The solution to 1 - cos(6x) is 2sin²(x).
Hence, option B) 2sin²(x) is the correct answer.
What is solution to 1 - cos(6x)?Given that; 1 - cos(6x) = ?
First, we rewrite using trig identity
1 - cos(2 × 3x)
Using the double angle identity, { cos2(x) = 1 - 2sin²(x) }
1 - ( 1 - 2sin²(x) )
Eliminate the parentheses
1 - 1 + 2sin²(x)
2sin²(x)
The solution to 1 - cos(6x) is 2sin²(x).
Hence, option B) 2sin²(x) is the correct answer.
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PLEASE HELP, TIMED
University students in an Iowa town have a mean hourly wage of $11.75, with a standard deviation of $1.25. The distribution of hourly wages is not assumed to be symmetric.
Between what two-hourly wages does Chebyshev's Theorem guarantee that we will find at least 75% of the people?
Round your answers to the nearest hundredth.
The Chebyshev Theorem guarantees that we will find at least 75% of the people with wages between $9.25 and $14.25.
What does Chebyshev’s Theorem state?When the distribution is not normal, Chebyshev's Theorem is used. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.At least 89% of the measures are within 3 standard deviations of the mean.An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].The Chebyshev Theorem guarantees that we will find at least 75% of the people with wages within 2 standard deviations of the mean, hence the bounds are:
11.75 - 2 x 1.25 = $9.25.11.75 + 2 x 1.25 = $14.25.More can be learned about the Chebyshev Theorem at https://brainly.com/question/25303620
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Given the vertex of a quadratic function, find the axis of symmetry.
(i) The equation of the axis of symmetry is x = - 5.
(ii) The coordinates of the vertex of the parabola are (h, k) = (4, - 18). The x-value of the vertex is 4.
(iii) According to the vertex form of the quadratic equation, the parabola opens down due to negative lead coefficient and has a vertex at (2, 4), which is a maximum.
How to analyze and interpret quadratic functions
In this question we must find and infer characteristics from three cases of quadratic equations. (i) In this case we must find a formula of a axis of symmetry based on information about the vertex of the parabola. Such axis passes through the vertex. Hence, the equation of the axis of symmetry is x = - 5.
(ii) We need to transform the quadratic equation into its vertex form to determine the coordinates of the vertex by algebraic handling:
y = x² - 8 · x - 2
y + 18 = x² - 8 · x + 16
y + 18 = (x - 4)²
In a nutshell, the coordinates of the vertex of the parabola are (h, k) = (4, - 18). The x-value of the vertex is 4.
(iii) Now here we must apply a procedure similar to what was in used in part (ii):
y = - 2 · (x² - 4 · x + 2)
y - 4 = - 2 · (x² - 4 · x + 2) - 4
y - 4 = - 2 · (x² - 4 · x + 4)
y - 4 = - 2 · (x - 2)²
According to the vertex form of the quadratic equation, the parabola opens down due to negative lead coefficient and has a vertex at (2, 4), which is a maximum.
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Identify an acute angle and give its measure.
Angle HEJ measures 15 degrees.
Please help I need to turn this in by Monday!
Answer: Rational, Irrational, Rational, Natural, Natural, Integer
Step-by-step explanation:
-4.2 is a rational number as it can be converted into a fraction
3√5 is an irrational number as it can't be converted into a fraction
5/3 is a rational number as it is a fraction
9 is a natural number as it is a positive whole number
√16 is a natural number as despite the square root, √16 is 4 which is a natural number
-8/2 is an integer as -8/2 is -4 which is a negative whole number
7x-3y=-7 slope of line perpendicular
Answer: -3/7
Step-by-step explanation:
The first step is to find the slope of the line
y = mx + c where m is the slope of the line
Rearrange the equation and we get
3y = 7x + 7
y = 7x/3 + 7/3
So the slope of the line 7x - 3y = -7 is 7/3
There is another rule that states: The product of the slopes of two lines perpendicular to each other is -1
So, the slope of the line perpendicular to 7x - 3y = -7 is -1/(7/3) = -3/7
One number is six more than three times another. If their sum is decreased by four, the result is twenty-two. Find
the numbers.
The smaller of the numbers is
Due Wed 08/10/
and the larger is
Answer: 5 is the smaller number and 21 is the larger number
Step-by-step explanation: let’s have the smaller of the numbers equal x and the larger one equal y. Y = 3x + 6 their sum is 3x + 6 + x or 4x + 6. This sum minus 4 is 22 so the sum is 26. 26-6 = 4x so 4x = 20 and x = 5 so r = 15+ 6 which is 21.
