Answers
Answer:
[tex]\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}[/tex]
Step-by-step explanation:
We are given the trigonometric equation of:
[tex]\displaystyle{\sin 4x = \dfrac{\sqrt{3}}{2}}[/tex]
Let u = 4x then:
[tex]\displaystyle{\sin u = \dfrac{\sqrt{3}}{2}}\\\\\displaystyle{\arcsin (\sin u) = \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}\\\\\displaystyle{u= \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}[/tex]
Find a measurement that makes sin(u) = √3/2 true within [0, π) which are u = 60° (π/3) and u = 120° (2π/3).
[tex]\displaystyle{u = \dfrac{\pi}{3}, \dfrac{2\pi}{3}}[/tex]
Convert u-term back to 4x:
[tex]\displaystyle{4x = \dfrac{\pi}{3}, \dfrac{2\pi}{3}}[/tex]
Divide both sides by 4:
[tex]\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}[/tex]
The interval is given to be 0 ≤ 4x < π therefore the new interval is 0 ≤ x < π/4 and these solutions are valid since they are still in the interval.
Therefore:
[tex]\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}[/tex]
Related Questions
need heeeelp please
Answers
Step-by-step explanation:
y = -f(x)
so, everything is mirrored around the x-axis.
what was below the x-axis, is now above the x-axis, what was above is now below. and what was on the x-axis, is still on the x-axis.
pick the corner points of f(x), their x-values stay the same, their y-values flip the sign. the points on the x-axis (y = 0) stay the same of course.
and then connect the points, so that the curve is upside-down to the original.
Income Statements under Absorption Costing and Variable Costing
The demand for aloe vera hand lotion, one of numerous products manufactured by Smooth Skin Care Products Inc., has dropped sharply because of recent competition from a similar product. The company's chemists are currently completing tests of various new formulas, and it is anticipated that the manufacture of a superior product can be started on December 1, one month in the future. No changes will be needed in the present production facilities to manufacture the new product because only the mixture of the various materials will be changed.
The controller has been asked by the president of the company for advice on whether to continue production during November or to suspend the manufacture of aloe vera hand lotion until December 1. The controller has assembled the following pertinent data:
Smooth Skin Care Products Inc.
Income Statement—Aloe Vera Hand Lotion
For the Month Ended October 31
Sales (400,000 units) $32,000,000
Cost of goods sold 28,330,000
Gross profit $3,670,000
Selling and administrative expenses 4,270,000
Loss from operations $(600,000)
The production costs and selling and administrative expenses, based on production of 400,000 units in October, are as follows:
Direct materials $15 per unit
Direct labor 17 per unit
Variable manufacturing cost 35 per unit
Variable selling and administrative expenses 10 per unit
Fixed manufacturing cost $1,530,000 for October
Fixed selling and administrative expenses 270,000 for October
Sales for November are expected to drop about 20% below those of the preceding month. No significant changes are anticipated in the fixed costs or variable costs per unit. No extra costs will be incurred in discontinuing operations in the portion of the plant associated with aloe vera hand lotion. The inventory of aloe vera hand lotion at the beginning and end of November is expected to be inconsequential.
Required:
Question Content Area
1. Prepare an estimated income statement in absorption costing form for November for aloe vera hand lotion, assuming that production continues during the month.
Smooth Skin Care Products Inc.
Estimated Income Statement—Absorption Costing—Aloe Vera Hand Lotion
For the Month Ending November 30
Sales
$Sales
32,000,000
Cost of goods sold:
Direct materials
$Direct materials
Direct labor
Direct labor
- Select -
- Select -
- Select -
$- Select -
Selling and administrative expenses:
$- Select -
- Select -
blank
blank - Select -
$- Select -
Question Content Area
2. Prepare an estimated income statement in variable costing form for November for aloe vera hand lotion, assuming that production continues during the month.
Smooth Skin Care Products Inc.
Estimated Income Statement—Variable Costing—Aloe Vera Hand Lotion
For the Month Ending November 30
$- Select -
Variable cost of goods sold:
$- Select -
- Select -
- Select -
blank
blank - Select -
$- Select -
- Select -
$- Select -
Fixed costs:
$- Select -
- Select -
blank
blank - Select -
$- Select -
Answers
The estimated income statement for the month shows a loss of $840000.
