Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas.tan(u) = 13/5, 0 < u < /2
Answers
The first step to answer this question is to find tan(2u) by using the double angle formula:
[tex]\begin{gathered} tan(2u)=\frac{2tan(u)}{1-tan^2(u)} \\ tan(2u)=\frac{2(\frac{13}{5})}{1-(\frac{13}{5})^2} \\ tan(2u)=\frac{\frac{26}{5}}{1-\frac{169}{25}} \\ tan(2u)=\frac{\frac{26}{5}}{-\frac{144}{25}} \\ tan(2u)=-\frac{65}{72} \end{gathered}[/tex]It means that tan(2u) is -65/72.
The next step is to rewrite the equations for sin(2u) and cos(2u) to have them in terms of the least number of variables possible, this way:
[tex]\begin{gathered} sin(2u)=2sin(u)cos(u) \\ sin(2u)=2sin(u)\frac{sin(u)}{tan(u)} \\ sin(2u)=\frac{2sin^2(u)}{tan(u)} \end{gathered}[/tex][tex]\begin{gathered} cos(2u)=cos{}^2(u)-sin^2(u) \\ cos(2u)=1-sin^2(u)-s\imaginaryI n^2(u) \\ cos(2u)=1-2sin^2(u) \end{gathered}[/tex]If we rewrite tan(2u) in terms of sin(2u) and cos(2u) we will have:
[tex]\begin{gathered} tan(2u)=\frac{sin(2u)}{cos(2u)} \\ tan(2u)=\frac{\frac{2s\imaginaryI n^{2}(u)}{tan(u)}}{1-2sin^2(u)} \end{gathered}[/tex]We know the values of tan(2u) and tan(u), so we can solve the equation for sin^2(u).
[tex]\begin{gathered} tan(2u)=\frac{2sin^2(u)}{tan(u)(1-2sin^2(u))} \\ -\frac{65}{72}=\frac{2s\imaginaryI n^2(u)}{\frac{13}{5}(1-2s\imaginaryI n^2(u))} \\ -\frac{65}{72}\cdot\frac{13}{5}\cdot(1-2sin^2(u))=2sin^2(u) \\ -\frac{169}{72}(1-2sin^2(u))=2sin^2(u) \\ -1+2sin^2(u)=\frac{72}{169}\cdot2sin^2(u) \\ -1+2sin^2(u)=\frac{144}{169}sin^2(u) \\ 2sin^2(u)-\frac{144}{169}sin^2(u)=1 \\ \frac{194}{169}sin^2(u)=1 \\ sin^2(u)=\frac{169}{194} \end{gathered}[/tex]Using this value we can find the values of sin(2u) and cos(2u):
[tex]\begin{gathered} sin(2u)=\frac{2sin^2(u)}{tan(u)} \\ sin(2u)=\frac{2\cdot\frac{169}{194}}{\frac{13}{5}} \\ sin(2u)=\frac{65}{97} \end{gathered}[/tex][tex]\begin{gathered} cos(2u)=1-2sin^2(u) \\ cos(2u)=1-2\cdot\frac{169}{194} \\ cos(2u)=1-\frac{169}{97} \\ cos(2u)=-\frac{72}{97} \end{gathered}[/tex]It means that sin(2u)=65/97, cos(2u)=-72/97 and tan(2u)=-65/72.
Related Questions
I NEED HELP WITH THIS ASAP 100 POINTS IF SOMEONE GETS THIS RIGHT.
Question 12(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
For triangle XYZ, m∠X = (4g + 13)° and the exterior angle to ∠X measures (3g + 48)°. Find the measure of ∠X and its exterior angle.
Interior angle = 48°; exterior angle = 74.25°
Interior angle = 74.25°; exterior angle = 48°
Interior angle = 81°; exterior angle = 99°
Interior angle = 99°; exterior angle = 81°
Answers
Answer:
Interior angle = 81°; exterior angle = 99°.
Step-by-step explanation:
For triangle XYZ:
m∠X = (4g + 13)° exterior angle to ∠X = (3g + 48)°Angle X and its exterior angle form a straight line.
Angles on a straight line sum to 180°.
