[-/5 Points] DETAILS LARPCALC11 5.5.021. Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. tan(u) = 5/3, 0
Answers
The exact values are:
sin(2u) = 2√8/9
cos(2u) = -7/9
tan(2u) = -5/8
To find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas, we'll need to use the given condition that tan(u) = 5/3.
The double-angle formulas for sine, cosine, and tangent are as follows:
sin(2u) = 2 * sin(u) * cos(u)
cos(2u) = cos^2(u) - sin^2(u)
tan(2u) = (2 * tan(u)) / (1 - tan^2(u))
Let's calculate the values step by step:
Step 1: Find sin(u) and cos(u) using the given condition tan(u) = 5/3.
We know that tan(u) = sin(u) / cos(u), so we can set up the following equation:
5/3 = sin(u) / cos(u)
To solve for sin(u) and cos(u), we can use the Pythagorean identity:
sin^2(u) + cos^2(u) = 1
Rearranging the equation, we get:
sin^2(u) = (5/3)^2 * (1 - cos^2(u))
Now, we can solve for cos(u):
cos^2(u) = 1 - sin^2(u)
cos^2(u) = 1 - (25/9) * (1 - cos^2(u))
cos^2(u) = 1 - 25/9 + (25/9) * cos^2(u)
(9/9 - 25/9) * cos^2(u) = (9/9 - 1) - 25/9
(-16/9) * cos^2(u) = -16/9
cos^2(u) = 1/9
Taking the square root of both sides, we get:
cos(u) = ±1/3
Since tan(u) = 5/3, we know that u is in the second quadrant where sine is positive. Therefore, we can conclude that sin(u) = √(1 - cos^2(u)) = √(1 - 1/9) = √(8/9) = √8/3.
Step 2: Use sin(u) and cos(u) to find sin(2u), cos(2u), and tan(2u).
sin(2u) = 2 * sin(u) * cos(u)
= 2 * (√8/3) * (1/3)
= 2√8/9
cos(2u) = cos^2(u) - sin^2(u)
= (1/3)^2 - (√8/3)^2
= 1/9 - 8/9
= -7/9
tan(2u) = (2 * tan(u)) / (1 - tan^2(u))
= (2 * (5/3)) / (1 - (5/3)^2)
= 10/3 / (1 - 25/9)
= 10/3 / (9/9 - 25/9)
= 10/3 / (-16/9)
= -5/8
Therefore, the exact values are:
sin(2u) = 2√8/9
cos(2u) = -7/9
tan(2u) = -5/8
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Related Questions
What innovation was made possible in part because of the Carterfone decision in 1968? Select one a. COBOL b. radiospectrum allocation c. the public Internet d. SMS
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The innovation that was made possible in part because of the Carterfone decision in 1968 is the public Internet. The correct answer is option C
The Carterfone decision was a landmark ruling by the Federal Communications Commission (FCC) that allowed for the interconnection of third-party devices to the telephone network. Prior to this decision, telephone companies had a monopoly on the equipment that could be used on their networks, and customers were not allowed to attach their own devices.
This decision paved the way for the development of the public Internet by allowing for the interconnection of third-party devices to the telephone network, which enabled the creation of new technologies, such as modems. Without the Carterfone decision, the public Internet as we know it today may not have been possible.
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You can buy 1 bunch of grapes for $2. How many can you buy with $18?
Answers
Answer:
9
Step-by-step explanation:
Find the unit rate.
88 flowers in 8 vases = flowers per vase
Submit
Answers
Answer:
11
Step-by-step explanation:
88/8=11
Answer:
10 flowers per vase
Step-by-step explanation:
8/8=1, and 88/8=10
-5+y=-3
3x-8y=24
***SHOW STEPS PLS***
Answers
-5+ y = -3
+5 +5
y = 2
_____________
3x-8y = 24
3x-8(2) = 24
3x-16 = 24
+16 +16
3x = 40
%3 %3
x = 40/3
(x , y) = (40/3 , 2)
Jim has an annual salary of $96,000. His monthly expenses include a $2,500 mortgage payment, a $250 lease payment, $500 in minimum credit card payments, and a $425 payment on his speed boat. He also receives $1,200 in interest from his savings and other accounts each month. Calculate Jim’s DTI (debt-to-income) ratio.
a.
