Solve the equation.
Cosine (StartFraction x Over 2 EndFraction) = cosine x + 1)
What are the solutions on the interval 0° ≤ x < 360°?
Solutions: { , }
Answers
Answer:
The correct answers are 120°, 180°
An equation is formed of two equal expressions. The solutions for the interval 0° ≤ x < 360° are 120° and 180°.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
cos(x/2) = cos(x) + 1
cos(x/2) - cos(x) - 1 = 0
Let u=(x/2), therefore, the equation can be rewritten as,
cos(u) - cos(2u) - 1 = 0
cos(u) - 2cos²(u) + 1 - 1 = 0
cos(u) - 2cos²(u) = 0
-2cos²(u) = -cos(u)
2cos²(u) / cos(u) = 1
2 cos(u) = 1
cos(u) = 1/2
u = cos⁻¹ (1/2)
u = 60°
Since u=(x/2), therefore, the value of x is,
u=(x/2)
x = 120°
Hence, the solutions on the interval 0° ≤ x < 360° are 120° and 180°.
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Related Questions
How many significant digits should the product of 11,435 m and 19.35 m have
Answers
Answer:
2 significants choes the least significant digets which is 19.35
result is 221,267.25
A person on a moving sidewalk travels 56 feet in 8 seconds. The moving sidewalk has a length of 210 feet. How long will it take to move from one end to the other?
**please help me **
Answers
Answer:
1470 seconds
Step-by-step explanation:
56=8 seconds
1 second= 56÷8=7
Ans=7×210=1470
The winning candidate in an election receives 0.52 of the votes. a. There are 1000 voters. How many votes does the winning candidate receive?
Answers
Answer:
520
Step-by-step explanation:
0.52 as a percent is 52%. 52% of 1000 is 520.
You deposit $500 into a savings account that increasing by 7% interest annually. Write the function that represents the balance after t years. Then what is the balance after 2 years.
Answers
Step-by-step explanation:
500 ×1.07^t <-- function (I think)
500 × 1 07^2 = $572.45 <-- balance after 2 years
In ΔABC, m∠CAB=60° and AD is angle bisector with D∈BC and AD = 8ft. Find the distances from D to the sides of the triangle.
( AD and BC have lines above them but i didn't know the symbol.)
Answers
Answer:
nope
Step-by-step explanation:
martin reads 19 pages of a novel in 12 minutes. complete the proportion and use it to find x, the number of pages he reads in 42 minutes
Answers
Answer:
67 pages in 42 minutes
Step-by-step explanation:
If the coefficient of determination for a data set containing 9 points is 1, how
many of the data points must lie on the regression line for the data set?
O A. 9
OB. 8
O C. 6
O D. 7
Answers
Answer: A
Step-by-step explanation:
The coefficient of determination is a number between 0 and 1 used to measure the level of precision with which the regression model created fits the data. A measure of means that the model explains the entire variation between the two variables without error.
Therefore, in this case, if means that the 9 points are on the line
Answer:
Therefore, in this case, it means that the 9 points are on the line
Step-by-step explanation:
Priya decomposed a square into 16 smaller, equal-size squares and then cut out 4 of the small squares and attached them around the outside of original square to make a new figure.
How does the area of her new figure compare with that of the original square?
Answers
The new square is smaller.
An 8-pack of batteries costs $9.44
What is the price in dollars, of one battery?
Answers
Answer:
1.18
Step-by-step explanation:
First we have established that 9.44 is the total, and we know that there are 8 batteries in each pack. This is a problem of division.
By first identifying key words like each and total, you can safely assume it will be a division problem.
First step: Dividing the total with the number of batteries in the singular pack gives you a valid answer
9.44÷8=1.18
Second step: To make sure you didn't miscalculate, you can use: 1.18×8, which is equal to the total.
100 POINTS PLEASE HELP
Please be accurate with this too.
Answers
Answer:
The answer is A :)
Step-by-step explanation:
Which describes the transformation shown below
A
B
C
D
Answers
Answer:
i think the answer is a to be honest
Step-by-step explanation:
What do the angles of a triangle add up to? If 2 angles are 34 and 18, what is the third angle?
Answers
Answer:
The third angle is 128 degrees
Step-by-step explanation:
The interior angles of a triangle add up to 180 degrees, therefore we can set up the equation x+34+18=180 to find the missing angle. Solving the equation gets us x=128
Answer:
Angles of a triangle add up to 180 degrees. The third angle would be 128 degrees.
Step-by-step explanation:
34 + 18 = 52
180 - 52 = 128
How much water should be added to 1 gallon of pure antifreeze to obtain a solution that is 80% antifreeze?