Therefore:
⇒ (4g + 13)° + (3g + 48)° = 180°
⇒ 4g + 13 + 3g + 48 = 180
⇒ 7g + 61 = 180
⇒ 7g + 61 - 61 = 180 - 61
⇒ 7g = 119
⇒ 7g ÷ 7 = 119 ÷ 7
⇒ g = 17
To find the measure of ∠X and its exterior angle, substitute the found value of g into the angle expressions:
⇒ m∠X = (4(17) + 13)°
⇒ m∠X = (68 + 13)°
⇒ m∠X = 81°
⇒ exterior angle to ∠X = (3(17) + 48)°
⇒ exterior angle to ∠X = (51 + 48)°
⇒ exterior angle to ∠X = 99°
Therefore:
Interior angle = 81°Exterior angle = 99°Answer: C
Step-by-step explanation: did the practice test!
Question 3 of 102 PointsWhat is the midpoint of the segment shown below?(-1,2)(73)O A. (6,3)O B. (3,3)O C. (3.)O D. (6,5)10
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The engine of a car has a displacement of 460 cubic inches. What is the displacement in cubic feet? Round your answer to 2 places.
Answers
Explanation
To find the displacement in cubic feet, divide the volume value by 1728.
[tex]\frac{460}{1728}=0.27[/tex]Answer: 0.27 cubic feet
7. Angela bought some sugar and strawberries to make strawberry jam.Sugar costs $1.80 per pound, and strawberries cost $2.50 per pound.Angela spent a total of $19.40. Which point on the coordinate plane couldrepresent the pounds of sugar and strawberries that Angela used to makejam?
Answers
Equation of the Line
Let's use the following variables:
x = pounds of sugar
y = pounds of strawberries
Angela spent a total of $19.40 to make strawberry jam, thus:
1.80x + 2.50y = 19.40
The equation of the line represents the relationship between x and y. Any point that solves the problem must lie in the line.
The image shows the graph of a line, but we need to be sure it represents the equation above. A small checkup will be done as follows:
For x = 0, solve for y:
1.80*(0) + 2.50y = 19.40
y = 19.4 / 2.5 = 7.76
This point corresponds to the y-intercept (0, 7.76). It can be correctly found on the graph.
For y = 0, solve for x:
1.80x + 2.50*(0) = 19.40
x = 19.40 / 1.8 = 10.78
This point corresponds to the x-intercept at (10.78, 0). It can also be found on the graph.
Now we are sure the line is the representation of our equation, the only point that lies on that line is B(8, 2).
If we substitute x = 8, y = 2:
1.80*(8) + 2.50*(2) = 19.40
14.4 + 5 = 19.40
19.40 = 19.40
The equation is satisfied, thus, the answer is:
Point B
2. The total sales for June at Jim's Candy Store were $7,785. The total sales for June and Julywere $12,603, what were the total sales for July?ExplorerPlanSolve:Examine:Answer:
Answers
Describe a situation that could be represented by theequation y=x-0.3x.Be sure to explain what x and y mean in your situation,
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We are asked to describe a situation that could be represented by the equation
[tex]y=x-0.3x[/tex]Suppose that y is the number of liters of water in a tank.
And x is the number of hours.
Each hour, 30% (0.3) of the water is evaporated from the tank. (subtracted)
So the equation completely models the above scenario.
[tex]y=x-0.3x[/tex]For example:
What will be the amount of water in the tank after 10 hours?
[tex]undefined[/tex]I need help with 4 problems
Answers
1)
[tex]c^2=5^2+5^2[/tex]then the solution is
[tex]c=\sqrt[]{25+25}=\sqrt[]{50}=5\sqrt[]{2}\approx7.1[/tex]2x - 11 = -3
What does x equal?
Answers
Answer :x=4
Step-by-step explanation:
x equals a point. If you are in the same exact area but at a different x, you dont know how to get to the area where x is. It is important to note that x does not equal a point, but a location.
natural number is also a whole number.TrueFalse
Answers
Answer
The statement istrue.
Natural numbers are also whole numbers.
Explanation
Natural numbers are counting numbers.
They are the numbers that are numerically used to count things.
Hence, all natural numbers (counting numbers) are whole numbers.
Hope this Helps!!!
