Answers
9514 1404 393
Answer:
(√17 -4√595)/102
Step-by-step explanation:
To use the sine of the angle sum formula, we need to know the sine and cosine of each of the angles.
sin(sin^-1(1/6)) = 1/6 . . . . a first-quadrant angle
cos(sin^-1(1/6)) = √(1 -(1/6)²) = √(35/36) = (√35)/6
sin(tan^-1(-4)) = -4/√(1+(-4)²) = -4/√17 . . . . a 4th-quadrant angle
cos(tan^-1(-4)) = √(1 -(-4/√17)²) = 1/√17
The sum of angles formula is ...
sin(α+β) = sin(α)cos(β) +cos(α)sin(β)
So, our sine is ...
[tex]\sin\left(\sin^{-1}\left(\dfrac{1}{6}\right)+\tan^{-1}(-4)\right)=\dfrac{1}{6}\cdot\dfrac{1}{\sqrt{17}}+\dfrac{\sqrt{35}}{6}\cdot\dfrac{-4}{\sqrt{17}}\\\\=\dfrac{1-4\sqrt{35}}{6\sqrt{17}}=\boxed{\dfrac{\sqrt{17}-4\sqrt{595}}{102}}[/tex]
Related Questions
PLEASE HELP ASAP
Mr. Green has a class of 15 students. He can spend $20 on each student to buy math supplies for the year. He first buys all of his students calculators, which
costs a total of $144.75. After buying the calculators, how much does he have left to spend on each student?
Answers
Answer:
10.35
Step-by-step explanation:
He has $300 (15x$20). He spends 144.75. He has 155.25 in total. That leaves 10.35 (155.25/15) to spend on each student.
The two lines below are parallel. If the slope of the red line is 3, what is the slope of the green line?
Answers
Find the 8th term in the
sequence
-1/2,-1, -2, -4,...
Hint: Write a formula to help you.
1st term . Common Ratio desired term – 1)
Answers
Answer:
-64
Step-by-step explanation:
By looking at the numbers, we can identify that this is a geometric sequence and the ratio would be 2. The formula to find the nth term in a geometric series is:
[tex]t *r^{n-1}[/tex]
where t is the first term and r is the ratio. We can substitute in the information we know:
[tex]-\frac{1}{2} *2^{n-1}[/tex]
We are looking for the eighth term, so we substitute 8 where n is:
[tex]-\frac{1}{2}*2^{8-1}[/tex]
We can simplify:
[tex]-\frac{1}{2}*2^7[/tex]
[tex]-2^6[/tex]
[tex]-64[/tex]
4) Jenee made a 99, 86, 76, and 95 on her first four spelling tests. Her mother told her
that her spelling test average had to be a 91 for Jenee to get a new video game. What
does Jenee need to make on her next test?
Answers
Answer: She needs to get 99 on her next test.
Step-by-step explanation:
If F(x) = +4, which of the following is the inverse of Fx)?
O A. F^1(x) = 2(x-4)
O B. F^1(x) = 7(x+4)
O C.F^1(x) = 7(x-4)
D. F1(x) = 2(x+4)
Answers
Answer:
[tex]f^{-1} = \frac{ 7(x-4)}{2}[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \frac{2x}{7} + 4[/tex]
Required
The inverse function
[tex]f(x) = \frac{2x}{7} + 4[/tex]
Replace f(x) with y
[tex]y = \frac{2x}{7} + 4[/tex]
Swap x and y
[tex]x = \frac{2y}{7} + 4[/tex]
Multiply through by 7
[tex]7x = 2y + 28[/tex]
Solve for 2y
[tex]2y = 7x - 28[/tex]
Solve for y
[tex]y = \frac{ 7x-28}{2}[/tex]
Factorize
[tex]y = \frac{ 7(x-4)}{2}[/tex]
Write as:
[tex]f^{-1} = \frac{ 7(x-4)}{2}[/tex]
a) -4/5
b) -5/4
c) 4/5
d) 5/4
Answers
Answer:
d) 5/4
Step-by-step explanation:
The gradient is change in y over change in x
hope it makes sense
:)
Write the explicit equation.