Answers
Answer:
The amount of water to be added is ¹/₄ gallon
Step-by-step explanation:
Given;
amount of pure antifreeze at 100% = 1 gallon
let the amount of water to be added with 0% antifreeze = (x) gallon
then, the amount of mixture at 80% antifreeze = (x + 1) gallon
For conservation of mass, we will have the following equation;
(1 x 1) + (0)(x) = 0.8(x +1)
1 = 0.8x + 0.8
0.8x = 1 - 0.8
0.8x = 0.2
x = 0.2 / 0.8
x = ²/₈
x = ¹/₄ gallon
Therefore, the amount of water to be added is ¹/₄ gallon
need help on this please
Answers
Michonne's Phone Service charges $11.06 for an activation fee plus $4 for every gigabyte (g) used.
Answers
Answer:
Graph the line of y=11.06x+4
Step-by-step explanation:
First write the equation of the line you want to graph. In this case the values are 11.06 as m, and 4 as the y-intercept (b). If you substitute the values into y=mx+b. Then you need to graph it. Plot the y-intercept, then use rise/run to complete the rest of the points and the line.
Consider the reduction of the triangle.
A triangle has side lengths 10 centimeters, 85 centimeters, and 62 centimeters. A smaller triangle has side lengths A, B, 6.2 centimeters.
Use the measurements of the original figure and the scale drawing to calculate the scale factor and missing measures.
What is the scale factor? 1/10
What is the length of A? 1
What is the length of B? 8.5
Answers
Answer:
What is the scale factor? 1/10
What is the length of A? 1
What is the length of B? 8.5
Step-by-step explanation:
The scale factor and missing measures are 1/10, A = 1, B = 8.5
What is scale factors?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.
Given are measurements of two triangles, we need to find the missing sides and the scale factors,
So, the scale factor = new measurement / original measurement = 6.2/62 = 1/10
Now, using the definition of the similar triangles, the ratio of the corresponding sides are equal,
62/6.2 = 85/B
10 = 85 / B
B = 8.5
Now,
62/6.2 = 10/A
10 = 10/A
A = 1
Hence, the scale factor and missing measures are 1/10, A = 1, B = 8.5
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Consider the integers x and y. When y is divided by x the remainder is 29. When y is divided by x/2, the remainder is 13. Determine x.
Answers
===============================================
Explanation:
When we divide y over x to get a remainder of 29, this means we are dividing over a value greater than 29. This means x > 29.
If we divided over a number 29 or less, then the remainder would be smaller than the divisor.
------------------------------------------
The variable x is some integer. When we divide y over (x/2) we get some other integer. This implies that x/2 itself is also an integer. That tells us that x is some even integer.
So far we know that x > 29 and x is some even number.
------------------------------------------
y divided by x leads to a remainder of 29. This means
y/x = q + 29/x
for some integer q, which is the quotient.
Multiply both sides by x
x*(y/x) = x*(q + 29/x)
y = qx + 29
We'll come back to this later.
------------------------------------------
Now divide y over (x/2) to get a remainder 13. We'll let n be the quotient this time
y/(x/2) = n + 13/(x/2)
which is equivalent to
y = n(x/2) + 13
We can multiply both sides by 2 further getting
2y = 2*( n(x/2) + 13 )
2y = nx + 26
Plug in y = qx+29 from earlier
2(qx+29) = nx + 26
2qx + 58 = nx + 26
Let's group the x terms to one side and everything else on the other side
2qx - nx = 26-58
2qx - nx = -32
-nx + 2qx = -32
nx - 2qx = 32
I multiplied both sides by -1 to turn that -32 into 32
Factoring x from the left side gives
nx - 2qx = 32
x(n - 2q) = 32
We have x as an integer, which is stated in the instructions.
In order to have x(n-2q) = 32 be true, this must mean n-2q is an integer.
We can say n-2q = 32/x, so 32/x is some integer because x is an integer.
------------------------------------------
In short, x and n-2q are both integers. In order for the two integers to multiply to 32, the factors must be smaller than 32 or equal to 32.
So [tex]x \le 32[/tex] and [tex]n-2q \le 32[/tex]
We don't need to worry about the second inequality since all we care about is x.
Recall that earlier we stated that x > 29 and x is even.
Combine this with [tex]x \le 32[/tex] and we form the compound inequality [tex]29 < x \le 32[/tex]
This basically says x is a value from the set {30, 32}
But x = 30 is not a factor of 32. There's no way to have x(n-2q) = 32 be a true equation if x = 30. We must rule x = 30 out.
The only thing left is x = 32. This is the final answer.
------------------------------------------
If x = 32 and y = 29, then we fit the requirements of the problem.
y/x = 29/32 = 0 remainder 29
y/(x/2) = 29/16 = 1 remainder 13
The solution has been confirmed.
Find the reciprocal of 7/12
Answers
The manager of the zoo where the ticket price for an adult is $9.50 and the ticket price for a child is $6.50 wants to make at least $800 on a Saturday. Let x be the number of adult tickets and y be the number of child tickets. Choose the inequality that shows the numbers of tickets that need to be sold.