Triangle is rotated 180° around the origin. What will be the coordinates for Triangle J'K'L'? A(6,7)(6,2)(3,7)B(7,-6)(2,-7)(-3,-7)C(-6,-7)(-6,-2)(-3,-7)D(-7,6)(2,-6)(-7,3)
Answers
Answer:
A. (6,7)(6,2)(3,7)
Explanation:
From the graph, the coordinates of J, K and L are:
[tex]J(-6,-7),K(-6,-2)\text{ and L}(-3,-7)[/tex]When a point (x,y) is rotated 180° around the origin, we have the transformation rule:
[tex](x,y)\to(-x,-y)[/tex]Therefore, the coordinates for Triangle J'K'L' are:
[tex]J^{\prime}(6,7),K^{\prime}(6,2)\text{ and L'}(3,7)[/tex]The correct choice is A.
Complete each equation in order to obtain the indicated solution
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Question 13.
Part (a).
Given the solution:
All real numbers
We have the expression:
3(4x + 2) = ________
Let's complete the equation in order to obtain the indicated solution.
For a solution to be all real numbers, the equation must be true.
hence, we have:
[tex]\begin{gathered} 3(4x+2)=3(4x+2) \\ \end{gathered}[/tex]After solving we have:
0 = 0
This means the system has infinitely many solutions, therefore, the solution is all real numbers.
ANSWER:
3(4x + 2) = 3(4x + 2)
what is a like term?
Answers
In an expression, two or more terms are like terms if they have the same variable and exponents.
For example the terms:
2a and -8a → these terms have the same variable "a" and the same exponent "1"
9y³ and 8x⁴ → these terms have different variables "y" and "x" and different exponents "3" and "4", so they are not like terms.
Constants, for example, -10 or 6, are also considered to be like terms.
Determine if the following statement is true or false regarding sets A and B.A = {3, 5, 7, 9, 11, 13}B = {3, 5, 11, 13}Every element of A is also an element of B.Choose the correct answer below.FalseTrue
Answers
We have the following sets:
A = {3, 5, 7, 9, 11, 13}
B = {3, 5, 11, 13}
If we look closely, all the elements of B are in A. But each element of A does not belong to B, therefore the statement is totally false.
Rain equation of a hyperbola given the foci and the asymptotes
Answers
The equation for a hyperbola that opens up and down has the following general form:
[tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1[/tex]Where the foci of the hyperbola are located at (h,k+c) and (h,k-c) with c given by:
[tex]c^2=a^2+b^2[/tex]And asymptotes with slopes given by a/b and -a/b.
The hyperbola with the equation that we have to find has these two foci:
[tex](3,2-\sqrt{26})\text{ and }(3,2+\sqrt{26})[/tex]This means that:
[tex]\begin{gathered} (h,k-c)=(3,2-\sqrt{26}) \\ (h,k+c)=(3,2+\sqrt{26}) \end{gathered}[/tex]So we get h=3, k=2 and c=√26.
The slope of the asymptotes have to be 5 and -5 which means that:
[tex]\frac{a}{b}=5[/tex]Using the value of c we have:
[tex]c^2=26=a^2+b^2[/tex]So we have two equation for a and b. We can take the first one and multiply b to both sides:
[tex]\begin{gathered} \frac{a}{b}\cdot b=5b \\ a=5b \end{gathered}[/tex]And we use this in the second equation:
[tex]\begin{gathered} 26=(5b)^2+b^2=25b^2+b^2 \\ 26=26b^2 \end{gathered}[/tex]We divide both sides by 26:
[tex]\begin{gathered} \frac{26}{26}=\frac{26b^2}{26} \\ b^2=1 \end{gathered}[/tex]Which implies that b=1. Then a is equal to:
[tex]a=5b=5\cdot1=5[/tex]AnswerNow that we have found a, b, h and k we can write the equation of the hyperbola. Then the answer is:
[tex]\frac{(y-2)^2}{5^2}-\frac{(x-3)^2}{1^2}=1[/tex]Differentiatey = -8 In x
Answers
Given:
[tex]y=-8lnx[/tex]Let's differentiate the equation.
