The solutions of the equation in the interval [0, 2π) are x = π/6 and x = 11π/6.
What are the values of x that satisfy the equation 2cos 3x cosx + 2 sin 3x sinx = √3 in the interval [0, 2π)?The equation 2cos 3x cosx + 2 sin 3x sinx = √3 can be rewritten using trigonometric identities as cos(3x - x) = √3/2. Simplifying further, we have cos(2x) = √3/2.
In the interval [0, 2π), the solutions for cos(2x) = √3/2 occur when 2x is equal to π/6 and 11π/6. Dividing both sides by 2 gives x = π/12 and x = 11π/12.
However, we need to find solutions in the interval [0, 2r). Since r represents a number, we cannot provide a specific value for it without further information. Therefore, we express the solutions in terms of T, where T represents a positive number. The solutions in the interval [0, 2r) are x = Tπ/6 and x = (6T - 1)π/6, where T is a positive integer.
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( will give brainlyest)
A firework is launched from the ground at a speed of 160 feet per second. It’s height after t seconds is given by the polynomial -16t^2+160t. What is the height of the firework after 4 seconds?
The weight of a baby during the birth is 3 kilograms and it increased to 6 kilograms after 8 months. find the average rate of change in weight.
The average rate of change in weight is 3/8.
According to the statement
Weight of baby during birth = 3 kg
Weight of baby after 8 months = 6 kg
Average rate of change of in weight is calculated by
Average rate = Increased weight - Real weight / Time period
Average rate = 6-3 / 8
Average rate = 3/8
So, the average rate of change in weight is 3/8.
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What is the 32nd term of an arithmetic sequence with a first term of 7 and a common difference of 4?
Select one:
a. 119
b. 123
c. 127
d. 131
Answer:
a₃₂ = 131
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 7 and d = 4 , then
a₃₂ = 7 + (31 × 4) = 7 + 124 = 131
Can someone help me out with these two problems and show work please !!
Answer :
( 6 y^4 + 3 y^2 -7) - (12 y^4 - y^2 + 5)
Step-by-step explanation:
(6 y^4+ 3 y^2-7) - (12 y^4 - y^2 + 5 )
=6 y^4 +3 y ^2 - 7 - 12 y^4 + y^2 - 5
=6 y ^4 - 12 y ^4 +3 y ^2 + y ^2 - 7 -5
= -6 y ^4 + 4 y ^2- 12
Hope this helps!
[tex]Y-intercept = -4 Slope = 1/4[/tex]
Please help i need this
Answer:
Step-by-step explanation:
Answer:
Refer to the attached image!!
Hope it helps!
How many different 2-digit numbers are there with the following property: it is evan and its digits are distinct?
By counting all the even 2-digit numbers between 10 and 100, there are 41 even and distinct digits.
What is an even number?An even number can be defined as a type of number which is divisible by two (2) without any remainder.
How to determine this 2-digit number?Since this 2-digit numbers are even and its digits are distinct, we can infer and logically deduce the following points:
They are between 10 and 100.They are not repeated.They must contain two digits only.By counting all the even 2-digit numbers between 10 and 100, there are 41 even and distinct digits.
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Giving away brainly for help ASAP
Answer:
[tex]g(f(x))=25x^2-15x-7[/tex]
domain: (-∞,∞)
Step-by-step explanation:
g of f means plug the function f(x) in to x in the function g(x)
[tex]g(f(x))=5(5x^2-3x-2)+3\\g(f(x))=25x^2-15x-10+3\\g(f(x))=25x^2-15x-7[/tex]
since this is a parabola with no interval, the domain (the graph on the x-axis from left to right) is all real numbers or (-∞,∞)
What percentage of its total accounts receivable does grainger feel are uncollectible at december 31, 2016?
Using percentage of its total accounts the $50,000 is the amount to be uncollectible. The amount of $50,000 will be reported as an allowance for uncollectible accounts for the Year 2 on December 31 in the balance sheet.
