What are all of the solutions to the trigonometric equation 2 times cosine squared theta minus 2 times sine squared theta equals radical 2 question mark
Answers
Explanation
Given the trigonometric expression
[tex]2cos^2\theta-2sin^2\theta=\sqrt{2}[/tex]We can find the solutions below;
From trigonometry identities;
[tex]cos^2\theta-sin^2\theta=cos2\theta[/tex]Therefore; we will have;
[tex]\begin{gathered} 2cos^2\theta-2s\imaginaryI n^2\theta=\sqrt{2} \\ 2(cos^2\theta-sin^2\theta)=\sqrt{2} \\ 2cos2\theta=\sqrt{2} \\ Divide\text{ both sides by 2} \\ \frac{\begin{equation*}2cos2\theta\end{equation*}}{2}=\frac{\sqrt{2}}{2} \\ cos2\theta=\frac{\sqrt{2}}{2} \end{gathered}[/tex]Therefore, the general solutions for the above is given as;
[tex]\begin{gathered} 2θ=\frac{\pi}{4}+2\pi n,\:2θ=\frac{7\pi}{4}+2\pi n \\ therefore; \\ \theta=\frac{\frac{\pi}{4}+2\pi n}{2},\theta=\frac{\frac{7\pi}{4}+2\pi n}{2} \\ \theta=\frac{\pi}{8}=\pi n,\theta=\frac{7\pi}{8}+\pi n \end{gathered}[/tex]Answer:
[tex]\theta=\frac{\pi}{8}+\pi n,\theta=\frac{7\pi}{8}+\pi n[/tex]Related Questions
Use the remainder theorem to find P (3) for P(x) = -x^4+3x^3-2x+3.
Specifically, give the quotient and the remainder for the associated division and the value of P (3).
Answers
The most appropriate choice for remainder theorem will be given by-
Quotient = [tex]-x^3-2[/tex]
Remainder = -3
What is remainder theorem?
When f(x) is divided by (x-a), the remainder will be f(a).
If the remainder is zero, (x-a) will become a factor of f(x)
Expression to be divided is called dividend, expression by which dividend is divided is called divisor, expression obtained on division is called Quotient and the other part is the remainder.
There is also a well known formula
Divisor x Quotient + Remainder = Dividend
Here,
P(x) = [tex]-x^4 +3x^3 -2x+3[/tex]
P(3) = [tex]-(3)^4+3(3)^3-2(3)+3[/tex]
= [tex]\\-81+81-6+3[/tex]
= -3
So by Remainder theorem, remainder is P(3)
So, Remainder = -3
Let the quotient be q(x)
divisor = [tex]x - 3[/tex]
We know,
Divisor x Quotient + Remainder = Dividend
[tex](x-3) \times q(x) +(-3) = -x^4 +3x^3 -2x+3\\(x-3) \times q(x) = -x^4 +3x^3 -2x+3 +3\\(x-3) \times q(x) = -x^4 +3x^3 -2x+6\\q(x) = \frac{-x^4 +3x^3 -2x+6}{x -3}\\q(x) =\frac{ -x^3(x-3)-2(x-3)}{x-3}\\q(x) = \frac{(x-3)(-x^3-2)}{x-3}\\q(x) = -x^3-2[/tex]
So, Quotient = [tex]-x^3-2[/tex]
Remainder = -3
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Simplify the expression,
Assume all variables are positive.
Answers
Answer:
x²[tex]\sqrt{5}[/tex]
Step-by-step explanation:
using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
given
5[tex]\sqrt{20x^4}[/tex] - 3[tex]\sqrt{45x^4}[/tex]
simplify the 20 and 45 inside the radicals
[tex]\sqrt{20}[/tex] = [tex]\sqrt{4(5)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{5}[/tex] = 2[tex]\sqrt{5}[/tex]
[tex]\sqrt{45}[/tex] = [tex]\sqrt{9(5)}[/tex] = [tex]\sqrt{9}[/tex] × [tex]\sqrt{5}[/tex] = 3[tex]\sqrt{5}[/tex]
Then
= 5(2[tex]\sqrt{5}[/tex] x² ) - 3(3[tex]\sqrt{5}[/tex] x² )
= 10[tex]\sqrt{5}[/tex] x² - 9[tex]\sqrt{5}[/tex] x²
= x²[tex]\sqrt{5}[/tex]
Determine which integer will make the inequality 5x + 12 > 2x + 6 false.
