Which values represent solutions to Cosine (StartFraction pi Over 4 EndFraction minus x) = StartFraction StartRoot 2 EndRoot Over 2 EndFraction sine x, where x Is an element of [0, 2Pi)?
Left-brace 0, pi right-brace
Left-brace 0, StartFraction 3 pi Over 2 EndFraction right-brace
Left-brace StartFraction pi Over 2 EndFraction, StartFraction 3 pi Over 2 EndFraction right-brace
Left-brace pi, StartFraction 3 pi Over 2 EndFraction
Answers
Answer:
C.
Step-by-step explanation:
got it right on edge :)
The given trig function consist of trig values of common angles;
The values that represent the solution to [tex]\mathbf{cos \left(\dfrac{\pi}{4} - x\right)} = \dfrac{\sqrt{2} }{2} \cdot sin \, x[/tex], x ∈ [0, 2·π) are;
[tex]x = \left\{\dfrac{\pi}{2} , \, or \ \dfrac{3 \cdot \pi}{2} \right \}[/tex]
Reason:
The given function is presented as follows;
[tex]cos \left(\dfrac{\pi}{4} - x\right) = \dfrac{\sqrt{2} }{2} \cdot sin \, x[/tex]
Where;
x ∈ [0, 2·π)
We have;
cos(A - B) = cos(A)·cos(B) - sin(A)·sin(B)
[tex]cos \left(\dfrac{\pi}{4} \right) = \dfrac{\sqrt{2} }{2}, \ sin\left(\dfrac{\pi}{4} \right) = \dfrac{\sqrt{2} }{2}[/tex]
Which gives
[tex]cos \left(\dfrac{\pi}{4} - x\right) =\dfrac{\sqrt{2} }{2} \cdot cos \, x + \dfrac{\sqrt{2} }{2} \cdot sin \, x[/tex]
Therefore, we get;
[tex]\dfrac{\sqrt{2} }{2} \cdot cos \, x = \dfrac{\sqrt{2} }{2} \cdot sin \, x - \dfrac{\sqrt{2} }{2} \cdot sin \, x = 0[/tex]
cos x = 0
[tex]cos \left(\dfrac{\pi}{2} \right) = 0[/tex]Therefore;
The possible solutions (x-values) to cos x = 0 are; [tex]0 \leq \dfrac{n \cdot \pi}{2} \leq 2 \cdot \pi[/tex]Where;
n = 1, 3, 5, ...
x ∈ [0, 2·π)
We get;
[tex]x = \left\{\dfrac{\pi}{2} , \, or \ \dfrac{3 \cdot \pi}{2} \right \}[/tex]Learn more here:
https://brainly.com/question/12774575
Related Questions
What is
1. -2(n-9)+4
2. 6x - (2 - 3x)
Answers
Answer:
1) -2n + 22
2) 9x - 2
Step-by-step explanation:
1. -2(n-9)+4
-2n + 18 + 4
-2n + 22
2. 6x - (2-3x)
6x - 2 + 3x
9x - 2
Find the distance between the points (0, 2) and (4, 5).
Answers
Answer:
it's going to be 5
Step-by-step explanation:
which is greater 8.7 or 8.5
Answers
8.7 is greater than 8.5 because the 7 is more than the 5 and the number 5 is less. Hope this helps :)
Plz help I am confusion
Answers
Answer :
Option D : ( 7 , 5 )
We can use x +y / 2 = midpoint,
Let x be point A and y be point B
((1,1) + x)/2 = (4,3)
(1,1) + x = 2(4,3)
x = (8,6)-(1,1)
x = (7,5)
Hope it helps :)
Mark it as Brainliest pls :)
5x + 10 > 35
How do you work this out?
Answers
Answer:
[tex]x > 5[/tex]
Step-by -step explanation:
Solving inequalities is similar to solving equations.
[tex]5x + 10 > 35[/tex]
Subtract 10 from both sides.
[tex]5x > 25[/tex]
Divide by 5 from both sides to isolate the x.
[tex]x > 5[/tex]
Step-by-step explanation:
[tex]5x + 10 > 35 \\ \: 5x > 35 - 10 \\ 5x > 25 \\ x > 5[/tex]
878 divided by 26 solve it
Answers
Answer:
33.7692307692 or for it to be rounded, 34 or 33.8
Step-by-step explanation:
Answer:
439/13
Step-by-step explanation:
One week, Sarah earned $192.00 at her job when she worked for 8 hours. If she is paid the same hourly wage, how many hours would she have to work the next week to earn $408.00?
Answers
answer: 17
Answer:
17
Step-by-step explanation:
Evaluate 26 + a if a = 8.