To differentiate since -8 is constant with resppect to x, the derivative will be:
[tex]\begin{gathered} \frac{d}{dx}(-8lnx) \\ \\ =-8\frac{d}{dx}(ln(x)) \end{gathered}[/tex]Where:
derivative of ln(x) with respect to x = 1/x
Thus, we have:
[tex]\begin{gathered} -8\frac{1}{x} \\ \\ =-\frac{8}{x} \end{gathered}[/tex]ANSWER:
[tex]-\frac{8}{x}[/tex]9. For each fraction, decimal, or percent, write the equivalent number from the list below 0.52, 38, 50, 0.35, 40% , 50 UN 76% 0.82 7 20 13 25
Answers
We have
In order to convert a fraction to a decimal, we divide the numerator between the denominator.
[tex]\frac{2}{5}=0.4=40\text{\%}[/tex][tex]0.82=\frac{82}{100}=\frac{41}{50}[/tex][tex]\frac{13}{25}=0.52[/tex][tex]76\text{\%}=\frac{76}{100}=\frac{38}{50}[/tex][tex]\frac{7}{20}=0.35[/tex]ANSWER
2/5=40%
0.82=41/50
13/25=0.52
76%=38/50
7/20=0.35
The two lines y y = x and y = x + 1 are parallel lines.
True
False
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By definition, the Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
The equation of a line that passes through the Origin has the following form:
[tex]y=mx[/tex]Where "m" is the slope of the line.
In this case, you have the first line that passes through the Origin:
[tex]y=x[/tex]You can identify that its slope is:
[tex]m_1=1[/tex]You also know the second equation, which is written in Slope-Intercept form:
[tex]y=x+1[/tex]You can identify that:
[tex]\begin{gathered} m_2=1 \\ b=1 \end{gathered}[/tex]By definition, the slopes of parallel lines are equal. Then, since:
[tex]m_1=m_2[/tex]These lines are parallel.
The answer is: True.
Write 12.5% as a decimal.
Answers
12.5% as a decimal is 0.125.
To convert a percentage in to a decimal, we divide the percentage by 100:
[tex]12.5\div100=0.125[/tex]f(x)= - 9x+2 Find the domain of the function. Type answer in interval notation.
Answers
ANSWER:
Domain: (-∞, ∞)
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f(x)=-\:9x+2\:[/tex]The domain of a function is the set of all possible input values of the function. In this case, it would be the interval of values that x can take.
In this function, x can take any value in real numbers.
Therefore, in that case, it will be:
[tex]D=(-\infty,\infty)[/tex]Art club has 12 members. Each member paysmonthly dues of $12.60. On the first day of themonth, 4 members paid their dues. The remainingmembers paid their dues on the second day of themonth. How much money was collected in dues onthe second day of the month?
Answers
Given:
Total number of members in a club is 12
Each member pays $12.60 on every month.
[tex]\begin{gathered} \text{Number of members paid the dues on second day=12-4} \\ \text{Number of members paid the dues on second day=}8 \end{gathered}[/tex][tex]\begin{gathered} \text{Money collected on the second day=8}\times12.60 \\ \text{Money collected on the second day= \$100.80} \end{gathered}[/tex]Money collected on the second day of the month is $100.80
Answer:
100.8
Step-by-step explanation:
12-4 = 8
the 4 is the people who payes the first day the 8 is the people who payes the second day
12.60 eight times = 12.60•8= 100.8
the eight people each payes 12.60 so that would be 12.60 8 times
A student bought a calculator and a textbook for a course in algebra. He told his friend that the total cost was $165 (without tax) and thatthe calculator cost $25 more than thrice the cost of the textbook. Whatwas the cost of each item? Let x = the cost of a calculator andy = the cost of the textbook. The corresponding modeling system is { x = 3y + 25x + y =Solve the system by using the method of= 165substitution
Answers
We know that the calculator price (x) was 25 more than 3 times the price of the textbook (y).
This can be represented as:
[tex]x=3y+25[/tex]We also know that the sum of the prices of the two items is equal to $165:
[tex]x+y=165[/tex]We have to solve this system of equations with the method of substitution.