S:{−3}
S:{3}
S:{−1}
S:{1}
Answers
Out of the given integer(s), {−3} is the integer which will make the inequality 5x + 12 > 2x + 6 false.
As per the question statement, we are supposed to determine which integer will make the inequality 5x + 12 > 2x + 6 false
Let's solve the inequality for range of x first,
5x + 12 > 2x + 6
5x - 2x > 6 - 12
3x > -6
x > -2
So for all values of x > -2, the inequality 5x + 12 > 2x + 6 is true and for all values of x < -2, the inequality 5x + 12 > 2x + 6 false.
And out of the given options only x = -3 < -2
Hence, we accept {−3} as our required integer.
Inequality: An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.To learn more about inequality and its properties, click on the link given below:
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Answer:
S:{−3}
Step-by-step explanation:
Got it right on a test.
The graph of f(x) is shown.
For what values of x does f(x) = 0?
A) −1, 1, 2
B) −2, −1, 1
C) −3, −1, 1
D) −1, 1, 3
Answers
Answer:
C
Step-by-step explanation:
f(x) =0
when the curve intersects the x axis
goodluck :)
i need 2 more please help me
Answers
A and B and C
the measure of the angle of a triangle are shown in the figure below. solve for x (8x-18)° 110° 40°
Answers
Answer:
x = 6
Step-by-step explanation:
180 = (8x - 18) + 110 + 40
180 = 8x + 132
48 = 8x
6 = x
If the measure of the angle is needed:
8(6) - 18 = 30
A total of 77 tornadoes have been documented in tuscaloosa county in the period beginning on january 1, 1950 and ending on december 31, 2020. What is the recurrence interval for tornadoes in tuscaloosa county?.
Answers
The Recurrence interval for tornadoes in tuscaloosa county is 0.909
What is recurrence interval ?
The time period in which a new occurrence of something that happened or appeared before : a repeated occurrence or The time frame in which a previously occurring event or appearance first occurs: a recurring occurrence
Given that,
Total number of tornadoes is 77
Total time for Recurrence is 70 years
Using these data,
Recurrence = Total time for recurrence / Total number of tornadoes
Substituting we get,
Recurrence interval = 70/77
= (70/77)
= (0.909)
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Mrs. Smith made 4 pizzas .with 11 oz of cheese How much cheese is
each pizza made with ?
Answers
Answer:
2.75
divide 11/4
help meeeeeeeeeeee pleaseeeeeeeeeeeeee!!
Answers
Answer:
Yes, is a function
Step-by-step explanation:
it does not repeat x's
Fill in the blanks to express the quantities given in ratio language. Ratios must be
expressed in simplest form.
Number of Animals in the Pet Store:
Animal Count
16 cats
8 dogs
For every __ cats in the pet store, there are __dogs.
Answers
Determine the rule for translating ABC to A'B'C'
Answers
Correct answer is A, the rule for translating ABC to A'B'C' is left 2, up 9.
What does translating a triangle mean?An example of a transformation is a translation, which moves every point in a figure uniformly and in one direction. are frequently called slides. You can use notation or words to express a translation, such as "moved up 3 and over 5 to the left."
A translation in geometry is a type of transformation that shifts a geometric figure in a certain direction without altering its size or orientation. The figures are congruent before and after the transformation since it is a type of stiff transformation.