-8, -2, 4, 10
Answers
Answer:
a*n = -8 + (n - 1)6
Step-by-step explanation:
Explicit formula:
a*n = a*1 + (n - 1)d
a*1 = first term
n = nth term or the place
d = difference
Set: -8, -2, 4, 10
-8 ---> -2 = 6 added
Fill it in.
a*1 = -8
n = n
d = 6
Solution:
a^n = -8 + (n -1)6
I Need helppp! Please helpp!!
Answers
9514 1404 393
Answer:
x = 1/2
Step-by-step explanation:
There are some different ways to find the area of a donut shape. One is to multiply its centerline length by its width. We'll use that here to find the shaded area of the sector.
The centerline radius of shaded area A is ...
(6x -2) cm + (1/2)(4x cm) = 8x -2 cm
The length of the centerline is ...
s = rθ = (8x -2)(π/4) . . . . . . for a central angle of 45° = π/4 radians
Then the area A is ...
area A = (π/4)(8x -2)(4x) = 2πx(4x -1) . . . cm^2
__
The radius of circle B is ((4 -4x) cm)/2 = (2 -2x) cm. The area of circle B is ...
A = πr^2 = π(2 -2x)^2 cm^2
We're told the two areas are equal, so we have ...
2πx(4x -1) = π(2 -2x)^2 . . . . . . . expressions for the areas are equal
8x^2 -2x = 4x^2 -8x +4 . . . . . . divide by π, eliminate parentheses
4x^2 +6x -4 = 0 . . . . . . . . . . . . subtract the right-side expression
2(2x -1)(x +2) = 0 . . . . . . . . . . . factor
x = 1/2 or -2 . . . . . . . only the positive solution is useful here
The value of x is 1/2.
Can someone help me out
Answers
Help please and explain how to get the answerm
Answers
Answer:
147 degrees
Step-by-step explanation:
all the angles of a triangle add up to 180 degrees. so, you must perform the operation 180-(83+64) which equals 33. this is the angle supplementary to angle 1. to find angle 1, you must subtract 180 and 33 since supplementary angles add up to 180 degrees. this is equal to 147 degrees.
Help me please can someone tell me how to do this
Answers
A property has been assessed at $225 000. The mill rate is 14.5. To find the property tax, you would multiply the mill rate by: *
a) 0.10
b) 0.001
c) 0.01
d) 0.0001
Answers
To find the property tax, you would multiply the mill rate by 0.01
To find the property tax, you would multiply the assessed value of the property by the mill rate.
Given that the assessed value is $225,000 and the mill rate is 14.5, we need to multiply these two values to calculate the property tax.
Property Tax = Assessed Value × Mill Rate
Property Tax = $225,000 × 14.5
To simplify the calculation, we can convert the mill rate to a decimal by dividing it by 1,000.
Mill Rate = 14.5 ÷ 1000 = 0.0145
Property Tax = $225,000 × 0.0145
Property Tax = $3,262.50
Therefore, to find the property tax, you would multiply the mill rate by 0.01 (option c).
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Each quarter the marketing manager of a retail store divides customers into two classes based on their purchase behavior in the previous quarter. Denote the classes as L for low and H for high. The manager wishes to determine to which classes of customers he should send quarterly catalogs. The cost of sending a catalog is $15 per customer and the expected purchase depends on the customer’s class and the manager’s action. If a customer is in class L and receives a catalog, then the expected purchase in the current quarter is $20, and if a class L customer does not receive a catalog his expected purchase is $10. If a customer is in class H and receives a catalog, then his expected purchase is $50, and if a class H customer does not receive a catalog his expected purchase is $25. The decision whether or not to send a catalog to a customer also affects the customer's classification in the subsequent quarter. If a customer is class L at the start of the present quarter, then the probability he is in class L at the subsequent quarter is 0.3 if he receives a catalog and 0.5 if he does not. If a customer is class H in the current period, then the probability that he remains in class H in the subsequent period is 0.8 if he receives a catalog and 0.4 if he does not. Assume a discount rate of 0.9 and an objective of maximizing expected total discounted reward.
a) Formulate this as an infinite-horizon discounted Markov decision problem.
b) For ???? = 0.1, find a near-optimal policy using value iteration.
c) Find an optimal policy using policy iteration starting with the stationary policy which has greatest one-step reward.
d) Formulate the problem as a linear program, giving its primal and dual. Solve both and interpret the solutions.