According to the question,
Under the approach of the balance sheet, the ending balance of the allowance for the uncollectible accounts is the percentage (%) of the ending balance of the accounts receivable.
The amount of uncollectible accounts should reflect the aggregate needed ending balance of the allowance which amounts to $50,000.
Hence, using percentage of its total accounts the $50,000 is the amount to be uncollectible.
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what the picture says
By applying the law of cosine, the length of side BM is equal to 7.05 cm..
What is a polygon?A polygon can be defined as a two-dimensional geometric shape that comprises straight line segments and a finite number of sides. Also, some examples of a polygon include the following:
TriangleQuadrilateralPentagonHexagonNonagonOctagonNote: The number of sides (n) of a pentagon is 5.
In Geometry, the interior angle of both a regular and irregular polygon is given by this formula:
Interior angle = 180 × (n - 2)/n
Interior angle = 180 × (5 - 2)/5
Interior angle = 180 × 3/2
Interior angle = 108°.
For the central angle, we have:
Central angle, O = 360/5
Central angle, O = 72°.
By applying the theorem of intersecting secants, angle OCB will be given by this formula:
<OCB = ½ × (180 - 72)
<OCB = ½ × 108
<OCB = 54°.
In order to determine the length of side BM, we would apply the law of cosine:
cos(θ) = Adj/Hyp
cos54 = BM/12
BM = 12 × cos54
BM = 12 × 0.5878
Side BM = 7.05 cm.
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The average amount of money held by each child in a group of 5 is $0.50. If one of the children loses a quarter, what is the new average of money held by each child
Answer:
$0.45.
Step-by-step explanation:
Total amount of money held by all 5 children
= 5 * 0.50 = $2.50.
After 0.25 is lost the total = $2.25.
So the new average = 2.25 / 5
= $0.45.
Which of the following is a characteristic of the circumcenter of a triangle? A. It is the center of the circle that can be inscribed in a given triangle. B. It is equidistant from all three sides of the triangle. C. It is equidistant from all the vertices in the triangle. D. It is the intersection of all three angle bisectors of the triangle.
An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 5.4 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 24 engines and the mean pressure was 5.7 pounds/square inch with a standard deviation of 1.0. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
The p-value from the hypothesis test is 0.142 i.e., greater than the given significance level of 0.05. So, the null hypothesis is not rejected. The z-score for the given sample is 1.471.
What is the decision rule for the p-value approach to hypothesis testing?The decision rule based on p-value states,
If p > α (significance level), then the null hypothesis is not rejectedIf p < α (significance level), then the null hypothesis is rejected in favor of the alternative hypothesis.Calculation:Since it is given that the valve would produce a mean pressure of 5.4 pounds/square inch. I.e., μ = 5.4 p/si
So, Defining the hypothesis:
Null hypothesis H0: μ = 5.4
Alternative hypothesis Ha: μ ≠ 5.4
It is given that,
The valve was tested on 24 engines. I.e., Sample size n = 24
The sample mean X = 5.7
Standard deviation σ = 1.0 and
The significance level = 0.05
Since the population distribution is approximately normal,
the test statistic is calculated as follows:
z = (X - μ)/(σ/[tex]\sqrt{n}[/tex])
On substituting the value,
z = (5.7 - 5.4)/(1.0/[tex]\sqrt{24}[/tex])
= (0.3)/0.204
= 1.471
Fron this z-score, the p-value is calculated as 0.142.
Since, the value of p > 0.05 (significance level), the null hypothesis is not rejected.
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What is the direction of a line with the slope 3/-2
a, vertical
c. upward, left to right
b, horizontal
d. downward, left to right
Answer: b
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Write the log equation as an exponential equation. You do not need to solve for x.