Answers
Answer:
34
Step-by-step explanation:
26 + 8 = 34
insert 8 into the equation where a is and add.
Geom_CQA1_20-21
Question: 1-5
The endpoints of MN are located at M (-4, 4) and N (2,-2). What are the coordinates of the point P that divides MN such that MP : PN is equal to 2: 1?
(-3.5, 2.5)
(-2,2)
(-1, 1)
(0,0)
Answers
Answer:
The coordinates of the point P is (0,0)
Step-by-step explanation:
Here, we want to find the coordinates of point P which divides the segment MN in the ratio 2 to 1.
Mathematically, what we shall use here is the internal division formula;
The internal division formula is given as follows;
(x,y) = (nx1 + mx2)/(m + n) , (ny1 + my2)/(m + n)
From the question;
x1 = -4
x2 = 2
y1 = 4
y2 = -2
m = 2
n = 1
By substituting, we have;
(1(-4) + 2)2))/(1 + 2) , (1(4) + 2(-2))/(1+2)
= (-4 + 4)/3 , (4-4)/3
= (0,0)
I only paid $69.65 for my new helmet as it was on sale for 30% off! How much would I have paid if it wasn't on sale?
Answers
Answer: $48.76
Step-by-step explanation:
69.65 * .30 = 20.89
69.65 - 20.89 = 48.76
Answer:
I think it is 90.545
Step-by-step explanation:
It may or may not be correct btw
what is one x 1 divided by 1
Answers
Answer:
1?
Step-by-step explanation:
which of the fillowing number are greater than 185/100
-1.08
190/100
-35/20
Answers
Answer:
190/100
Step-by-step explanation:
185/100 is greater than 1, so two of those answers are already out.
185/100= 1.85
-1.08 < 1.85 so no
-35/20 = -1.75
-1.75 < 1.85 so this also no
Then the last one is 190/100 = 1.90
1.90 > 1.85
So 190/100 is the answer
{6 + [(3 * 2) - (2 * 2)]} ÷ 2
Answers
1st: 3*2 = 6, 2*2 = 4
2nd: 6 - 4 = 2
3rd: 6 + 2 = 8
4th: 8 divided by 2 = 4
Answer: 4
Overview
Question Progress
Homework Progress
12756
Which 2 grids have 25% shaded?
b)
a)
d)
Introduction to Percentages
View One Minute Version
Overview
Answers
Answer:
7
Step-by-step explanation:
what is 3/4f-4g+8 how many terms
Answers
Answer:
0 = 2f + 3g + 4f + -4g + 8
Step-by-step explanation:
Maggie is participating in her school reading challenge. She read 18 of the total 25 books. Wh
percent of books did she read?
Answers
Answer:
The answer is 72
Please help ASAP! Will give brainleist Thank you!
Answers
Answer:
b,d,e,g
Step-by-step explanation:
Write a linear equation with a slope of 14 and y-intercept -12.
Answers
Answer:
y=14x-12
Step-by-step explanation:
in the standard format y=mx+b, m is the slope and b is the y-intercept, so this equation would be y=14x-12 since the slope is 14 and the y-intercept is -12.
-5t^2+10t+22 does the ball reach a height of 35m
Answers
Answer:
Step-by-step explanation:
35=-5t²+10t+22
5t²-10t+13=0
disc =b²-4ac=(-10)²-4×5×13=100-260=-160<0
t is imaginary.
So ball never reaches a height of 35 m
A recipe calls for 4 cans of 12.6 oz of chicken broth. how many ounces of chicken broth does the recipe require? A. 3.15. B. 8.6 C. 16.6 D 50.4
Answers
Answer:
50.4
Step-by-step explanation:
Answer:
Yes, The correct answer is 50.4 oz
Step-by-step explanation:
Consider these similar triangles were ALMN - ARSN.
What is the length of x?
Answers
Answer:
x = 15
Step-by-step explanation:
48/12 = 4
60/4 = 15
Essentially, find the growth rate and divide the larger number by that number, or if you were given the smaller number (15), you would simply need to multiply 15 by 4 to find 60.
Evaluate f(x) = X(With an exponent of 2) -3x +2, given f(x + 1).
Answers
Answer:
f(x + 1) = x² - x
Step-by-step explanation:
f(x) = x² - 3x + 2 when f(x + 1)
f(x + 1) = (x + 1)² - 3(x + 1) + 2
f(x + 1) = (x² + 2x + 1) + (-3x - 3) + 2
f(x + 1) = x² - x + 0
f(x + 1) = x² - x
Best of Luck!
Write the prime factorization of the number.
1: 42
2: 50
3: 66
Answers
50: 2 x 5 x 5 or 2 x 5^2
66: 2 x 3 x 11
is 5/x+y=-7 linear or nonlinear
Answers
Answer:
Not linear.
Step-by-step explanation:
A linear equation is an equation of a straight line, which means that the degree of a linear equation must be 0 or 1 for each of its variables. In this case, the degree of variable y is 1 , the degrees of the variables in the equation violate the linear equation definition, which means that the equation is not a linear equation.
point) Arrange the four numbers shown in order from least to greatest. 6.7% 0.67 6.7 x 10-3 6/9
Answers
Answer:
I'm pretty sure the answer is: 6.7 x 10^-3, 6.7%, 6/9, 0.67.
Step-by-step explanation:
Convert everything into decimal form.
6.7 x 10^-3 = 0.0067
6.7% = 0.067
6/9 = 0.66... (repeating decimal)
0.67 = 0.67 (already a decimal)
Once you have converted your numbers into decimals then you can compare them from least - greatest.
Abdul was scuba diving 76 feet below the surface of the ocean. To get a closer look at a school of fish, he swam up 28 feet
Answers
Answer:
He is at 48 feet below the surface
Step-by-step explanation:
76-28= 48
Answer: -48 ft.
Step-by-step explanation: -76+28= -48
Hudson has a balance of -$12.50 in his bank account. Daniel has a balance of $6.25 in his bank account. Use absolute value to find the difference between their balances.
Answers
Answer:
The absalute value is $6.25 because $12.50-$6.25=$6.25 and thats how much daniel has in his bank account.
Answer:
$18.75
Step-by-step explanation:
6.25 - negative 12.50 = 18.75
Find AB if A(-1,7) and B (11, -1). Round your answer to the nearest tenth.
Answers
Answer:
The answer is 14.4 unitsStep-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\[/tex]
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
A(-1,7) and B (11, -1)
The distance between them is
[tex] |AB| = \sqrt{( { - 1 - 11})^{2} + ( {7 + 1})^{2} } \\ = \sqrt{ ({ - 12})^{2} + {8}^{2} } \\ = \sqrt{144 + 64} \: \: \: \: \: \: \: \\ = \sqrt{208} \\ = 4\sqrt{13} \\ =14.42220510...[/tex]
We have the final answer as
14.4 units to the nearest tenthHope this helps you
Madelyn and her children went into a movie theater and she bought $39 worth of bags of popcorn and pretzels. Each bag of popcorn costs $6.50 and each pretzel costs $3.25. She bought 4 times as many pretzels as bags of popcorn. Graphically solve a system of equations in order to determine the number of bags of popcorn, x,x, and the number of pretzels, y,y, that Madelyn bought.
***(just need equations)***
Answers
Answer:
Madelyn bought 2 bags of popcorn and 8 pretzels.
Step-by-step explanation:
Madelyn and her children went into a movie theater and she bought $39 worth of bags of popcorn and pretzels. Each bag of popcorn costs $6.50 and each pretzel costs $3.25. She bought 4 times as many pretzels as bags of popcorn. Graphically solve a system of equations in order to determine the number of bags of popcorn, x,x, and the number of pretzels, y,y, that Madelyn bought.
\underline{\text{Variable Definitions:}}
Variable Definitions:
x=
x=
\,\,\text{the number of bags of popcorn}
the number of bags of popcorn
y=
y=
\,\,\text{the number of pretzels}
the number of pretzels
One bag of popcorn costs $6.50, so xx bags of popcorn cost 6.50x.6.50x. One pretzel costs $3.25, so yy pretzels cost 3.25y.3.25y. The total 6.50x+3.25y6.50x+3.25y equals \$39:$39:
6.50x+3.25y=39
6.50x+3.25y=39
Since Madelyn bought 4 times as many pretzels as bags of popcorn, there are more pretzels, so if we multiply 4 by the number of bags of popcorn, we will get the number of pretzels, meaning yy equals 4x.4x.
y=4x
y=4x
\underline{\text{Write System of Equations:}}
Write System of Equations:
6.50x+3.25y=
6.50x+3.25y=
\,\,39
39
y=
y=
\,\,4x
4x
\underline{\text{Solve for }y\text{ in each equation:}}
Solve for y in each equation:
6.50x+3.25y=39
3.25y=−6.50x+39
3.25
3.25y
=
3.25
−6.50x+39
y=−2x+12
y=4x
0
the number of bags of popcorn
the number of pretzels
x
y
(2, 8)
0
the number of bags of popcorn
the number of pretzels
The xx variable represents the number of bags of popcorn and the yy variable represents the number of pretzels. Since the lines intersect at the point \left(2, 8\right)(2,8) we can say:
Madelyn bought 2 bags of popcorn and 8 pretzels.
6.99 x 10^2 in standard form