Answers
Answer:
55
Step-by-step explanation:
help me please. thank you if you do
Answers
Answer:
B
Step-by-step explanation:
Sarah's dad bought her a scooter that cost $89.95. He figures he can spend up to $30.05 on a helmet before he spends too much money in all. Let x represent how much money Sarah's dad wants to spend in all. Which inequality describes the problem?
Answers
Answer:
x - 89.95 ≤ 30.05= x ≤ 120
add 89.95 to both sides of the equation. Since on the right side 89.95 is already there it cancells eachother out leaving x. After adding 89.95 to 30.05 you should get an answer of 120.
The money Sarah's dad wants to spend in all if Sarah's dad bought her a scooter that costs $89.95, He can spend up to $30.05 on a helmet, which is less than or equal to $120, x ≤ 120.
What is inequality?Inequality is a relationship that compares two numbers or other mathematical expressions in an unequal way. Inequalities are the name given to certain algebraic mathematical expressions.
Given:
Sarah's dad bought her a scooter that cost $89.95,
He can spend up to $30.05 on a helmet,
Assume the x is the money Sarah's dad wants to spend in all,
Write the inequality as shown below,
x - 89.95 ≤ 30.05
Solve the inequality by adding 89.95 on both sides,
x - 89.95 + 89.95 ≤ 30.05 + 89.95
x ≤ 120
To know more about inequality:
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URGENT NEED HELP CLICK TO SEE
Answers
Answer:
4.20
Step-by-step explanation:
First find the total cost of the nametags
105 * .12
12.60
Then divide by the 3 teachers
12.60/3 =4.20
Each teacher will pay 4.20
30 POINTS AND BRAINLIEST Alexis needs to paint the four exterior walls of a large rectangular barn. The length of the barn is 80 feet, the width is 50 feet, and the height is 30 feet. The paint costs $28 per gallon, and each gallon covers 420 square feet. What is the area of the barn Alexis needs to paint? ______________ Explain how you found your answer.
Answers
Answer:
It will cost $532 to paint the barn
Step-by-step explanation:
First we need to find the area of the barn's walls.
2 (length x height) + 2 (width x height)
=2 (80x30) + 2 (50x30)
=2 (2400) + 2(1500)
=4800+3000
=7800 ft^2
Now we can find the amount of gallons needed, then the total cost.
7800 ft^2/420 ft^2
=18.57 gallons
=19 gallons
19 gallons x $28
=$532
Answer:
520
Step-by-step explanation:
Area:
[tex]2(80*30) + 2(50*30) = 7800[/tex]
Price
[tex]\frac{7800}{420}*28 = 520[/tex]
Solve triangle ABC
B=56 degrees, a=14
Answers
Help please :) love yall. select three choices that are ways to show 0.48. last one is forty-eight tenths
Answers
Answer: The first, The second, and the number line one love!
Step-by-step explanation:
Write one way of representing the equation of the given line in point-slope form. Then rewrite the equation in slope-intercept form.
Answers
step-by-step explanation:
points (0, 3) and (7, 4)
point-slope form = y - y1 = m(x - x1)
y - 3 = 1(x - 0)
just add y and x from either point to complete the form
slope-intercept form = y = mx + b
y = (0, -3)
m = 1
y = x - 3
x is the slope and -3 is the y-intercept
The height of the equilateral triangle below is 15 units. What is the value of x?
An equilateral triangle is shown. A perpendicular bisector cuts the triangle into 2 equal parts. They hypotenuse has a measure of x.
15 StartRoot 3 EndRoot
30 StartRoot 3 EndRoot
StartFraction 15 Over StartRoot 3 EndRoot EndFraction
StartFraction 30 Over StartRoot 3 EndRoot
Answers
Answer: b
Step-by-step explanation: on edge
Answer: C. 30 StartRoot 3 EndRoot
Step-by-step explanation:
Took the test/exam
Is this is a math question?