Answer:
x² - 5x + 17 = [tex](2x)^{3x}[/tex]
Step-by-step explanation:
using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
given
[tex]log_{2x}[/tex] (x² - 5x + 17) = 3x , then
x² - 5x + 17 = [tex](2x)^{3x}[/tex]
When I flip a coin, the outcome can be either heads or tails; it is uncertain. However, in a large number of flips, the distribution of heads and tails is very regular. We say that flipping a coin is Group of answer choices predictable. deterministic. none of the above. random.
If the distribution of heads and tails of a fair coin is very regular in a large number of flips, then flipping a fair coin is: D. random.
What is a fair coin?A fair coin can be defined as an idealized type of coin that has an equal probability of revealing both heads and tails when randomly flipped or tossed by anybody.
This ultimately implies that, the outcome of flipping a fair coin is generally going to produce only one of two results and these include the following:
HeadTailIn this context, we can infer and logically conclude that if the distribution of heads and tails of a fair coin is very regular in a large number of flips, then flipping a fair coin is considered as being random.
In conclusion, it is important to note that a fair coin is considered as being random when the distribution of heads and tails of a fair coin is very regular in a large number of flips.
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Rewrite the expression in the form x^n
Answer:
x ^ (1/3)
Step-by-step explanation:
solution:
the answer is in the picture I have sent.
I hope this will help you
?? math-domain and range
Answer:
Domain: All real numbers (infinite) Range: [tex]y \leq -4[/tex]
Step-by-step explanation:
For the domain, the x-axis will continue to be used for the parabola, because the parabola can go on forever and can use an x- value on the x-axis. For the range, the largest number the parabola will go up to is -4. Therefore, if that is the highest point/ where the vertex is, the highest point on the y-axis is -4, resulting in the answer y can be equal to or less than -4 (y [tex]\leq[/tex] -4), since the parabola will continue to go down with the reflection over the x-axis.
Help me please help me fast
The value of [tex]f^{-1}(49)[/tex] is 4
Inverse of a function
The given function is:
[tex]f(x)=(x+3)^2[/tex]
Let f(x) be represented by y
[tex]y=(x+3)^2[/tex]
Make x the subject of the formula
[tex]\sqrt{y} =x+3[/tex]
Subtract 3 from both sides
[tex]x=\sqrt{y} -3[/tex]
Replace x by [tex]f^{-1}(x)[/tex] and let y be replaced by x
[tex]f^{-1}(x)=\sqrt{x} -3[/tex]
Substitute x = 49 into the inverse function
[tex]f^{-1}(x)=\sqrt{49} -3\\\\f^{-1}(x)=7-3\\\\f^{-1}(x)=4[/tex]
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Zara is preparing a juice blend.In her recipe, the amount of water is twice the amount of strawberry juice, and amount of lemon juice is 1/5 the amount of strawberry juice. What is the ratio of the lemon water?
The ratio of the lemon water is 10:1
How to determine the ratioFrom the information, we have that;
The ratio of water to strawberry juice is 2 : 1
That of strawberry juice to lemon juice is 5: 1
The, we have that of water to lemon juice to be 10: 1 when compared
Hence, the ratio of the lemon water is 10: 1
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A group of friends is on a rafting trip. They plan to travel 5 miles downstream and then 5 miles back upstream. They need to finish their rafting trip in 6 hours to allow enough time to get back to their hotel. The group knows that the river is moving at a rate of 2 miles per hour.
Answer:
I don't understand what the question is what do you need to find?
X+y=5 7x+37=27 solve the system of equations: x=3; y=2 x=4; y=4 x=6;y=1 x=3; y=5
Answer:
(a) (x, y) = (3, 2)
Step-by-step explanation:
The correct answer to the given system of equations can be found by trying the offered choices.
The equations are ...
x + y = 57x +3y = 27Evaluating "solutions"The first equation tells you the sum of the x and y values is 5. Here's what we get for a sum from the different answer choices:
A: 3 +2 = 5 . . . . a viable choice
B: 4 +4 = 8 . . . . doesn't work
C: 6 +1 = 7 . . . . doesn't work
D: 3 +5 = 8 . . . . doesn't work
__
Checking (x, y) = (3, 2) in the other equation, we have ...