How to illustrate the income statement?The estimated income statement for the month will be:
Sales = $25,600,000
Less: Cost of goods sold
Direct materials (320000 × 15) = $4,800,000
Direct labor (320000 × 17) = $5,440,000
Variable costing (320000 × 15) = $11,200,000
Fixed manufacturing cost = $1,530,000
Total cost of goods sold = $22970000
Gross profit = $25,600,000 - $22970000 = $2,630,000
Gross profit = $2,630,000
Less:
Variable selling and administrative expense = $3200000
Fixed selling and administrative = $270000
Loss from operations = $840000
Therefore, the estimated income statement for the month shows a loss of $840000.
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PQR has the vertical P(0,4), Q(4,5), and R(4,1). Determine if PQR is the right triangle.
Answers
Answer:
no
Step-by-step explanation:
no it is not a right triangle
two angles share the same x but no angles share the same y
you can see this clearly when graphed
the answer is no
27. Identify the domain of the set (6,2), (-1,-5), (4,4), (9, 2) and tell if the relation is a function.
O {-1, 4, 6, 9); not a function
O {-5, 2, 4}; a function
O {-1,4,6,9}; a function
O {-5, 2, 4); not a function
Answers
Answer:
the third one
Step-by-step explanation:
it is function that contain four domain
2. This month Tania saved
6 times as much money
as last month. Last
month she saved $24.
How much did Tania
save this month?
3.
Answers
Answer:
$144
Step-by-step explanation:
24*6 = 144
6 A car covers 162 km in 3 hrs 36min, Find the average speed of a car in km/hr?
Answers
Answer:
[tex]\huge\boxed{\sf v = 45 \ km/hr}[/tex]
Step-by-step explanation:
Given Data:Distance = S = 162 km
Time = t = 3hr 36/60 min = 3 hr 0.6 hr = 3.6 hr
Required:Average Speed = v = ?
Formula:[tex]\displaystyle v = \frac{S}{t}[/tex]
Solution:Put the givens in the above formula
[tex]\displaystyle v = \frac{162}{3.6} \\\\v = 45 \ km/hr\\\\\rule[225]{225}{2}[/tex]
find the price, discount, markup, or cost to store.
Markup=80%
Selling price= $21.60
Cost to store?
Answers
Using proportions and the markup concept, it is found that the cost to store is of $12.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
The markup price of 80% means that the selling price is of 180% = 1.8 of the cost to store of x. The selling price is of $21.60, hence:
1.8x = 21.60
x = 21.60/1.8
x = $12.
The cost to store is of $12.
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2. This month Tania saved
6 times as much money
as last month. Last
month she saved $24.
How much did Tania
save this month?
3.
Answers
Hope this helps :)))
Answer:
144
Step-by-step explanation:
24*6
Because this month she saved 6 times as MUCH money compared to last month
Find y'' y = 3 cot x/8
Answers
If y = 3 cot x/8, the double differentiation of y gives,
y'' = (3/32) (cosec x/8)(cot x/8)
Given value of y is,
y = 3 cot x/8
Differentiation of the above equation will give us the following,
y' = d(3 cot x/8) / dx
y' = 3d(cot x/8) / dx ........... (1)
Now, we know that the differentiation of cot x is -cosec²x
Therefore, d(cot x/8) / dx = -(cosec²x/8)/8
Thus, equation (1) transforms as follows,
y' = -3(cosec²x/8)/8
Taking differentiation of the above equation, we get,
y'' = -3d((cosec²x/8)/ 8dx
y'' = -6d(cosec x/8) / 8dx [Using chain rule] .......... (2)
As we know, the differentiation of cosec x is -(cosec x)(cot x),
d(cosec x/8) / dx = -(cosec x/8)(cot x/8) / 8 [Using chain rule]
Therefore, equation (2) can be written as,
y'' = -(-6(cosec x/8)(cot x/8) / (8×8)
∴ y '' = 3(cosec x/8)(cot x/8) / 32
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Suppose follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of so that the following is true.
Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.
Answers
Answer:
c = 2.25
Step-by-step explanation:
The normal distribution function is symmetrical, so the area not in the central zone is split evenly between the lower and upper tails.