Geometry and Modeling:
Mike completely filled the container shown below with 616 small cubes that were each [tex]\frac{1}{2}[/tex] inch long.
Part A: Calculate the volume of the prism.
Part B: Crate a graphical model of a prism with base 5.5 by 3.5 that has the same volume as Part A.
Show how Mike can calculate the volume of the prism, in cubic inches, by using a volume formula instead of filling the container with small cubes.
the product of 6
and the sum of five
and a number
Answer:
6 * (5 + n)
Explanation:
Sum = addition
Difference = subtraction
Product = multiplication
Quotient = division
The distance from TJ's house to school and back is 0.4 km. In one week TJ travelled 2 km. How many times did TJ go to school?
$$
Answer: 5 times
Step-by-step explanation: The distance from his house to school and back is 0.4 km. Since he traveled 2km in a week, we have to divide 2 by0.4. 0.4x5 = 2 so he went to school 5 times a week.
P = √mx_ £x MX t make x the subject
[tex]p = \sqrt{ \frac{mx}{t} } - t {}^{2}x \: \: make \: x \: the \: subject [/tex]
So, making x subject of the formula, x = [m - 2pt³ ±√(m² - 4pt²m)]/{2t⁵}
How to make x subject of the formula?Since p = √(mx/t) - t²x
So, p + t²x = √(mx/t)
Squaring both sides, we have
(p + t²x)² = [√(mx/t)]²
p² + 2pt²x + t⁴x² = mx/t
Multiplying through by t,we have
(p² + 2pt²x + t⁴x²)t = mx/t × t
p²t + 2pt³x + t⁵x² = mx
p²t + 2pt³x + t⁵x² - mx = 0
t⁵x² + 2pt³x - mx + p²t = 0
t⁵x² + (2pt³ - m)x + p²t = 0
Using the quadratic formula, we find x.
[tex]x = \frac{-b +/-\sqrt{b^{2} - 4ac} }{2a}[/tex]
where
a = t⁵, b = (2pt³ - m) and c = p²tSubstituting the values of the variables into the equation, we have
[tex]x = \frac{-(2pt^{3} - m) +/-\sqrt{(2pt^{3} - m)^{2} - 4(t^{5})(p^{2}t) } }{2t^{5} }\\= \frac{-(2pt^{3} - m) +/-\sqrt{4p^{2} t^{6} - 4pt^{2}m + m^{2} - 4p^{2}t^{6} } }{2t^{5}}\\= \frac{-(2pt^{3} - m) +/-\sqrt{m^{2} - 4pt^{2}m } }{2t^{5}}\\= \frac{m - 2pt^{3} +/-\sqrt{m^{2} - 4pt^{2}m } }{2t^{5}}[/tex]
So, making x subject of the formula, [tex]x = \frac{m - 2pt^{3} +/-\sqrt{m^{2} - 4pt^{2}m } }{2t^{5}}[/tex]
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If the next two Junior Athletics events are sold out, the new table will look like this: Event 1 Event 2 Event 3 Event 4 Event 5 Event 6 Event 7 Junior Athletics Sold Out Sold Out Not Sold Out Not Sold Out Sold Out Sold Out Sold Out What is the new probability of the event being sold out? Give your answer as a fraction.
0.7 is the new probability of the event being sold out given that total number of events is 7 and 5 events are sold out. This can be obtained by using the formula for probability.
Find the new probability of the event being sold out:Probability is the chance of occurrence of an event.
⇒ The formula for finding probability,
Probability = [tex]\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ outcomes}[/tex]
Here it is given in the question that,
Total number of outcomes = Total number of events = 7 Number of events sold out = 5 Number of events not sold out = 2Therefore by using the formula of probability we get,
⇒ Probability (Junior Athletics being sold out) = [tex]\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ outcomes}[/tex]
Probability (Junior Athletics being sold out) = [tex]\frac{Number\ of\ events\ sold\ out}{Total\ number\ of\ events}[/tex]
Probability (Junior Athletics being sold out) = 5/7
⇒ Probability (Junior Athletics being sold out) = 0.7
Hence 0.7 is the new probability of the event being sold out given that total number of events is 7 and 5 events are sold out.