7(3) +3(2) = 21 +6 = 27 . . . . as required
The solution is x = 3; y = 2.
__
Additional comment
Often, the easiest way to find the answer to a multiple-choice question is to see which answer works to solve the problem. It can sometimes be easier to check the answer than to develop it in the first place.
Substitution can work for this problem to find the correct y-value. (The answer choices differ by y-values, so knowing y tells the answer.)
7(5 -y) +3y = 27 . . . . substitute x=5-y
35 -4y = 27 . . . . . . simplify
8 = 4y . . . . . . . . . add 4y-27
2 = y . . . . . . . . . divide by 2. Matches the first answer choice.
Mario's car cost $15,999. Each year the car's value decreases by $1,550. This relationship is described by the equation V = 15,999 − 1,550t, when V is the value of the car and t is the age of the car in years. What is the value of his car after 5 years?
The value of Mario's car after 5 years is $8,249.
What is the value of the car after 5 years?Deprecation is when the value of an asset declines with the passage of time as a result of wear and tear.
V = 15,999 − 1,550t
V = 15,999 − 1,550(5)
V = 15,999 - 7,750
V =$8,249
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2. Is x² + 4√x a polynomial ? Justify your answer.
Answer:
No it isn't
As the variable "x" has root in it which means it isn't a whole number and for a expression to be a polynomial the variable must be whole no.
Hope it helps you!
Answer:
yes
Step-by-step explanation:
A polynomial is an algebraic expression of two or more terms
[tex]x^{2} +4\sqrt{x}[/tex] It is an algebraic expression of two terms, It is more common to label it binomial, but it is also a polynomial.
Hope this helps
What is the end behavior of the graph
Answer:
as x is approaching positive infinity, y approaches positive infinity
as x is approaching negative infinity, y is approaching negative infinity
Aiden evaluated the expression to find the volume of a cylinder. What could be dimensions of the cylinder
The dimensions of the given cylinder are that its height is 12cm, while its base radius is 4cm, which implies its diameter is 8 cm.
Thus, the first option, The height is 12 cm, and the diameter of the base is 8 cm, is the right choice.
The volume of a cylinder is calculated using the formula, V = πr²h, where V is its volume, r is its radius, and h is its height.
The expression used by Aiden to calculate the volume of a cylinder is π(16)(12), or, π(4²)(12).
Comparing this expression with the general formula of the volume of a cylinder, V = πr²h, where V is its volume, r is its radius, and h is its height, we can say that the radius can be 4 units and the height can be 12 units.
Assuming the units to be cm, we can say that:
The dimensions of the given cylinder are that its height is 12cm, while its base radius is 4cm, which implies its diameter is 8 cm.
Thus, the first option, The height is 12 cm, and the diameter of the base is 8 cm, is the right choice.
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The complete question is:
Aiden evaluated the expression π(16)(12) to find the volume of a cylinder. What could be the dimensions of the cylinder?
The height is 12 cm, and the diameter of the base is 8 cm.
The height is 12 cm, and the area of the base is 16 cm².
The height is 16 cm, and the diameter of the base is 6 cm.
The height is 16 cm, and the area of the base is 12 cm².
Find the remainder when:
(75*56)^28+(58*34)^31 is divided by 19
Answer:
Exact form: 19 multiply 4200^28 + 1972^31 / 19
Decimal form: 3.55481422 multiply 10^101
In the following table, the age (in years) of the respondents is given as the x value, and the earnings (in thousands of dollars) of the respondents are given as the y value. Use Excel to find the best fit linear regression equation in thousands of dollars. Round the slope and intercept to three decimal places.