30%
b.
35%
c.
40%
d.
45%
Answers
Answer:
the answer is 46% which is option d.
Step-by-step explanation:
To calculate Jim's DTI (debt-to-income) ratio, we need to divide his total monthly debt payments by his gross monthly income.
His total monthly debt payments are:
$2,500 (mortgage payment)
$250 (lease payment)
$500 (credit card payments)
$425 (speed boat payment)
Total Monthly Debt Payments = $2,500 + $250 + $500 + $425 = $3,675
His gross monthly income is his annual salary of $96,000 divided by 12 months which is $8,000
DTI = Total Monthly Debt Payments / Gross Monthly Income = $3,675 / $8,000 = 0.46 or 46%.
The value of Jim's DTI (debt-to-income) ratio is 40%.
What is Debt to Income Ratio?Debt to income ratio is usually calculated as a percentage of the gross monthly debt payments divided by the gross monthly income.
Given that,
Annual salary = $96,000
Monthly income = 96000/12 = $8000
Total income per month = $8000 + $1,200 = $9,200
Monthly expenses = $2,500 + $250 + $500 + $425
= $3675
DTI = 3675 / 9,200 = 0.399 = 39.9% ≈ 40%
Hence the DTI of Jim is 40%.
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Please help……………………….
Answers
Let’s start with the easy part: half of the base is 3.
Therefore, 3 x h + 1 = 18
3 x h = 3h and 3 x 1 = 3
3h + 3 = 18
To solve these equations, you have to do the inverse. First you would need to minus 3:
3h = 15
3h is a simpler way of saying 3 x h, so the inverse would be a divide.
h = 5
m∠XYZ = 35º. What is the measure of its complement?
Answers
The measure of the complement of angle XYZ is: 55°.
What is the Complement of an Angle?The complement of an angle is the angle that, when added to the original angle, forms a right angle (90 degrees). The complement of an angle is also known as the complementary angle.
For example, the complement of a 45-degree angle is 45 degrees because 45 + 45 = 90. The complement of a 30-degree angle is 60 degrees because 30 + 60 = 90.
The complement of an angle is often used in geometry and trigonometry to solve problems involving angles in triangles and other shapes. It is also used in everyday life, such as when hanging a picture or constructing a building, to ensure that the angles are properly aligned.
Thus, given that angle XYZ measures 35°, to find the complement of angle XYZ, subtract 35 from 90 degrees.
Therefore:
Measure of the complement of angle XYZ = 90 - 35 = 55°.
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PLEASE HELP
WORTH 30 PTS!!
Choose the step that shows where a mistake is made (if there is one).
-2(x + 4) + 4x = 16
Step 1 -2x + 8 + 4x = 16
Step 2 2x + 8 = 16
Step 3 2x = 8
Step 4 x = 4
a Step 1
b Step 2
c Step 3
d Step 4
e No mistakes were made. The steps are correct and the answer is x = 4.
Answers
Answer:
The mistake is in step 1 when you do -2(x+4) you do the distributive property first -2 times x is -2x that's correct but -2 times 4 is not 8 it is -8
when you multiply by negatives the answer will always be a negative unless your multiply 2 negative number together then itll be positive ex. 4 × -4 = -16 (negative) but -4 × -4 = 16 (positive)
What is the slope for (4,3)
Answers
Answer:
The slope is 0
Step-by-step explanation:
Answer:
0
Step-by-step explanation:
Please help me I’ll make u brainliest I swear please
Answers
Since the provided equation is inconsistent, it cannot intersect.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Here,
we can see that the second set of equation,
4x+2y=12
20x+10y=30
4/20=2/10≠12/30
1/5=1/5≠2/5
The given equation is inconsistent so it does not intersect.
