To show that p^2 = 4q^2(1-q^2), we use trigonometric identities and algebraic manipulations to prove the given equation sin((θ-1)p) = 2cos((θ-1)q). By taking the inverse sine, squaring both sides, and applying trigonometric identities, we arrive at the desired result.
Explanation:To show that p^2 = 4q^2(1-q^2), we need to start with the equation sin((θ-1)p) = 2cos((θ-1)q). We can use the trigonometric identities and algebraic manipulations to prove this equation.
Start by taking the inverse sine of both sides: (θ-1)p = sin^(-1)(2cos(θ-1)q).Next, use the identity sin^(-1)(x) = θ: (θ-1)p = sin^(-1)(2cos(θ-1)q) becomes p = sin^(-1)(2cos(θ-1)q)/(θ-1).Square both sides of the equation to eliminate the inverse sine: p^2 = (sin^(-1)(2cos(θ-1)q)/(θ-1))^2.Apply the identity sin^2(θ) = 1 - cos^2(θ) to the right side of the equation: p^2 = (1 - cos^2(sin^(-1)(2cos(θ-1)q)/(θ-1))))Finally, simplify the equation using algebraic manipulations to arrive at p^2 = 4q^2(1-q^2).Learn more about Trigonometry here:https://brainly.com/question/31896723
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Solve the system by elimination
2x+6y= -12
5x-5y= -10
What is the unit rate for 4543.08 km in 52.4 h? Enter your answer, as a decimal, in the box. km/h
Final answer:
The unit rate, or average speed, for traveling 4543.08 km in 52.4 hours is calculated by dividing the distance by the time, resulting in an average speed of 86.70 km/h.
Explanation:
The question asks for the unit rate of 4543.08 km traveled in 52.4 hours, which is essentially asking for the average speed in kilometers per hour (km/h). To find this, you would divide the total distance traveled by the total time taken.
Mathematically, this is expressed as:
Distance (km) / Time (h) = Speed (km/h)Substituting the given values:
4543.08 km / 52.4 h = 86.70 km/hTherefore, the unit rate or average speed is 86.70 km/h. It's important to note that when calculating such problems, it's essential to maintain consistency in the units (in this case, km for distance and hours for time) to ensure the accuracy of your result.
What is y-10=9(x+8) written in standard form?
Answer:
-9x+y=82
Step-by-step explanation:
hope this helped!
The equation y-10=9(x+8) can be transformed into standard form by distributing, simplifying, and rearranging terms to get 9x - y = -82.
Explanation:The given equation is y-10=9(x+8), and we're asked to change this slope-intercept form into the standard form. First, we'll start by distributing the 9 to both x and 8 which will result in y-10 = 9x + 72. Then, we'll bring terms involving x and y to one side of the equation, leading to -9x + y = 82. This is almost in standard form, but typically we want the leading coefficient (the coefficient of x) to be positive, so we'll multiply the equation by -1. This gives us 9x - y = -82, which is the equation in standard form.
Learn more about Algebra here:https://brainly.com/question/32436021
A chicken soup recipe calls for
9
cups of chicken stock. How much is this in quarts?
A plane is traveling at a speed of 400 miles per hour.How far will the plane travel in 5 hours?
Answer:
Step-by-step explanation:
Nola hiked down a trail at a steady rate for 10 minutes. Her change in elevation was -200 feet. Then she continued to hike down for another 20 minutes at a different rate. Her change in elevation for this part of the hike was -300 feet. During which portion of the hike did she walk down at a faster rate ? Explain your reasoning
An aircraft travels with the wind for 120 miles in 0.75 of an hour. The return trip is flown against the wind and takes exactly 1 hour.
Which system of linear equations represents x, the speed of the plane in miles per hour, and y, the speed of the wind in miles per hour? Recall the formula d = rt.
Answer:
its A
Step-by-step explanation:
Ryan earned $376 by working for 4 days. If he earned the same amount each day, how much could he earn working 5 days?