The required equation based on the information given is y =0.433x + 24.493
How to illustrate the information?It should be noted that one can simply copy and paste the data set into excel sheet
Then, use intercept and the slope formula to find slope and intercept. We will have
slope = SLOPE(y values, x values)
= 0.433
intercept = INTERCEPT(y values, x values)
= 24.493
Therefore, the required equation is y =0.433x + 24.493
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arrange the steps in the correct order to express cos3x in terms of cosx
The correct order to express cos3x in terms of cosx is; As shown in steps 1 to 9 below.
How to simplify Trigonometric Identities?The steps to simplify the trigonometric identities cos 3x in terms of cos x are as follows;
Step 1; cos x = cos(2x + x)
Step 2; cos(2x) cosx - sin(2x) sinx
Step 3; 1 - 2sin^2x(cosx) -(2sinxcosx)sinx
Step 4; cosx - 2sin²x cosx - 2sin²x cosx
Step 5; cosx - 4sin²x cosx
Step 6; cosx( 1 - 4sin²x)
Step 7; cosx{1 - 4(1 - cos²x)}
Step 8; cosx{-3 + 4cos²x}
Step 9; 4cos³x - 3cosx
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Several different roadways are in the same region as the railroad.
Part A: A highway's path can be found using the equation 2x+3y=21. Use the graphs of the functions to determine the number of intersections there will be between the railroad and the
highway, and explain completely. (5 points)
Part B: A turnpike's route is determined by the equation y=x2 Prove algebraically how many intersections there will be between the railroad and the turnpike, showing all necessary
work. (5 points)
There are 0 intersections between the railroad and the highway and there are 2 intersections between the railroad and the turnpike
The number of intersections there will be between the railroad and the highwayFrom the graph, we have the following points on the railroad
(x, y) = (3, 3) and (0, 5)
The slope is calculated as:
m = (y2 - y1)/(x2 - x1)
This gives
m = (5 -3)/(0 - 3)
Evaluate
m = -2/3
The equation is then calculated as:
y = mx + b
This gives
y = -2/3x + b
Substitute (0, 5)
5 = -2/3 * 0 + b
This gives
b = 5
Substitute b = 5 in y = -2/3x + b
y = -2/3x + 5
Multiply through by 3
3y = -2x + 15
Rewrite as:
2x + 3y = 15
The equation of the highway's path is
2x+3y=21
So, we have:
2x+3y=21
2x + 3y = 15
Subtract the equations
2x - 2x + 3y - 3y = 21 - 15
Evaluate
0 = 6
The above equation is false because 0 and 6 are not equal.
This means that the system of equations have no solution
Hence, there are 0 intersections between the railroad and the highway.
How many intersections there will be between the railroad and the turnpike?Here, we have
y = x^2 and 2x + 3y = 15
Substitute y = x^2 in 2x + 3y = 15
2x + 3x^2 = 15
Rewrite as:
3x^2 + 2x - 15 = 0
Calculate the discriminant using
d =b^2 - 4ac
This gives
d = 2^2 - 4 * 3 * -15
Evaluate
d = 184
The discriminant d is greater than 0.
This means that the equation has 2 real solutions
Hence, there are 2 intersections between the railroad and the turnpike
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if the area of a rectangle is represented by 25x^3y^6 and its width is represented by 10xy, express the length of the rectangle in terms of x and y
The length of the rectangle in terms of x and y, given that its area is represented by 25x³y⁶ and its width is represented by 10xy is 2.5x²y⁵.
The area of a figure is the total space enclosed in two dimensions within its boundary.
The area of a rectangle is given as, area = length*width.
In the question, we are given that the area of a rectangle is represented by 25x³y⁶ and its width is represented by 10xy, and are asked to express the length of this rectangle in terms of x and y.
We know that the area of a rectangle is given as, area = length*width.
Substituting the known values in the equation, we get:
25x³y⁶ = length*10xy.
Rearranging this equation, we get:
length = 25x³y⁶/10xy = (5x²y⁵)/2 = 2.5x²y⁵.
Thus, the length of the rectangle in terms of x and y, given that its area is represented by 25x³y⁶ and its width is represented by 10xy is 2.5x²y⁵.
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