We can use the first equation, as we have already clear the value of x, to substitute x in the second equation and then solve for y:
[tex]\begin{gathered} x+y=165 \\ (3y+25)+y=165 \\ 4y+25=165 \\ 4y=165-25 \\ 4y=140 \\ y=\frac{140}{4} \\ y=35 \end{gathered}[/tex]With the value of y we can calculate x using the first equation:
[tex]\begin{gathered} x=3y+25 \\ x=3\cdot35+25 \\ x=105+25 \\ x=130 \end{gathered}[/tex]Answer: the solution as ordered pair is (x,y) = (130, 35)
can you answer 3 please show a table graph and work
Answers
To solve the question, choose values for x to find its corresponding image y. Then, plot the points and connect them.
Step 01: Choosing x = -2.
Substituting x by -2 in the equation:
[tex]\begin{gathered} y=2\cdot3^{-2} \\ y=2\cdot(\frac{1}{3})^2 \\ y=2\cdot\frac{1}{9} \\ y=\frac{2}{9} \end{gathered}[/tex]So, the first point is (-2, 2/9).
Step 02: Choosing x = -1.
Substituting x by -1 in the equation:
[tex]\begin{gathered} y=2\cdot3^{-1} \\ y=2\cdot(\frac{1}{3})^1 \\ y=2\cdot\frac{1}{3} \\ y=\frac{2}{3} \end{gathered}[/tex]So, the second point is (-1, 2/3).
Step 03: Choosing x = 0.
Substituting x by 0 in the equation:
[tex]\begin{gathered} y=2\cdot3^0 \\ y=2\cdot1 \\ y=2 \end{gathered}[/tex]So, the third point is (0, 2).
Step 04: Choosing x = 1.
Substituting x by 1 in the equation:
[tex]\begin{gathered} y=2\cdot3^1 \\ y=2\cdot3 \\ y=6 \end{gathered}[/tex]So, the fourth point is (1, 6).
Step 05: Write the points in a table.
x y (x, y)
-2 2/9 (-2, 2/9)
-1 2/3 (-1, 2/3)
0 2 (0, 2)
1 6 (1, 6)
Step 06: Plot the points and connect them.
The figure below shows the points and the graph.
Done! Your question is solved!
A line is graphed on the coordinate plane below.Line y = -2 +2 will be graphed on the same coordinate plane to create a system of equations.What is the solution to that system of equations?4A (-2,4)B (0-4)C (2,-4)0 (4,-2)Rod End TeeFlagOptionsBackNext
Answers
Solution:
Step 1: Find the equation of the line in the graph.
Two points the line pass through are (0, -4) and (2, -3)
Thus,
[tex]\begin{gathered} x_1=0,y_1=-4 \\ x_2=2,y_2=-3 \end{gathered}[/tex][tex]\begin{gathered} The\text{ equation of the line can be calculated with the formula} \\ \frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1} \\ \\ \frac{-3-(-4)}{2-0}=\frac{y-(-4)}{x-0} \\ \\ \frac{-3+4}{2}=\frac{y+4}{x} \\ \frac{1}{2}=\frac{y+4}{x} \end{gathered}[/tex][tex]\begin{gathered} 2(y+4)=x \\ 2y+8=x \\ 2y=x-8 \end{gathered}[/tex]The equation of the graph is 2y = x - 8
Step 2:
Solve the two equations simultaneously to detemine the solution to the systems of equations
2y = x - 8 ------------------------equation (1)
y = -x + 2 ----------------------equation (2)
Add both equations to eliminate x
2y + y = x - 8 + (-x) + 2
3y = x -8-x+2
3y = -8 + 2
3y = -6
y = -6/3
y = -2
Substitute y = -2 into equation (2)
y = -x + 2
-2 = -x + 2
-2 -2 = -x
-4 = -x
-x = -4
Divide both sides by -1
x = 4
Hence, the solution to the system of equations is (4, -2)
The correct option is option D
Select the correct answer from each drop-down menu.Wayne, Winston, and Wilfred walked for an hour. Winston and Wilfred walked the same number of miles. Winston walked 2 miles less than 2 themiles Wayne walked. Wilfred walked 2 miles more than 3 the miles Wayne walked.A variable selected to solve this problem should represent the number of mileswalked in an hour.In that hour, Wayne would have walkedmiles and Winston and Wilfred would have walkedmiles each. So, WaynewalkedWinston and Wilfred.