Write two numbers so that
The first number is less than the second number, and
The absolute value of the first number is greater than the absolute value of the second number
what is equivalent to the square root of -27
What radius of a circle is required to inscribe an equilateral triangle with an area of 35.074 in2 and an altitude of 7.794 in? (round to nearest tenth)
Answer:
[tex]r[/tex]≈[tex]5.2 in[/tex]
Step-by-step explanation:
It is given that a circle is required to inscribe an equilateral triangle with an area of [tex]35.074 in^2[/tex] and an altitude of [tex]7.794 in[/tex],
Also, we know that the centroid divides the altitude into 2:1 form, thus
[tex]r=\frac{2}{3}(h)[/tex]
Substituting the value of an altitude, we have
[tex]r=\frac{2}{3}(7.794)[/tex]
[tex]r=5.196 in[/tex]
[tex]r[/tex]≈[tex]5.2 in[/tex]
Therefore, the radius of the circle is [tex]5.2 inches[/tex].
adding fractions 4/9 + 1/3=
find x when y= 14, if y=7 when x=8
Answer: The required value of x is 16.
Step-by-step explanation: Given that the value of y is 7 when the value of x is 8.
We are to find the value of x when y is 14.
The ratio of y to x is given by
[tex]y:x=7:8.[/tex]
Therefore, when y = 14, we must have
[tex]14:x=7:8\\\\\\\Rightarrow \dfrac{14}{x}=\dfrac{7}{8}\\\\\\\Rightarrow x=\dfrac{14\times8}{7}\\\\\Rightarrow x=16.[/tex]
Thus, the required value of x is 16.
If $16,400 is deposited into a CD paying 5.1% annually, how much will be in the account after 20 years? Enter your answer rounded to the nearest cent.
16,400 x (1 + 0.051)^20 =
16400 x (1.051)^20 =
16400 x 2.70429659 =
$44,350.46
A recipe uses 6 cups of cheese to serve 30 people. How much cheese is needed for 50 people
what percent of 25 is 30? (round to nearest hundredth if necessary) please help.
If 40% is equal to the fraction x/30, what is the value of X?
The value of x is 12 and this can be determined by using the arithmetic operations and the given data.
Given :
40% is equal to the fraction x/30.
The following steps can be used in order to determine the value of 'x':
Step 1 - The arithmetic operations can be used in order to determine the value of 'x'.
Step 2 - According to the given data, the 40% is equal to the fraction x/30.
Step 3 - So, the value of X is calculated as:
[tex]\dfrac{40}{100}=\dfrac{x}{30}[/tex]
Step 4 - Simplify the above expression.
x = 12
For more information, refer to the link given below:
https://brainly.com/question/25834626
Sandy is observing the velocity of a runner at different times. After one hour, the velocity of the runner is 4 km/h. After two hours, the velocity of the runner is 2 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the runner at different times. Show your work and define the variables used. (5 points)
Part B: How can you graph the equations obtained in Part A for the first 4 hours? (5 points)
Answer:
As per the statement: Sandy is observing the velocity of a runner at different times.
Also, after one hour, the velocity of the runner is 4 km/h. and after two hours, the velocity of the runner is 2 km/h..
(A)
Let x represents the time in hours and y represents the velocity of the runner(in km/hr)
Then, we have two points from the given statement:
(1, 4) and (2, 2)
An equation of line for two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by;
[tex]y-y_1 = \frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
For the given two points (1, 4) and (2, 2) we have an equation:
[tex]y-4 = \frac{2-4}{2-1}(x-1)[/tex]
[tex]y-4 = \frac{-2}{1}(x-1)[/tex]
or
[tex]y-4 = -2(x-1)[/tex]
Using distributive property: [tex]a\cdot(b+c) = a\cdot b+ a\cdot c[/tex]
[tex]y-4 = -2x + 2[/tex]
Add 4 on both sides we get;
[tex]y-4 +4= -2x + 2+4[/tex]
Simplify:
[tex]y= -2x + 6[/tex]
Add 2x on both sides we get;
[tex]y + 2x=-2x+6+ 2x[/tex]
Simplify:
[tex]y + 2x = 6[/tex]
[Since, standard form for linear equations in two variables is Ax+By=C]
Therefore, an equation in two variables in the standard form that can be used to describe the velocity of the runner at different times is:
[tex]2x+y= 6[/tex] ; where x represents the time in hours and y represents the velocity of the runner.