SolutionWe can find -c from ...
P(x < -c) = (1 - 0.9756)/2 . . . . . the area in the lower tail
The calculator tells us -c = -2.25.
c = 2.25
Solve the following...
-35= 5+7(a + 2)
~ Thanks!!!!
Answers
Answer:
a=-54/7
Step-by-step explanation:
-35=5+7(a+2)
by opening the bracket we have
-35=5+7a+14
-35=7a+19
collect like terms
we have:
-35-19=7a
-54=7a
a=-54/7
Answer:
a = -54/7
Step-by-step explanation:
multiply 7 with the number in brackets
-35 = 5 + 7(a + 2)
-35 = 5 + 7a + 14
then add the numbers without symbols
-35 = 19 + 7a
make a the subject
-7a = 19 + 35
-7a = 54
divide the subject with the same number + the answer
-7a ÷ -7 = 54 ÷ -7
a = -54/7 or -7 5/7
hope this helps :)
Determine the inverse of the function: h(x)= 2x-3/1-x
Answers
Create a linear equation based on an experience in your everyday life. In this experience, a variable should depend on at least one other variable (the independent variable(s)). If your equation has 2 variables, graph it on the coordinate plane.
Answers
The equation that represent the total salary that I earn for working x hours in a week is y = 10x
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
Let y represent the total salary earned by working x hours, hence, if I earn $10 per hour:
y = 10x
The equation that represent the total salary that I earn for working x hours in a week is y = 10x
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A project is expected to provide cash flows of and over the next four years , respectively . At a required return of 8.5 percent , the project has a profitability Index of .898 . For this to be true , what is the project's cost at Time ? \$12.150,\$12.600,\$15.700,; \$10.200
Answers
Project's cost at time 0 is $46,272.84
What is profitability index?
Profitability index is the present value of future cash flows divided by the project cost at time 0.
The present value of each future cash flow can be determined using the present value formula of a single cash flow as below;
PV=FV/(1+r)^N
FV=future cash inflows in years 1-4
r=discount rate=8.5%
N=the year of cash flows, 1 for year 1 , 2 for year 2, 3 for year 3 and 4 for year 4.
PV of future cash flows=$12,150/(1+8.5%)^1+$12,600/(1+8.5%)^2+$15,700/(1+8.5%)^3+$10,200/(1+8.5%)^4
PV of future cash flow=$41,553.01
Profitability index=PV of future cash flows/Project cost
Profitability index= .898
Project cost=unknown(assume it is X)
.898=$41,553.01 /X
X=$41,553.01/ .898
X=project's cost=$46,272.84
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What is the answer?im having trouble
Answers
Answer:
130
Step-by-step explanation:
let the inside value be,x
x+30°+20°=180°(Being sum of interior angle of triangle)
or,x+50°=180°
or,x=180°-50°
or,x=130°
Now,
let the exterior angle be,a
a=x(VOA)
a=130°
Therefore the value of a is 130°.
At Indianapolis Motor Speedway, one lap is 2.5 miles in length. The average speed of an Indy racing car is 190 miles per hour.
15. Find the length of one lap in yards.
16. How many seconds would it take to complete one lap?
Answers
Answer:
15. 4400 yards
16. 47.4 seconds
Step-by-step explanation:
15. 1 mile = 1760 yards
2.5 miles:
2.5(1760) = 4400 yards
16. t = 2.5/190 = 0.013150 h
1 hour = (60)(60) = 3600 seconds
Then 1 lap take
=(0.013150)(3600) = 47.4 seconds
Hope this helps
Help asap please!
What is sin(B)?
5
√61
sin(B):
6 [?]√[]
B
=
Answers
Answer:5SQRT61/
61
Step-by-step explanation:
What are the leading coefficient and degree of the polynomial?
2+18u^4+9u-u^8
Leading coefficient:
Degree:
Answers
Answer:
-1 and degree 8
Step-by-step explanation:
the highest degree carry the leading coefficient, and the highest power take the highest degree
A stamp collection consisting of 23 stamps includes 4¢ stamps and 9¢ stamps. The total value of the stamps is $1.27. Find the number of each type of stamp in the collection.