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I REALLY NEED HELP PLEASE THIS WORK IS FOR MONDAY.can y’all please help me:(
Answers
The statement that best describes the total cost of the Screened Loam, Round stone, and Crushed stone is; D: The total cost is greater than $325
How to solve Algebra Word Problems?We are given the amount of each material required for the Landscaping Project as;
Screened Loam = 3.25 cubic yards
Round stone = 1.5 cubic yards
Crushed stone = 2.5 cubic yards
Likewise we are given the cost of each of these materials per cubic yard as;
Cost of Screened Loam = $26 per cubic yards
Cost of Round stone = $112.5 per cubic yards
Cost of Crushed stone = $37.5 cubic yards
Thus;
Total Cost = (26 * 3.25) + (112.5 * 1.5) + (37.5 * 2.5)
Total Cost = 84.5 + 168.75 + 93.75
Total Cost = $347
Looking at the given options, the most appropriate is option D
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9(w + 1) = 99
w =
if you tell me the answer then ur a W
Answers
w = 10.
Step-by-step explanation:
9(w+1) = 99
9w+9 = 99
9w = 99-9
9w = 90
w = 90/9
w = 10.
[tex]{ \boxed{ \red{ \sf{w = 10}}}}[/tex]
Step-by-step explanation:
[tex]{ \purple{ \sf{9(w + 1) = 99}}}[/tex]
[tex]{ \purple{ \sf{9w + 9 = 99}}}[/tex]
[tex]{ \purple{ \sf{9w = 99 - 9}}}[/tex]
[tex]{ \purple{ \sf{9w = 90}}}[/tex]
Divide both the sides by 9 then
[tex]{ \purple{ \sf{ \frac{9w}{9} = \frac{90}{9} }}}[/tex]
[tex]{ \pink{ \boxed{ \blue{ \sf{w = 10}}}}}[/tex]
Find the value of x.
(5x − 17)°
13
132
12
48
Answers
Answer:
its 12
Step-by-step explanation:
Write an equation is point slope form of a line given that the slope is 2/3 and that the line goes through the point (5,-2)
Answers
Answer:
[tex](y+2)=\frac{2}{3} (x-5)[/tex]
Step-by-step explanation:
Point slope form is shown below:
[tex](y-y_1)=m(x-x_1)[/tex]
We are given the slope m = 2/3 and the point x1 = 5, y1 = -2
Simply plug in these numbers into the above equation.
[tex](y--2)=\frac{2}{3} (x-5)[/tex]
Simplify:
[tex](y+2)=\frac{2}{3} (x-5)[/tex]
Which of the contexts below could not be modeled by an exponential function?
A certain population of 16 aggressive zombies quintuples every day.
A taxi charges a flat fee of $2.00 for pick-up, then an additional fee of 4.75 per mile.
A coin collection appreciates at a rate of 5.2% per year.
A car depreciates at a rate of 4.9% per year.
Answers
The answer choice which could not be modelled by an exponential function among the given answer choices is; A taxi charges a flat fee of $2.00 for pick-up, then an additional fee of 4.75 per mile.
Which context could not be modelled by an exponential function?It follows from the task content that the expression which could not be modelled by an exponential expression be identified among the answer choices.
An exponential function is one in which case the change factor is expressed as an exponent of the independent variable.
However, the function described as; A taxi charges a flat fee of $2.00 for pick-up, then an additional fee of 4.75 per mile is termed a linear model in which case;
The rate of change is constant and is equal to; $4.75 per mile.
Hence the required answer choice which cannot be modelled by an exponential function is; A taxi charges a flat fee of $2.00 for pick-up, then an additional fee of 4.75 per mile.
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THERE IS 5 QUESTIONS I NEED TO GET DONE IN TOTAL, BUT IT WONT LET ME PUT MANY PICS IN ONE QUESTION SO PLS GO TO MY ACC AND VIEW THE OTHER ONES !!I NEED THIS BY **TODAY**
Answers
Answer:
[tex]y=\frac{1}{2}x-3[/tex]
Step-by-step explanation:
The equation of a line is y=mx+c, where m is the slope and c is the y-intercept (where the line crosses the y-axis).