Answers
Answer:
[tex]9.5x+6.5y\geq $800[/tex]
Step-by-step explanation:
9.5 in value of adult tickets. 6.5 is value of children's tickets. combined selling of all of them should be greater than or equal to 800 ("atleast" in the question shows it can be more but cannot be less)
Which expression is equivalent to (r^-7)^6?
Answers
A new surgery is successful of the time. If the results of such surgeries are randomly sampled, what is the probability that more than of them are successful
Answers
Complete question is;
A new surgery is successful 85% of the time. If the results of 7 such surgeries are randomly sampled, what is the probability that more than 4 of them are successful?
Carry your intermediate computations to at least four decimal places, and round your answer to at least two decimal places
Answer:
P(X > 4) = 0.93
Step-by-step explanation:
This is a binomial probability distribution problem with the formula;
P(X = x) = C(n, x) × p^(x) × (1 - p)^(n - x)
We are told that a new surgery is successful 85% of the time. Thus;
p = 85% = 0.85
n = 7
probability that more than 4 of them are successful would be;
P(X > 4) = P(5) + P(6) + P(7)
P(5) = C(7,5) × 0.85^(5) × (1 - 0.85)^(7 - 5)
P(5) = 0.2097
P(6) = C(7,6) × 0.85^(6) × (1 - 0.85)^(7 - 6)
P(6) = 0.3960
P(7) = C(7,7) × 0.85^(7) × (1 - 0.85)^(7 - 7)
P(5) = 0.3206
P(X > 4) = 0.2097 + 0.3960 + 0.3206
P(X > 4) = 0.9263 ≈ 0.93
(giving brainly if u helpp mee)
What is static electricity?
A) Build up of electrical charges on the surface of an object
B) Build up of light energy that causes electrical charges to move
C) The flow of electrical charges in a conductor
D) The movement of electrical charges through an insulator
Answers
If p + 2q = 20, what is the value of 101p + 202q?
Answers
Answer:
bhvigjcgujj
Step-by-step explanation:
Jessica is walking home from a friend's house. After two minutes she is 0.6 miles from home. Twelve minutes after leaving, she is 0.1 miles from home. What is her rate in miles per hour
Answers
Jorge bought 16 apples for $8.00.
Let x represent the number of apples purchased, and let y represent the total cost.
Graph the line that represents the proportional relationship.
i go to wiva
Answers
Answer:
x=16
y=8.00
8/16=0.5 (50 cents per apple)
y=0.5x+0
Samuel's lunch account begins with $50 and has $4 taken out each day.
Susie's lunch account begins with $36 and has $3 taken out each day.
Which inequality can be used to find x, how many days the balance in
Samuel's account will be less than the balance in Susie's account?
50 - 4x > 36 - 3x
50 + 4x > 36 + 3x
50 - 4x < 36. 3x
50+ 4x < 36. 3x
Answers
Answer:
C. 50 - 4x < 36 - 3x
Step-by-step explanation:
PLEASE HELP: Tangent, Sine, or Cosine? Please only answer if you know I genuinely need help. WILL GIVE BRAINLIEST IF CORRECT
Answers
Answer:
cosine
Step-by-step explanation:
cos 27=x/20
x=20 cos 27≈17.82
The area of a rectangular vegetable garden is 200 feet. The width is 10 feet. What is the length?
Answers
Answer:
The length is 20 ft. 10ft times 20ft = 200ft^2
Step-by-step explanation:
PLS MARK AS BRAINLIEST
Answer:
20
Explanation:
200 = 20 x 10
Instead of using the values {1,2,3,4,5,6}
on dice, suppose a pair of dice have the
following: {1,2,2,3,3,4} on one die and
{1,3,4,5,6,8} on the other. Find the
probability of rolling a sum of 7 with
these dice. Be sure to reduce.
?
]
Answers
Answer:
[tex]Probability(sum7)=\frac{4}{24}=\frac{1}{6}[/tex]
Step-by-step explanation:
The dice form pairs of outcomes, so if the dice has repeating sides then the set of outcomes will be pairs of elements from the set {1,2,3,4} and {1,3,4,5,6,8}. The number of possible two pair combinations is 4 times 6 which equals 24 possible pairs. Now we find which of these pairs would have values summing up to 7: [tex](1,6),(2,5),(3,4),(4,3)[/tex] So 4 outcomes out of a possible 24 outcomes have this qualityThat's [tex]Probability(sum7)=\frac{4}{24}=\frac{1}{6}[/tex]Answer:
1/6
Step-by-step explanation:
Please help me, thanks!
Answers
Answer:
Algebraic expression for 75 less than twice Mabel's score is 2m-75
Step-by-step explanation:
We need to translate the phrase 75 less than twice Mabel's score into algebraic expression.
Translating into algebraic expression
Let m represent Mabel's score
Twice Mabel's score = 2m
75 less than Twice Mabel's score = 2m-75
So, algebraic expression for 75 less than twice Mabel's score is 2m-75