Answers
SOLUTION:
Winston =
[tex]Win\text{ston = }\frac{3}{2}\text{ (Wayne) - 2}[/tex][tex]\text{Wilfred = }\frac{1}{3\text{ }}\text{ wayne }+\text{ }\frac{3}{2}[/tex][tex]\frac{3}{2}\text{ wayne - 2 = }\frac{1}{3}\text{ wayne }+\frac{3}{2}[/tex][tex]\frac{3}{2}\text{ wayne - }\frac{1}{3}\text{ wayne = }\frac{3}{2}\text{ + 2}[/tex]Upon simplification, the number of miles wayne walked was 3
Substituting wayne = 3 into the second equation
[tex]\text{Wilfred = }\frac{1}{3\text{ }}\text{ (3) }+\text{ }\frac{3}{2}[/tex]Wilfred = 2.5
Since Wilfred and Winston walked the same number of miles,
Winston = 2.5
The first drop menu is Wilfred
The second drop menu is 3
The third drop menu is 2.5
The fourth drop menu is faster than.
Solve the equation without using a calculator
[tex]x^2+\big(4x^3-3x\big)^2=1[/tex]
Answers
Answer:
[tex]x= \dfrac{\sqrt{2}}{2}, \quad x=-\dfrac{\sqrt{2}}{2},\\\\x=\dfrac{\sqrt{2 - \sqrt{2}}}{2}, \quad x=-\dfrac{\sqrt{2 - \sqrt{2}}}{2}, \quad x= \dfrac{\sqrt{2 + \sqrt{2}}}{2}, \quad x= -\dfrac{\sqrt{2 + \sqrt{2}}}{2}[/tex]
Step-by-step explanation:
Given equation:
[tex]x^2+(4x^3-3x)^2=1[/tex]
Expand and equal the equation to zero:
[tex]\begin{aligned}x^2+(4x^3-3x)^2&=1\\x^2+(4x^3-3x)(4x^3-3x)&=1\\x^2+16x^6-24x^4+9x^2&=1\\16x^6-24x^4+x^2+9x^2-1&=0\\16x^6-24x^4+10x^2-1&=0\end{aligned}[/tex]
Let u = x²:
[tex]\implies 16u^3-24u^2+10u-1=0[/tex]
Factor Theorem
If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x)
[tex]\textsf{As\;\;$f\left(\dfrac{1}{2}\right)=0$\;\;then\;$\left(u-\dfrac{1}{2}\right)$\;is a factor of $f(u)$}.[/tex]
Therefore:
[tex]\implies \left(u-\dfrac{1}{2}\right)\left(16u^2+bu+2\right)=0[/tex]
Compare the coefficients of u² to find b:
[tex]\implies b-8 = -24[/tex]
[tex]\implies b = -16[/tex]
Therefore:
[tex]\implies \left(u-\dfrac{1}{2}\right)\left(16u^2-16u+2\right)=0[/tex]
Factor out 2:
[tex]\implies 2\left(u-\dfrac{1}{2}\right)\left(8u^2-8u+1\right)=0[/tex]
[tex]\implies \left(u-\dfrac{1}{2}\right)\left(8u^2-8u+1\right)=0[/tex]
Zero Product Property
If a ⋅ b = 0 then either a = 0 or b = 0 (or both).
Using the Zero Product Property, set each factor equal to zero and solve for u.