Looking at the graph, we can see that the line crosses the y-axis at y=-3, so we know c= -3.
The slope of a line can be found by taking two points on the line, [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex], and subbing them into the formula [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]. Let's take the two points (2,-2) and (4:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{(-1)-(-2)}{4-2}=\frac{1}{2}[/tex]
Therefore, since the equation of a line is y=mx+c, our answer is [tex]y=\frac{1}{2}x-3[/tex]
Answer:
y=1/2x-3
Step-by-step explanation: given: (0,-3) (2,-2)
y=mx+b
-3=(m*0)+b
-3=b
-2= (m*2)-3
1=2m
m=1/2
y=mx+b
y=1/2x-3
a textbook store sold 324 a combined total of chemistry and biology textbooks in a week. the number of chemistry textbooks sold was three times the number of biology textbooks sold. how many textbooks of each type were sold?
Answers
Total number of Chemistry textbooks sold is 81 and total number of Biology textbooks sold is 243
How is the number of each textbooks sold, calculated?Let there are x biology textbooks sold.
No of chemistry textbooks sold = 3 the number of biology textbooks sold
ATQ,
A textbook store sold a combined total of 324 biology and chemistry textbooks in a week.
x + 3x = 324
4x = 324
x = 81
It means there are 81 biology textbooks sold and 3x = 3(81) = 243 chemistry textbooks sold.
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X - 11 = -44 solve one step equation.
Answers
Answer: x = -33
Explanation:
Given the following question:
x - 11 = -44
Step 1: collect the like terms
x = -44 + 11
x = -33
Therefore, x = -33
Question 4(Multiple Choice Worth 1 points)
(03.01 MC)
Simplify square root of three times square root of twenty one.
square root of twenty four
square root of sixty three
three square root of seven
nine square root of seven
Answers
The Simplification of square root of three times square root of twenty one is; C: three square root of seven
How to use law of Exponents?The Laws of Exponents are;
When multiplying like bases, ensure that the base is kept the same while we add the exponents. When raising a base with a particular power to another specific power, ensure that the base is kept the same and multiply the exponents. When dividing like bases, ensure that the base is kept the same and subtract the denominator exponent from the numerator exponent.We have the expression;
√3 * √21
= √3 * √3 * √7
= (√3 * √3) * √7
= 3√7
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C = dn or C = 2rn
(What is the radius of a circle with a circumference of 25cm?)
Answers
Hello!
Let's take this problem step by-step:
What is the formula for the circumference of a circle:
[tex]\text{Circumference} = 2\pi *\text{radius}[/tex]
Since the circumference is 25 cm
[tex]25 = 2\pi *\text{radius}\\\\\text{radius} = \dfrac{25}{2\pi }[/tex]
Answer: [tex]\text{radius} = \dfrac{25}{2\pi }[/tex]
Hope that helps!
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Determine the range of the following graph:
Answers
Answer:
The range is the allowed values of y.
Set notation: { y | -9 [tex]\leq[/tex] y [tex]\leq[/tex] 0, y ∈ R}
Interval notation: [-9,0]
Hope that helps
An eighteen-acre building lot is five times as long as it is wide. What are its dimensions? [Note: 1 acre = 43,560 ft2.]
Answers
The dimensions of building lot are 396 feet width and 1980 feet length.
Let the width of building lot be x. So, the length of the same building lot will be 5x. According to the formula, the area will be length × width.
18 acre = x×5x
Keep the value of acre in the above mentioned relation
18 × 43,560 = 5x²
Performing multiplication on Left Hand Side of the equation
784,080 = 5x²
Performing division by 5
x² = 156,816
Now taking square root to find the value of x
x = ✓156,816
x = 396 ft
Thus, the width of building lot is 396 feet
The length of building lot = 5×396
Performing multiplication
The length of building lot = 1980 feet
Therefore, the length and width of building lot is 1980 feet and 396 feet respectively.
