by collecting data and where there will be variability in that data. For example, there will likely be variability in the data collected to answer the question,
The question to ask to get statistical answers back would be: How many hours do you play the instrument a day?
Each student would answer and you would see who has the most hours.
Final answer:
Minnie should collect quantitative data on the hours spent playing instruments by her classmates to determine who spends the most time. The original survey question is not statistical because it does not allow for analysis of a group trend, but changing the question to inquire about the typical number of hours spent by students each week would make it statistical.
Explanation:
Part A: Expected Data Collection
The data Minnie would expect to collect from her survey question would consist of quantitative information. Specifically, she should gather the number of hours each classmate spends playing musical instruments per week. This data allows her to determine which student spends the most time practicing.
Part B: Statistical Question Analysis
The question, "Which student spends the most time playing musical instruments?" is not a statistical question because it seeks a singular answer rather than understanding a trend, variation, or distribution within a group. To make it statistical, the question could be modified to: "How many hours do students typically spend playing musical instruments each week?" This revised question allows for the collection, analysis, and interpretation of data, which can lead to conclusions about the musical habits of Minnie's classmates.
Two students were asked if they liked to read. Is this a good example of a statistical question? Why or why not?
Yes, this is a good statistical question because a variety of answers are given.
Yes, this is a good statistical question because there are not a variety of answers that could be given.
No, this is not a good statistical question because there are not a variety of answers that could be given.
No, this is not a good statistical question because there are a variety of answers that could be given. First gets brainiest
Answer:
Yes, this is a good statistical question because a variety of answers are given.
Step-by-step explanation:
A question can be called a good statistical question because of the variety of the answers it can bring to data. The answers to the same question will be different for different people.
Hence,
Yes, this is a good statistical question because a variety of answers are given ..
Answer:
C
Step-by-step explanation:
Did Unit Test Review B)
x^2+y^2=25 find the distance of point (x,y) from origin
Answer:
5
Step-by-step explanation:
The radius is 5.
All I do was think of the center-radius form a circle
(x-h)^2+(y-k)^2=r^2
x^2 + y^2 =25
(x-0)^2+(y-0)^2=5^2
The center is (0,0) and the radius is 5.
So a point on the circle (x,y) has a distance of 5 from the center
and the center's case here is (0,0).
Josh wants to buy 15 pounds of shrimp and 10 pounds of crawdads. He has 4 buckets that can each hold 6 pounds. How many pounds of shrimp and crawdads will not fit in the 4 buckets?
1 pound
Step-by-step explanation:
15+10=25
25÷6=24.1
On a unit circle, the vertical distance from the x-axis to a point on the perimeter of the circle is twice the horizontal distance
from the y-axis to the same point. What is sin theta?
Check the picture below.
since the vertical distance, namely the y-coordinate, is twice as much as the horizontal, then if the horizontal is "x", the vertical one must be 2x.
let's find the hypotenuse first.
[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{x}\\ b=\stackrel{opposite}{2x}\\ \end{cases} \\\\\\ c=\sqrt{x^2+(2x)^2}\implies c=\sqrt{x^2+4x^2}\implies c=\sqrt{5x^2}\implies c=x\sqrt{5} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf sin(\theta )=\cfrac{\stackrel{opposite}{2~~\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }}{\stackrel{hypotenuse}{~~\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ \sqrt{5}}}\implies \stackrel{\textit{and rationalizing the denominator}~\hfill }{\cfrac{2}{\sqrt{5}}\cdot \cfrac{\sqrt{5}}{\sqrt{5}}\implies \cfrac{2\sqrt{5}}{(\sqrt{5})^2}\implies \cfrac{2\sqrt{5}}{5}}[/tex]
The value of Sin θ for a given circle and given condition is (2√5)/5.
What is Circle?
A circle is the set of all points in the plane that are a fixed distance (the radius) from a fixed point (the center). Any interval joining a point on the circle to the center is called a radius.
Here, let the horizontal side be x.
vertical side be y
then as per the given condition
Vertical distance = 2 X horizontal distance
y = 2x
By Pythagoras Theorem,
r = [tex]\sqrt{x^2+y^2}[/tex]
1 = [tex]\sqrt{x^2+(2x)^2}[/tex]
1 = x² + 4x²
5x² = 1
x² = 1/5
x = 1/√5
then, y = 2/√5
Now, Sin θ = perp. / Hypo.
Sin θ = y/1
Sin θ = 2/√5
or Sin θ = (2√5)/5
Thus, the value of Sin θ for a given circle and given condition is (2√5)/5.
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help me please!!!!!!!!!!!!!
Answer:
C. √xy\y
Step-by-step explanation:
Multiply the denominator and the numerator by the conjugate of the numerator to arrive at your answer.