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Find the measures of angles a and b when 0=47
Answer:
b = 133, a = 47
Step-by-step explanation:
If the two lines are parallel, then angle b is equal to 180-47 = 133 (same side interior angles), and angle is equal to angle 0 (alternate interior angles)
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
a = 47°b = 133°[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:a = \theta[/tex]
( by Alternate interior angle pair )
[tex]\qquad \therefore\: \sf \:a = 47 \degree[/tex]
Next,
[tex]\qquad❖ \: \sf \:b = 180 - \theta[/tex]
( by co - interior angle pair )
[tex]\qquad❖ \: \sf \:b = 180 - 47[/tex]
[tex]\qquad \therefore \: \sf \:b = 133 \degree[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\qquad❖ \: \sf \: \:a = 47 \degree[/tex]
and
[tex]\qquad❖ \: \sf \:b = 133 \degree[/tex]
Urgent help needed will give brainiest
We can write the integration domain as
[tex]D = \left\{(x,y) \mid -1 \le y \le 1 \text{ and } 2y-2 \le x \le -y+1\right\}[/tex]
so that the integral is
[tex]\displaystyle \iint_D -\sin(y+x) \, dA = \int_{-1}^1 \int_{2y-2}^{-y+1} -\sin(y+x) \, dx \, dy[/tex]
Compute the integral with respect to [tex]x[/tex].
[tex]\displaystyle \int_{2y-2}^{-y+1} -\sin(y+x) \, dx = \cos(y+x)\bigg|_{x=2y-2}^{x=-y+1} \\\\ ~~~~~~~~ = \cos(y+(2y-2)) - \cos(y+(-y+1)) \\\\ ~~~~~~~~ = \cos(3y-2) - \cos(1)[/tex]
Compute the remaining integral.
[tex]\displaystyle \int_{-1}^1 (\cos(3y-2) - \cos(1)) \, dy = \left(\frac13 \sin(3y-2) - \cos(1) y\right) \bigg|_{y=-1}^{y=1} \\\\ ~~~~~~~~ = \left(\frac13 \sin(3-2) - \cos(1)\right) - \left(\frac13 \sin(-3-2) + \cos(1)\right) \\\\ ~~~~~~~~ = \boxed{\frac13 \sin(1) - 2 \cos(1) + \frac13 \sin(5)}[/tex]
What is the measure of
angle x?
Enter your answer in the box.
X =
Answer:
x = 48°
Step-by-step explanation:
Complementary angles
Angles that sum to 90°.
Vertical Angle Theorem
When two straight lines intersect, the vertical angles are congruent (equal).
Therefore, angle x is equal to the angle that is complementary to 42°.
To find x, subtract 42° from 90°:
⇒ x = 90° - 42°
⇒ x = 48°
IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
In the given figure, the measure of the central angle CAD is 80°, the major arc is arc CBD, and minor arc is arc CD. The measure of arc BEC is 2.27r and that of arc BC is 0.87r.
About the Central Angle:
An angle formed by two radii of a circle is known as a central angle. Thus, arc BC and arc CD both subtends central angles at the center.
Since BD is the diameter of the circle,
∠BAC + CAD = 180°
It is given that ∠BAC = 100°
⇒ ∠CAD = 180° - 100°
⇒ ∠CAD = 80°
About Major Arc:
The arc which subtends an angle greater than 180° at the center, is called a major arc.
Angle subtended by arc BEC = 360° - m(arc CD)
= 360° - 80°
= 280° > 180°
∴ Arc BEC is the major arc
About Minor Arc:
The arc which subtends an angle less than 180° at the center, is called a minor arc.
⇒ Arc CD is the minor arc.
Calculating arc BEC and arc BC:
Let us assume the radius of the circle is r.
Then, the formula of the measure of an arc is given by,
θ × (π/180) × r
Here, θ is the angle ( in degrees) subtended by the arc at the center.
Arc BEC = 260 × (π/180)r ......... [Put π = 3.14]
= 2.27r
Similarly, arc BC = 100 ×(π/180) × r .......... [Put π = 3.14]
= 0.87r
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A chemist has three different acid solutions. The first acid solution contains
20
%
acid, the second contains
30
%
and the third contains
60
%
. They want to use all three solutions to obtain a mixture of
72
liters containing
35
%
acid, using
2
times as much of the
60
%
solution as the
30
%
solution. How many liters of each solution should be used?
Let [tex]x,y,z[/tex] denote the amounts (in liters) of the 20%, 30%, and 60% solutions used in the mixture, respectively.