(B)
Equation in part A
It is given as; [tex]2x+y= 6[/tex] .....[1]
To graph this equation; for the first 4 hours.
x y = -2x+6
1 4
2 2
3 0
4 -2
Now, using these points (1, 4) , (2, 2) , (3, 0) and (4, -2) plot the graph as shown below in the attachment.
Convert this improper fraction to a mixed number. 56/5
11 r 1
11 1/5
11.2
5/56
Maryam had to sail 4 2⁄3 miles to reach her destination. At the end of the day, she had sailed 3 1⁄3 miles. How far was she from her destination?
subtract the distance she traveled from the total distance she has to go
4 2/3 - 3 1/3 = 1 1/3 miles to go
Ronald is saving money to buy a bicycle. He has $37.80 in his savings account and saves 20% of his paper route
what is the square root of 658
Using a calculator or long division, the square root of 658 is approximately 25.66.
To find the square root of 658, we can use a calculator or the long division method.
Using the long division method:
Step 1: Guess a number whose square is close to 658. Let's start with 25, since [tex]\(25^2 = 625\)[/tex], which is close to 658.
Step 2: Divide 658 by 25. [tex]\(658 \div 25 = 26.32\)[/tex]
Step 3: Take the average of the quotient and the divisor: [tex]\((25 + 26.32) \div 2 = 25.66\)[/tex]
Step 4: Repeat steps 2 and 3 using the new guess until the desired level of accuracy is achieved.
By repeating these steps, we'll get closer to the square root of 658. However, using a calculator will give a more accurate result.
What is the probability that two people have a birthday on the same day of the same month?
HELPPPPPPPPP STATTTSSSSS
Please help asap! I do not understand questions 9-12
https://my.hrw.com/content/hmof/math/hsm/na/gr10/diff_resources_aga_9780544398887_/NA_Practice_U2M04L05_C.pdf
Which step could be used to solve x + 3.6 = -1.7 for x in one step? Check all that apply.
[ ] add 3.6 to both sides
[ ] add -3.6 to both sides
[ ] add 1.7 to both sides
[ ] add -1.7 to both sides
[ ] subtract 3.6 from both sides
[ ] subtract 1.7 from both sides
Answer: Option (2) and (5) are the correct options.
Step-by-step explanation:
Since, the given expression, x+3.6= -1.7
If we add -3.6 in both sides then we get x+3.6+(-3.6)=1.7-3.6⇒x= -1.9
while,
If we subtract 3.6 from both sides then we get x+3.6-3.6=1.7-3.6⇒x= -1.9
Thus, In the above by adding -3.6 and by subtracting 3.6 we get the value of x in one step.(because after this only x remains in LHS of the given expression)
Therefore, Option (2) and (5) are correct.
Note: Except these two options we can not get x in one step. (we can not get single x in LHS of the given expression by the other options.)
Answer:
b e
Step-by-step explanation:
How many lines can be drawn through points j and k?
it takes Joaquin 1/3 hours to walk to the library 3/4 miles away what is his walking pace in miles per hour
help asap need answer
If f(x) = 9 cos2(x), compute its differential df. df = (−18cos(x)sin(x))dx correct: your answer is correct. approximate the change in f when x changes from x = π 6 to x = π 6 + 0.1. (round your answer to three decimal places.) δf = .738 incorrect: your answer is incorrect. approximate the relative change in f as x undergoes this change. (round your answer to three decimal places.)
Given: f(x) = 9 cos (2x)
The differential equation is df = - 18 sin(2x) dx
When x contrasts from π/6 to π/6 + 01, then dx = 0.1.
The variation in f is δf = - 18 sin(π/3) *(0.1) = -1.5588 ≈ -1.559
The computation in the change in f directly:
f(π/6) = 9 cos(π/3) = 4.5
f(π/6 + 0.1) = 9 cos(π/3 + 0.2) = 2.6818
δf = 2.6818- 4.5 = -1.6382 ≈ -1.638
Direct computation of δf is near to the real value but in error.
The two outcomes will be closer as dx gets smaller.
Answer would be:
δf = -1.559 (correct answer)
δf = -1.638 (approximate answer)
Answer:
a
Step-by-step explanation: