It looks like the equation is
cos(2x) + cos(x) = 0
Use the double angle identity for cosine to write this as
(2 cos²(x) - 1) + cos(x) = 0
2 cos²(x) + cos(x) - 1 = 0
Factorize the left side:
(2 cos(x) - 1) (cos(x) + 1) = 0
Then either
2 cos(x) - 1 = 0 or cos(x) + 1 = 0
2 cos(x) = 1 or cos(x) = -1
cos(x) = 1/2 or cos(x) = -1
[x = cos⁻¹(1/2) + 2nπ or x = -cos⁻¹(1/2) + 2nπ]
… or [x = cos⁻¹(-1) + 2nπ]
(where n is any integer)
x = π/3 + 2nπ or x = -π/3 + 2nπ or x = π + 2nπ
We get the following solutions in the interval [0, 2π):
x = π/3 and x = π and x = 5π/3
What is an equation of the line that passes through the points (-8, 1) and (7, 1)
ANSWER: y = 1
STEPS:
first, find the slope by using the formula
which is also represented as m
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
where from point (-8, 1) x1 is -8 and y1 is 1
then from point (7, 1) x2 is 7 and y2 is 1
so we substitute into the formula
[tex] \frac{1 - 1}{7 - ( - 8)} = \frac{0}{7 + 8} = \frac{0}{15} [/tex]
[tex]m = \frac{0}{15} [/tex]
Then we solve for the equation of the line by using the formula
[tex](y - y1) = m(x - x1)[/tex]
but we have only y1, m and x1 so we substitute given us
[tex](y - 1) = \frac{0}{15} (x - ( - 8))[/tex]
but also, we must get rid of the fraction 0/15
so we multiply through by the denominator 15
[tex]15 \times (y - 1) = 15 \times \frac{0}{15} (x - (8))[/tex]
we get
[tex]15(y - 1) = 0(x - ( - 8))[/tex]
now we expand all brackets
[tex]15y - 15 = 0[/tex]
but we want the equation so we make y stand alone
[tex]15y = 15 \\ \\ \frac{15y}{15} = \frac{15}{15} \\ \\ y = 1[/tex]
the equation of the line is y=1
4,238 as the sum of three different four digits numbers
Answer:
Step-by-step explanation:
Option 1: 1000 + 2000 + 1238
Option 2: 1500 + 1700 + 2038
what is equivalent for 2/3 and 3/4 using 12 as a denominator
Answer:
8/12 and 9/12
Step-by-step explanation:
hope this helps loves x
Rosa and her two brothers do not like taking out the trash. Rosa's mother wrote each child's name on a piece of paper and put it into a bag. QuestionThen Rosa's mother chose a name from the bag without looking to see who would take out the trash. What is the probability that either of Rosa's brothers were chosen?
A 1/3 B 1/2
C 2/3 D 2/1
Answer:
C 2/3
Step-by-step explanation:
There are only three names and two of them are boys sooo 2/3
A shelf contains 3 fashion magazines and 4 health magazines. You randomly choose one to read, set it aside, and randomly choose another for your friend to read. Which of the following describes the error in finding the probability that both events $A$ and $B$ occur? Event $A:$ The first magazine is fashion. Event $B:$ The second magazine is health.
Answer:
B
Step-by-step explanation:
The probability of getting both fashion and health magazine without replacement is 2/7.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.
Given that, a shelf contains 3 fashion magazines and 4 health magazines.
Total number of books = 7
Number of fashion magazines = 3
Number of health magazines= 4
Probability of getting fashion magazines = 3/7
Probability of getting health magazines = 4/6
Probability of getting both the events = 3/7 ×4/6
= 1/7 ×4/2
= 2/7
Therefore, probability of getting both fashion and health magazine without replacement is 2/7.
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A cyclist rides her bike at a speed of 27 kilometers per hour. What is this speed in kilometers per minute? How many kilometers will the cyclist travel in 20 minutes?
Answ2
Step-by-step explanati
Suppose that a cylinder has a radius of r units, and that the height of the cylinder is also r units. The lateral area of the cylinder is 882 π square units. Find the value of r.
Answer:
21 units²
Step-by-step explanation:
the area of a circle is
pi×r²
the lateral area of a cylinder is the area only if the "mantle" of the cylinder : the round area all around the cylinder in its side.
in other words : everything but the ground and the top area.
how can we get the area of the side "mantle" ?
we can imagine, we take a knife and cut a straight line (and at 90°) from the top to the bottom, and then cut off the ground and the top circles by cutting along their circumference.
what do we get ?
if we put that remaining area in the table and press it flat, it is ... a rectangle. simply a rectangle.
its width is the height of the cylinder (the length of our initial top-bottom cut).
and its length is the length of the circle circumference that e just cut off.
and the circumference of a circle is
2×pi×r
so, the lateral area of the cylinder is
2×pi×r × h
r being the radius
h being the height of the cylinder.
and we get
LA = 2×pi×r×r = 882×pi
pi × r² = 441 × pi
r² = 441
r = 21 units²
Select all of the properties that a parallelogram that is not a rectangle has. A. 2 pairs of parallel sides B. exactly 1 pair of sides with equal length C. 4 right angles D. 2 acute angles, 2 obtuse angles E. exactly 1 pair of parallel sides
Answer and Explanation:
B, because a rectangle has 2 pairs.
Theoretically, D could also be correct, but not in every scenario; all rectangles are parallelograms, but not all parallelograms are rectangles.
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
can you send a better picture of the question so it can be clearer
Step-by-step explanation:
Calculate: a) of 36 =
Answer: 9
Step-by-step explanation:
=> 1/4 of 36
=> 'of' always refers to multiplication:
=> 1/4 × 36
=> By cross cancellation of 4 and 36 we get:
=> 1 × 9
=> 9 Answer...
hope that helps...
15.5% of what number is 65?
Answer:
1007.5
Step-by-step explanation:
1007.5 because if you do the math, 15.5% of 65:
65 * 15.5% = x
x=1007.5
double check:
1007.5 / 15.5%= 65
triple check:
1007.5 / 65 = 15.5%
Please help. Find the lateral area of the square pyramid
Answer:
960 in squared
Step-by-step explanation:
[tex]\sqrt{16^{2} +12^{2} }[/tex]=20
4*[tex]\frac{1}{2}[/tex]*24*20=960
I will give Brainliest!!! :D
Match each situation to an equation.
(You can just write the color of the equation card and the fraction in the situation, ex. Green card to 2/5) :)
Answer:
Purple to 1/4
red to 13/10
blue to 2/5
green to 1/5
Step-by-step explanation:
I think that is correct, butttt I am not postive
In which number does the digit 6 have a value that is 10 times as great as the value of the digit 6 in 283,691?
360,281
486,732
573,674
678,832
HELP PLEASE!!!!!!!!!
Answer:
The answer is 486,732
Find the both term of the arithmetic sequence –27, -24, -21, ...
Answer:
-18 is the ans you can calculate it
9 Look at the descriptions in the table below. Decide whether each shape is possible or not possible. • For each shape, mark an X in the correct box under "Possible" or "Not Possible." • If the shape is possible, draw an example. Possible Not Possible Example Trapezoid that is a rhombus Rectangle that is not a square
there is no image here, no one can't answer u until u upload the image
Please answer asap. Also, explain the process of getting the answer. Thank you!
Answer: No cheating
Step-by-step explanation: Cheating isn’t allowed
At a concession stand, three hot dog(s) and four hamburger(s) cost $12.00; four hot dog(s) and three hamburger(s) cost $10.75. Find the cost of one hot dog and the cost of one hamburger.
Answer:
hotdog is $1.25
hamburger is 1.75
Step-by-step explanation:
CAN SOMEBODY EXPLAIN THE EQUATION TO ME PLEASE
Answer:
15,000(0.81)^x
can anybody help me? i need it
4 servings = 1/3 cups
| ×7.5 |×7.5
30 servings=7.5/3 cups
=2.5 cups
= 2 1/2c
which of the following graphs represents the equation 2x+3y=12
△OMN ~ △RPQ
Find θ. Please help me
Answer:
the angle is equal to 60 degrees
Answer: the angle is equal to 60 degrees
Step-by-step explanation:
FREE BRAINLY JUST HELP ME
Jordan took out a loan for
14
months and was charged simple interest at an annual rate of
5.75
%
. If the amount of the loan was
$
850
, what is the amount of interest she had to pay?
Answer:
57.02 dollars
Step-by-step explanation:
850 * 14/12 * .0575 =
The required, Jordan had to pay $53.03 in interest on her loan.
What is simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.
here,
To find the amount of interest Jordan had to pay, we can use the simple interest formula,
I = P × r × t
Where I is the amount of interest, P is the principal (the initial amount of the loan), r is the annual interest rate as a decimal, and t is the time in years.
In this case, P = $850, r = 0.0575 (5.75% expressed as a decimal), and t = 14/12 (since the loan was for 14 months, which is 1 year and 2 months or 1.16667 years).
Substitute the value in equation 1.
I = $850 × 0.0575 × 14/12
= $57.02
Therefore, Jordan had to pay $53.03 in interest on her loan.
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Mr. Rodriguez has 8 packs of pencils to divide equally among his class of 26 students. If each pack
contains 15 pencils, how many pencils will each student receive? How many will be leftover? Show
your work.
Enter the coordinates of the
point on the unit circle at the
given angle.
-225°
Answer:
Step-by-step explanation:
hello :
the coordinates of the point on the unit circle at the given angle.-225°:
x= cos(-225°)= -√2/2
y = sin (-225°)= √2/2
The coordinates of the point on the unit circle at an angle -225°° are [tex](\frac{-\sqrt{2} }{2} , \frac{\sqrt{2}} {2} )[/tex].
What are coordinates of the point?" The coordinates of the point is defined as the pair of such points which represents the exact location of the point."
What is unit circle?" Unit circle means a circle with radius equals to 1unit."
Formula used
Equation of the circle with center (0, 0) and radius r
[tex]x^{2} +y^{2} =r^{2}[/tex]
Coordinates of the point on the circle (rcosθ , rsinθ)
cos(-θ) = cosθ
sin (-θ) = -sinθ
cos ([tex]\frac{3\pi }{2}[/tex] -θ) = -cosθ
sin ([tex]\frac{3\pi }{2}[/tex] -θ) = -sinθ
According to the question,
Given θ = -225°
Unit circle 'r' = 1
Therefore Coordinates are,
'x' coordinates represented by rcosθ
'y' coordinates represented by rsinθ
Substitute the value of r and θ in the coordinates of the point we get,
x = rcosθ
= 1 × cos (-225°)
= cos (225°)
= cos ( 270° - 45°)
[tex]=cos(\frac{3\pi }{2} -\frac{\pi }{4} )[/tex]
[tex]= - sin(\frac{\pi }{4}) \\= - \frac{1}{\sqrt{2} } \\=-\frac{\sqrt{2} }{2}[/tex]
y = rsinθ
= 1 × sin (-225°)
= -sin (225°)
= -sin ( 270° - 45°)
[tex]=-sin(\frac{3\pi }{2} -\frac{\pi }{4} )[/tex]
[tex]= -( - cos(\frac{\pi }{4})) \\= \frac{1}{\sqrt{2} } \\=\frac{\sqrt{2} }{2}[/tex]
Hence, coordinates of the point on the unit circle at an angle -225°° are [tex](\frac{-\sqrt{2} }{2} , \frac{\sqrt{2}} {2} )[/tex].
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Two lines are perpendicular. If one line has a slope of 1/2, what is the slope the other line?
The slope of the perpendicular line would be the negative reciprocal of the other line.
negative reciprocal of 1/2 = -2
answer: -2
77
Look at the two division problems below. Will they have the same quotient?
Explain how you can find the answer without calculating.
747925
7.492.5
A researcher wants to compare the mean score on the Achenbach Youth Self Report form for a sample of youth displaced by a
hurricane to the population mean of 50 and a population standard deviation of 10. The researchers report a sample mean of 48 for their
sample of 36 youth. What is the standard error (aka standard error of the mean) for this sample? Round each step to two decimal
places.
Using the Central Limit Theorem, it is found that the standard error for this sample is of 1.67.
What does the Central Limit Theorem state?It states that for a population of standard deviation [tex]\sigma[/tex], the sampling distribution of sample means of size n has standard error [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this problem, we have that [tex]\sigma = 10, n = 36[/tex], hence the standard error is given by:
[tex]s = \frac{10}{\sqrt{36}} = 1.67[/tex]
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Maribel factored y2 −30y + 81 as (y−9)2 . Was she right or wrong? How do you know?
Answer:
Wrong
Step-by-step explanation:
If you multiply (y-9)(y-9) the answer equal y2-18y+81.
Find the greatest common factor of 34 and 49.
Answer:
7
Step-by-step explanation:
We found the factors and prime factorization of 34 and 49. The biggest common factor number is the GCF number.
So the greatest common factor 34 and 49 is 7.
Answer:
1
Step-by-step explanation:
Factors of 34 are going to be 1, 2, 17, and 34.
Whilst the factors of 49 are 1, 7, and 49. They do not share any other factor other than 1