The chemist wants to end up with 72 L of solution, so
[tex]x+y+z=72[/tex]
while using twice as much of the 60% solution as the 30% solution, so
[tex]z = 2y[/tex]
The mixture needs to have a concentration of 35%, so that it contains 0.35•75 = 26.25 L of pure acid. For each liter of acid solution with concentration [tex]c\%[/tex], there is a contribution of [tex]\frac c{100}[/tex] liters of pure acid. This means
[tex]0.20x + 0.30y + 0.60z = 26.25[/tex]
Substitute [tex]z=2y[/tex] into the total volume and acid volume equations.
[tex]\begin{cases}x+3y = 72 \\ 0.20x + 1.50y = 26.25\end{cases}[/tex]
Solve for [tex]x[/tex] and [tex]y[/tex]. Multiply both sides of the second equation by 5 to get
[tex]\begin{cases}x+3y = 72 \\ x + 7.50y = 131.25\end{cases}[/tex]
By elimination,
[tex](x+3y) - (x+7.50y) = 72 - 131.25 \implies -4.50y = -59.25 \implies \boxed{y=\dfrac{79}6} \approx 13.17[/tex]
so that
[tex]x+3\cdot\dfrac{79}6 = 72 \implies x = \boxed{\dfrac{65}2} = 32.5[/tex]
and
[tex]z=2\cdot\dfrac{79}6 = \boxed{\dfrac{79}3} \approx 26.33[/tex]
A shipping company charged $15 to ship a package and 5% to insure the package.What was the total cost to ship this particular item?
Answer:
5% of 15 is 0.75 i think
Step-by-step explanation:
15/5% is 0.75
Help me with this question asap!
Answer:
false
Step-by-step explanation:
The converse of the statement is
If two angles are not a linear pair of angles, they are not adjacent.This is false by definition.
An agricultural company called Phatsima Pty. Ltd. owns an rectangular fuel tank that measures 75 cm by 65 cm by 30 cm.
How many millilitres of fuel are needed to fill their tank?
If the fuel price is R20.35 per liter. How much will it cost to fill half of their tank?
Choose an option below that has both answers correct.
a.
1. 146 250.00 ml and 2. R 1 488.10
b.
1. 150 000.00 ml and 2. R 2 976.19
c.
1. 73 125.00 ml and 2. R 1 488.10
d.
1. 146 250.00 ml and 2. R 2 000.00
Please help due today. (43/7÷ x+32/9) ÷25/6=4/3
The solution to the equation as given in the task content is; x = -3.47.
What is the solution of the equation in discuss?It follows from the task content that the equation given is; (43/7÷ x+32/9) ÷25/6=4/3
(43/7÷ x+32/9) = 25/6 × 4/3
(43/7÷ x+32/9) = 100/18
x +32/9 = 43/7 ÷ 100/18
x + 32/9 = 774/700
x = 774/700 - 32/9
x = -3.47.
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2. What is the solution for the system of equations?
16x - 32y = 27
8x - 16 = 16y
a) Use the linear combination (elimination) method to solve the system of equations.
b) What does the solution tell you about the two lines of the system?
Answer:
no solution
Step-by-step explanation:
16x - 32y = 27 → (1)
8x - 16 = 16y ( subtract 16y from both sides )
8x - 16 - 16y = 0 ( add 16 to both sides )
8x - 16y = 16 → (2)
multiply (2) by - 2 and add to (1)
- 16x + 32y = - 32 → (3)
add (1) and (3) term by term
0 + 0 = - 5
0 = - 5 ← not possible
this indicates the system has no solution
(b)
the solution to a system is the point of intersection of the 2 lines
since there is no solution, no point of intersection, then
this indicates the lines are parallel and never intersect
Answer:
a) no solution
b) the two lines never intersect
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases} 16x-32y=27\\8x-16=16y \end{cases}[/tex]
Part (a)To solve by linear combination (elimination):
Step 1
Write both equations in standard form: Ax + By = C
[tex]\implies 16x-32y=27[/tex]
[tex]\implies 8x-16y=16[/tex]
Step 2
Multiply one (or both) of the equations by a suitable number so that both equations have the same coefficient for one of the variables:
[tex]\implies 16x-32y=27[/tex]
[tex]\implies 2(8x-16y=16) \implies 16x-32y=32[/tex]
Step 3
Subtract one of the equations from the other to eliminate one of the variables:
[tex]\begin{array}{l r l}& 16x-32y & = 32\\- & 16x-32y & = 27\\\cline{1-3}& 0 & =\:\: 5\end{array}[/tex]
Therefore, as 0 ≠ 5, there is no solution to this system of equations.