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please try to answer quickly my brainly app is crashing
Answers
The formula to calculate the lateral area of a cone is given by
[tex]LA=pi*r*l[/tex]where
LA=10.5pi in2
r=2.1 in
l=? slant height
substitute given values
[tex]\begin{gathered} 10.5pi=pi*2.1*l \\ solve\text{ for l} \\ l=\frac{10.5pi}{pi*2.1} \\ \\ l=5\text{ in} \end{gathered}[/tex]The answer is 5 inchesA pedestrian is walking at a speed of 3 km/hr. Express the distance in kilometers, d, as a function of time in hours, t.
The question format : d(t) =
Answers
This is because
distance = rate*time
Rate is another term for speed.
The employees at a baseball bat factory need to make 350,000 bats in 6 months. They make 2,750 bats each day and work 127 days in the 6 months. Do the employees make enough bats?
Answers
Answer:
75 boxes
Step-by-step explanation:
If you divide 24000 bats by 50 boxes, you get 480. Then, if you divide the 36000 by 480, you will get 75
What are the The values of X and why that satisfy this equation (x+yi)+(4+9i)=9-4i
Answers
The values of x and y that satisfy the equation (x+yi)+(4+9i)=9-4i is x = 5 and y = -13 .
In the question ,
the equation is given as
(x+yi)+(4+9i)=9-4i
to find the value of x and y , we solve LHS and RHS of the equation separately
So LHS =
(x+yi)+(4+9i)
x+yi+4+9i
Adding the real and imaginary terms , we get
(x+4)+(y+9)i which is equal to RHS that is 9-4i
So , on comparing , we get
x+4 = 9 and y+9 = -4
x= 9-4 and y = -4-9
x = 5 and y = -13
Therefore , the values of x and y that satisfy the equation (x+yi)+(4+9i)=9-4i is x = 5 and y = -13 .
The given question is incomplete , the complete question is
What are the The values of X and Y that satisfy this equation (x+yi)+(4+9i)=9-4i ?
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Evaluate g(18), when g(x)=−8x+14
Answers
Answer:
-130
Step-by-step explanation:
g(18)= -8(18)+14
=-144+14
=-130
suppose you give 10 people a taste test where they each try samples of two different brands of soda. after drinking both samples they tell you which soda they liked best. what is a/the confounding variable in this experiment?
Answers
Confounding variables are any other variable that also has an effect on your dependent variable.
What is a confounding variable?
A confounding variable, also called a confounder or confounding factor, is a third variable in a study examining a potential cause-and-effect relationship.
A confounding variable is related to both the supposed cause and the supposed effect of the study. It can be difficult to separate the true effect of the independent variable from the effect of the confounding variable.
In your research design, it's important to identify potential confounding variables and plan how you will reduce their impact.
For example, if you are researching whether drinking both sample lead to taste test, then drinking both sample is your independent variable and taste test is your dependent variable. Confounding variables are any other variable that also has an effect on your dependent variable.
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under what circumstances can a very small treatment effect still be significant? group of answer choices if the standard error of m (s m) is very large if the sample size (n) is very large all of the other factors are likely to produce a significant result. if the sample standard deviation (s) is very large
Answers
A minor treatment effect may nonetheless be significant under certain circumstances if the sample size is large and the sample variance is low.
What is the standard error, and sample size?The standard error calculates the discrepancy between a sample's estimate and the actual value for the population. Therefore, the standard error should be smaller the better. In fact, a standard error of zero or extremely close to it would indicate that the projected value and the actual value are identical.Sample size determination is the process of deciding how many observations or replicates to include in a statistical sample. The sample size is an important consideration in any empirical study that aims to infer information about a population from a sample.Therefore, a minor treatment effect may nonetheless be significant under certain circumstances if the sample size is large and the sample variance is low.
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