Answers
A simultaneous equation is a set of equations that has to be solved in relation to each other at the same time. Thus the required number of stamps are:
4¢ stamps = 16
5¢ stamps = 7
A simultaneous equation is a set of equations that has to be solved in relation to each other at the same time. This process is required so as to determine the values of two unknowns e.g x and y.
From the given question, let the number of 4¢ stamps be represented by n, and that of the 9¢ stamp be represented by m.
So that,
n + m = 23 ............ 1
But 100¢ = $1, so that;
4¢ = x
x = [tex]\frac{4}{100}[/tex]
= $0.04
also,
9¢ = x
x = [tex]\frac{9}{100}[/tex]
= $0.09
Thus, we have;
0.04n + 0.09m = 1.27 ......... 2
From equation 1, make n the subject of the formula, such that;
n = 23 - m ........... 3
Substitute equation 3 into equation 2
0.04(23 - m) + 0.09m = 1.27
0.92 - 0.04m + 0.09m = 1.27
collect like terms to have;
0.05m = 1.27 - 0.92
= 0.35
m = [tex]\frac{0.35}{0.05}[/tex]
m = 7
Now substitute the value of m into equation 3
n = 23 - m ........... 3
= 23 - 7
n = 16
Therefore the number of 4¢ stamps is 16, while that of the 5¢ stamps is 7.
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anna bought a sweater at 40% off the original price. if she paid $12 what was the original price of the sweater?
Answers
Answer:
The original price was $30
Step-by-step explanation:
40% = 40/100 = 0.4
[tex]\frac{12}{0.4} =30[/tex]
Hope this helps
Two factory plants are making tv panels yesterday plant A produced 3000 panels. Ten percent of the panels from plant A were defective and Three percent from plant B were defective. How many panels did plant be produce if the overall percentage of defective panels from the two plants was 6%. Thanks for the help
Answers
Answer: Plant B produced 4000 panels
Step-by-step explanation: Let the number of panels produced by plant A = a and the number of panels produced by plant B = x. In total, we have 3000 + x. Now for the defective panels. 10% of plant a + 3% of plant b = 6% of both a and b. 300 + 3/100(x) = 6/100(3000 + x). 300 + 0.03x = 180 + 0.06x. Now, we simplify. 300 - 180 = 0.06x = 0.03x. So, 120 = 0.03x and 40 = 1% of x. This means x = 4000. So, therefore, Plant B produced 4000 panels. We can check our work by using the value of x we got. 4000 + 3000 = 7000. 6% of 7000 = 420. 120 = 3% of 4000. 120 + 300 = 420 so the answer we got is correct. Hope this helped
Look at the way this plane figure moved. Which set of transformations was performed? Help me please it's urgent!
A) reflect horizontally and reflect vertically
B) reflect vertically and rotate clockwise
C) translate right and rotate counter-clockwise
Answers
Using translation concepts, the set of transformations that was performed on the triangle are given as follows:
A) reflect horizontally and reflect vertically.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, the orientations of the triangle changed both horizontally and vertically, with no change in the format, hence there were reflections, which means that the correct option is:
A) reflect horizontally and reflect vertically.
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In the figure, AB = 10, and CE = 11. Find the length of AD. Round your answer to the nearest tenth.
Answers
Applying the Chords of a Circle Theorem, the length of AD is: 1.6 units.
What is the Chords of a Circle Theorem?The theorem states that if the radius of a circle is perpendicular to a chord, it divides the chord into two equal halves.
Therefore, we have:
CD = DE = 11/2 = 5.5.
AB = BE = 10
Find DB using the Pythagorean theorem
DB = √(BE² - DE²)
DB = √(10² - 5.5²)
DB = 8.4
AD = AB - DB
AD = 10 - 8.4
AD = 1.6 units.
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A cone has a height of 10cm. The base radius is 2.5cm. Calculate the volume of the cone.
Answers
Answer:
65.41 u³Step-by-step explanation:
A cone has a height of 10cm. The base radius is 2.5cm. Calculate the volume of the cone.
The formula for the volume of a cone is ⅓ r²h cubic units, where r is the radius of the circular base and h is the height of the cone.