Answers
it says mathematics 5 points
Solve for x 5x - 10 = -10
Answers
Answer:
the answer is x = 0
Step-by-step explanation:
Cancel equal terms on both sides of the equation:
[tex]5x = 0[/tex]
Divide both side of the equation by 5.
[tex]x = 0[/tex]
Therefore, the answer is x = 0
Answer:
5x - 10 = -10
+10 +10
5x = 0
divide by 5 on both sides:
x = 0
Two of the statements are true; one is a lie.
Select the one that is a lie.
Then explain your reasoning.
Use the sketching tool to help explain if you'd like.
The measure of ∠CAF is 25 degrees.
∠DAE ≌ ∠FAB.
∠BAF and ∠EAB are complementary.
Answers
Answer:
Step-by-step explanation:
The last statement is false.
∠BAF and ∠EAB are supplementary angles.
Car = V-8 sedan
Years driven = first and second
Miles driven = 15.500 miles first year and 14,500 miles second year
The cost of depreciation will be $
Answers
Answer:
$500
Step-by-step explanatioThe numberber of years driven is the first and second year
= 2
Miles driven
First year= 15,500
Second year= 14,500
Therefore the cost of depreciation can be calculated as follows
15,500-14,500/2
= 1000/2
= 500
Hence the cost of depreciation is $500
The answer is: 2,318
First year on the graph: 8.5
Second year on the graph: 6.9
First year:
15,500 x 8.5 = 131,750
131,750/100 = 1,317.50
Second year:
14,500 x 6.9 = 100,050
100,050/100 = 1,000.50
1,317.50 + 1,000.50 = 2,318
a. -3/2
b. 0
c. 3/2
d. DNE
Answers
HELP ME PLEASEEEEEEEEEEEE
Answers
Answer: 20 cm²
Step-by-step explanation:
A bike ride event is 10 miles. A first aid tent is put 3/5 of the way from the start. What is the distance from the starting point to the first aid tent?
Answers
don't know but the distance between the starting point to the first aid tent is 6cm or miles don't know but this much far
. A point P is equidistant from R(-2, 4) and S(6,-4)
and its x-coordinate is twice its y-coordinate.
(0) Find the coordinates of P.
(ii) Hence, determine whether P, R and S are
collinear, showing your working clearly.
Answers
Answer:
I) coordinate of P is (11, 5.5)
II) Points are not collinear
Step-by-step explanation:
I) Let the coordinates of P be (a, b)
We are told that its x-coordinate is twice its y-coordinate. Thus, a = 2b
Now, P is equidistant from R(-2, 4) and S(6,-4). Thus;
PR = PS
Using the formula for distance between two coordinates, we have;
√((a - (-2))² + (b - 4)²) = √((a - 6)² + (b - (-4))²)
This gives;
(a + 2)² + (b - 4)² = (a - 6)² + (b + 4)²
Since a = 2b,then we have;
(2b + 2)² + (b - 4)² = (2b - 6)² + (b + 4)²
4b² + 8b + 4 + b² - 8b + 16 = 4b² - 12b + 36 + b² + 8b + 16
Simplifying this gives;
20 = 42 - 4b
42 - 20 = 4b
4b = 22
b = 22/4
b = 11/2
b = 5.5
Since a = 2b
Then a = 2 × 5.5
a = 11
Thus, coordinate of P is (11, 5.5)
II) Formula for area of triangle formed by three points is given as;
A = ½|(x1 - x2) (x2 - x3)|
|(y1 - y2) (y2 - y3)|
x1 - x2 = 11 - (-2) = 13
x2 - x3 = -2 - 6 = -8
y1 - y2 = 5.5 - 4 = 1.5
y2 - y3 = 4 - (-4) = 8
Thus;
A = ½|13 -8|
|1.5 8|
A = ½((13 × 8) - (1.5 × - 8))
A = ½(104 + 12)
A = 58
Since the area is not zero, then it means the points are not collinear.
Given the piecewise function below, which equation represents piece "B"?
Answers
Answer:
y=1
Step-by-step explanation:
x is 0 so there is no point putting that in in the equation y=mx+b you do have the b which is 1 so that is your equation