Part (b)
The solution to a system of equations is the point(s) of intersection.
As there is no solution to the given system of equations, this tells us that the two lines never intersect.
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From the top of the Eiffel tower, which is 984 feet tall, you look down and see your friend at a 60°
angle of depression. How far is your friend from the foot of the tower?
The answer is 492 feet.
If we picture the scenario as a right triangle, using trigonometric ratios, this problem can be solved.
cos 60° = x / 984
1/2 = x/984
x = 984/2
x = 492 feet
Will mark brainliest!
Answer:
Area under the graph = 6 sq.units
I've shown the complete calculation over the attached page
Select ALL expressions that have a value less than 9.
A
B
C
D
E
2
5.9 +
23
√10
2√21
55
2
√85-2√3
Answer:
What is this?
Can't understand anything!
Answer : what is this question?
Write an expression involving exponents to represent the shaded area in square inches of the diagram than use that expression to calculate the shaded area in squares inches of the diagram
The expression involving exponents to represent the shaded area in square inches of the diagram is: 6²- (3² + 2²). The shaded area in squares inches of the diagram is: 23 square inches.
Expression involving exponents and shaded areaThe expression is:
6²- (3² + 2²)
The shaded area:
Shaded area=6²- (3² + 2²)
Shaded area=36-(9+4)
Shaded area=36-13
Shaded area=23 square inches
Therefore the expression involving exponents to represent the shaded area in square inches of the diagram is: 6²- (3² + 2²). The shaded area in squares inches of the diagram is: 23 square inches.
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Hunter leaves his house to go on a bike ride. He starts at a speed of 15 km/hr. Hunter's
brother decides to join Hunter and leaves the house 30 minutes after him at a speed of
18 km/hr. How long will it take to Hunter's brother to catch up to him?
The time requires to catch up to him will be 3 hours.
What is speed?Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance. Speed is a scalar quantity it does not require any direction only needs magnitude to represent.
Given that Hunter leaves his house to go on a bike ride. He starts at a speed of 15 km/hr. Hunter's brother decides to join Hunter and leaves the house 30 minutes after him at a speed of 18 km/hr.
The time will be calculated as below:-
30 minutes = 0.5 hour
15x = 18(x - 0.5)
15x = 18x - 9
-3x = -9
x = 3 hours
Therefore, the time requires to catch up to him will be 3 hours.
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Evaluate 3|12−x|−4 when x=15
Answer:
5
Step-by-step explanation:
3 x |12 - x| - 4
3 x |12 - 15| - 4
3 x 3 - 4
9 - 4
5
Someone help me with this question !,
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
The side opposite to the largest angle is the longest side of a triangle.
[tex] \qquad \large \sf {Conclusion} : [/tex]
hence, we can conclude that longest side is e
( since it's opposite angle is the largest, i.e 86° )
The perimeter of a rectangular field is 282 yards. If the width of the field is 52 yards, what is its length?
Answer: 89 yards
Step-by-step explanation: The perimeter is all the sides added up together. Since the width of the field is 52, the two sides are 52 yards which in total is 104 yards. 282- 104 = 178 yards. The length is 178/2 yards which is 89 yards.
Answer:
75
Step-by-step explanation:
math
Suppose each edge of the cube shown in the figure is 10 inches long. Find the sine and cosine of the angle formed by diagonals DE and DG.
Check the picture below.
[tex]sin(EDG )=\cfrac{\stackrel{opposite}{10}}{\underset{hypotenuse}{10\sqrt{3}}}\implies sin(EDG )=\cfrac{1}{\sqrt{3}}\implies sin(EDG )=\cfrac{1}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}} \\\\\\ \stackrel{\textit{rationalizing the denominator}}{sin(EDG )=\cfrac{\sqrt{3}}{\sqrt{3^2}}\implies sin(EDG )=\cfrac{\sqrt{3}}{3}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]cos(EDG )=\cfrac{\stackrel{adjacent}{10\sqrt{2}}}{\underset{hypotenuse}{10\sqrt{3}}}\implies cos(EDG )=\cfrac{\sqrt{2}}{\sqrt{3}}\implies cos(EDG )=\cfrac{\sqrt{2}}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}} \\\\\\ \stackrel{\textit{rationalizing the denominator}}{cos(EDG )=\cfrac{\sqrt{6}}{\sqrt{3^2}}\implies cos(EDG )=\cfrac{\sqrt{6}}{3}}[/tex]