1/3π2.5²×10 =
1/3π6.25×10 =
1/3π62.5 =
1/3×196.25 =
196.25:3 =
65.41 u³
Trapezoid FGHJ is inscribed in P as shown. If FG = 24, JH = 10, and the diameter of P is 26, find the area of the trapezoid. (Hint: draw in auxiliary lines). Round to the nearest tenth if necessary.
Answers
Answer:
221
Step-by-step explanation:
If the diameter is 26, the radius is 13 (which is the same as the perpendicular from P to JH)
So, the area is
[tex]\frac{1}{2}(13)(24+10)=221[/tex]
Graph this system of inequalities. Identify the solution region on the graph.
y<-x+4, y>-x 2
Answers
The system of inequalities y < -x+4 and y >-x 2 do not have a solution
What are inequalities?Inequalities are expressions that have unequal values when compared or evaluated
How to determine the solution to the system?The system of inequalities is given as
y < -x+4
y >-x 2
Next, we plot the inequalities on a graphing tool
See attachment for the graph
From the attached graph, the lines of the inequalities do not intersect
This means that the system of inequalities do not have a solution
Hence, the system of inequalities y < -x+4 and y >-x 2 do not have a solution
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Find the surface area of the figure. For calculations involving pi , give both the exact value and an approximation to the nearest hundredth of a unit. Let r=10 and h = 3.
Answers
Answer:
exact: SA = 260π in.²
approximate: SA = 816.81 in.²
Step-by-step explanation:
SA = 2πr² + 2πrh
r = 10 in.
h = 3 in.
SA = 2πr(r + h)
SA = 2π(10 in.)(10 in. + 3 in.)
SA = 260π in.²
SA = 816.81 in.²
Mo is on a baseball team and hears that a ball thrown at a 45-degree angle from the ground will travel the furthest distance. How should Mo release the ball for the furthest travel distance?
Answers
Mo must release this ball approximately halfway between straight-ahead and straight-up because the angle subtended must be 45 degrees with the horizontal axis.
What is distance?Distance can be defined as the amount of ground covered (traveled) by a physical object, regardless of its direction, starting point or ending point.
How should Mo release the ball?In order to achieve the furthest travel distance, Mo must release this ball approximately halfway between straight-ahead and straight-up because the angle subtended must be 45 degrees with the horizontal axis, as shown in the image attached below.
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For each equation, determine whether it represents a direct variation, an inverse variation, or neither.
Find the constant of variation when one exists and write it in simplest form.
Answers
The equation 15x + 5y = 0 is a direct variation and the constant of variation is -3 while the equation -5x + 8y = 3 is neither a direct variation nor an inverse variation
How to categorize the type of each equation?As a general rule, we have the following forms of equation:
Direct variation: y =kx
Inverse variation: y = k/x
Where k represents the constant of variation
The equations 15x + 5y = 0 can be rewritten as:
5y = -15x
Divide by 5
y = -3x
The above equation take the form y = kx
This means that k = -3
Hence, the equation 15x + 5y = 0 is a direct variation and the constant of variation is -3
However, the equation -5x + 8y = 3 do not take any of the given forms
Hence, the equation -5x + 8y = 3 is neither a direct variation nor an inverse variation
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MARCELLA LANDON WINS THIRD PRIZE IN THE CLEARINGHOUSE SWEEPSTAKES AND
RECEIVES A CHECK FOR $250,000. AFTER SPENDING $10,000 ON VACATION, SHE
DECIDES TO INVEST THE REST IN A MONEY MARKET ACCOUNT THAT PAYS 1.5%
INTEREST COMPOUNDED MONTHLY. HOW MUCH MONEY WILL BE IN THE ACCOUNT
AFTER 10 YEAR
Answers
The amount of money in the account after 10 years is $278,814.10.
What will be the value of the account after 10 years?The first step is to determine the amount she has left to invest.
Amount invested = amount won - amount spent on vacation
$250,000 - $10,000 = $240,000
The second step is to determine the future value of the account. The formula for calculating future value:
FV = P (1 + r)^nm
FV = Future value P = Present value R = interest rate = 1/5/12 = 0.125%m = number of compounding =12N = number of years240,000 x 1.00125^(12 x10) = $278,814.10
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