[tex]\implies u-\dfrac{1}{2}=0 \implies u=\dfrac{1}{2}[/tex]
Use the quadratic formula to solve the quadratic:
[tex]\implies u=\dfrac{-(-8) \pm \sqrt{(-8)^2-4(8)(1)}}{2(8)}[/tex]
[tex]\implies u=\dfrac{8 \pm \sqrt{32}}{16}[/tex]
[tex]\implies u=\dfrac{8 \pm 4\sqrt{2}}{16}[/tex]
[tex]\implies u=\dfrac{2 \pm \sqrt{2}}{4}[/tex]
Therefore:
[tex]u=\dfrac{1}{2}, \quad u=\dfrac{2 - \sqrt{2}}{4}, \quad u=\dfrac{2 + \sqrt{2}}{4}[/tex]
Substitute back u = x²:
[tex]x^2=\dfrac{1}{2}, \quad x^2=\dfrac{2 - \sqrt{2}}{4}, \quad x^2=\dfrac{2 + \sqrt{2}}{4}[/tex]
Solve each case for x:
[tex]\implies x^2=\dfrac{1}{2}[/tex]
[tex]\implies x=\pm \sqrt{\dfrac{1}{2}}[/tex]
[tex]\implies x=\pm \dfrac{\sqrt{2}}{2}[/tex]
[tex]\implies x^2=\dfrac{2 - \sqrt{2}}{4}[/tex]
[tex]\implies x=\pm \sqrt{\dfrac{2 - \sqrt{2}}{4}}[/tex]
[tex]\implies x=\pm \dfrac{\sqrt{2 - \sqrt{2}}}{2}[/tex]
[tex]\implies x^2=\dfrac{2 + \sqrt{2}}{4}[/tex]
[tex]\implies x=\pm \sqrt{\dfrac{2 + \sqrt{2}}{4}}[/tex]
[tex]\implies x=\pm \dfrac{\sqrt{2 + \sqrt{2}}}{2}[/tex]
Solutions
[tex]x= \dfrac{\sqrt{2}}{2}, \quad x=-\dfrac{\sqrt{2}}{2},\\\\x=\dfrac{\sqrt{2 - \sqrt{2}}}{2}, \quad x=-\dfrac{\sqrt{2 - \sqrt{2}}}{2}, \quad x= \dfrac{\sqrt{2 + \sqrt{2}}}{2}, \quad x= -\dfrac{\sqrt{2 + \sqrt{2}}}{2}[/tex]
A dairy produced 8.1 liters of milk in 2 hours. How much milk, on average, did the dairyproduce per hour?
Answers
To answer this question, we need to find the unit rate in this case. For this, we need to divide the given liters by the hours. Then, we have:
[tex]\frac{8.1l}{2h}=4.05\frac{l}{h}[/tex]Then, the dairy produces 4.05 liters per hour.
A box contains four red marbles three green marbles and to blue marbles one marble is removed from the box and it's not replaced another marble is drawn from the box does the following represent in and a independent event
Answers
The correct option is Yes, which is option A
Why?
The reason is that the probability that marble is removed from the box does not affect the probability that a marble is drawn from the same box. i.e the two events do not affect each other
Section 1- Question 1Ryan is solving the equation - 6x = 12 by completing the square. What number should be added to both sides of the equation to complete the square?
Answers
Solution:
Given the equation below
[tex]x^2-6x=12[/tex]Applying the completing the square method
Where the general form of a quadratic equation is
[tex]ax^2+bx+c=0[/tex]For the completing square method,
[tex]Add\text{ }(\frac{b}{2})^2\text{ to both sides of the equation}[/tex]Where
[tex]b=-6[/tex]The number that should be added to both sides of the equation to complete the square is
[tex]=(\frac{-6}{2})^2=(-3)^2=9[/tex]Hence, the number is 9 (option B)
4^3/(-12+ 2^2)
(2x2)^2 + (-5 x 2 x 3 ) + 2
[tex] \frac{4^3/(-12 +2^2)}{(2x3)^2 +(-5 x2 x 3)+2} [/tex]
i need help!!
Answers
Answer:
-1
Step-by-step explanation:
[tex]\frac{\frac{64}{-12+4}}{(6)^2+(-30)+2} \\ \\ =\frac{\frac{64}{-8}}{36-30+2} \\ \\ =\frac{-8}{8} \\ \\ =-1[/tex]
the amount of money a worker earns is directly proportional to the number of hours worked.at this rate.thag worker makes $104 in an 8 hour shift.weite a direct variation equation that relates the earnings (e) of the worker to the number of hours (n) worked. use the correct lowercase variables given ,and use no spaces
Answers
the amount of money a worker earns is directly proportional to the number of hours worked.at this rate.thag worker makes $104 in an 8 hour shift.weite a direct variation equation that relates the earnings (e) of the worker to the number of hours (n) worked. use the correct lowercase variables given ,and use no spaces
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form e=kn
In this problem we have
e -----> amount of money a worker earns
n -----> number of hours worked
k is the constant of proportionality
k=e/n
Find the value of k
we have
For n=8 hours, e=$104
sibstitute
k=104/8
k=$13 per hour
The linear equation is
e=13n