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HELP Asap please!!!!!
Answers
Answer:
x should be 55
Step-by-step explanation:
the acute angle is 55 and we know that the whole horizontal is 180 so calculate 180-55 to find the obtuse angle which is 125. Then subtract 70 from that to isolate for x and you get 55.
a) Which of the following statements about the maximum likelihood estimator (MLE) are true? i) The MLE achieves asymptotically the Cramer-Rao lower bound under certain regularity conditions; ii) The distribution of the MLE stays unchanged by a parameter transformation; iii) The MLE is asymptotically normally distributed under certain regularity conditions; iv) None of the above are true.
Answers
the correct answer is: i) The MLE achieves asymptotically the Cramer-Rao lower bound under certain regularity conditions; iii) The MLE is asymptotically normally distributed under certain regularity conditions
TheThe true statements about the maximum likelihood estimator (MLE) are:
i) The MLE achieves asymptotically the Cramer-Rao lower bound under certain regularity conditions.
iii) The MLE is asymptotically normally distributed under certain regularity conditions.
Statement ii) is false. The distribution of the MLE can change when a parameter transformation is applied.
Therefore, the correct answer is: i) The MLE achieves asymptotically the Cramer-Rao lower bound under certain regularity conditions; iii) The MLE is asymptotically normally distributed under certain regularity conditions.
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I need help someone?
Answers
Answer:
Graph A proportional graph B not proportional graph C not proportional
Step-by-step explanation:
Please help me with these two, i’ll give 15 points!!
Answers
You invested 12,000 in an account at 2.3% compounded monthly. How long will it take you to get to 20000
Answers
It will take 22 years and 3 months to get the present value of $12,000 invested at 2.3% compounded monthly to get to $20,000 (future value).
How the period is determined:The period that it will take the present value to reach a certain future value can be determined using an online finance calculator with the following parameters for periodic compounding.
I/Y (Interest per year) = 2.3%
PV (Present Value) = $12,000
PMT (Periodic Payment) = $0
FV (Future Value) = $20,000
Results:
N = 266.773
266.73 months = 22 years and 3 months (266.73 ÷ 12)
Total Interest = $8,000.00
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find the missing length indicated
Answers
Answer:
108Step-by-step explanation:
Use the ratio of corresponding sides of similar triangles:
81 / x = x / 144x² = 81*144x = \(\sqrt{81*144}\)x = 9*12x = 108Answer:
x = 108
Step-by-step explanation:
x is the height
from the Euclidian theorem we know that :
x^2 = 81*144
x^2 = 11664 find the root for both
x = 108
A baseball concession stand sells soft pretzels for $4.50 and bags of popcorn for
$3.25.
If the concession stand sold 137 soft pretzels, how many bags of popcorn would they
need to sell to make at least $1,000?
Answers
Answer:
y ≥ 118
Step-by-step explanation:
soft pretzels = $4.50
bags of popcorn = $3.25
Let
x = number of soft pretzels sold
y = number of bags of popcorn
The inequality:
4.50x + 3.25y ≥ 1,000
4.50(137) + 3.25y ≥ 1,000
616.50 + 3.25y ≥ 1,000
3.25y ≥ 1,000 - 616.50
3.25y ≥ 383.50
y ≥ 383.50 / 3.25
y ≥ 118
118 bags of popcorn would
need to be sold to make at least $1,000
HELP MEEEEEEEEEEEEEEEE PLEASEEEEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
t ≈ 7.7
Step-by-step explanation:
r ^nt
A = P ( 1 + ------- )
n
A = 3000
P = 1500
n = 12
r = 0.09
t = ?
0.09
3000 = 1500 ( 1 + ------- ) ^(12)(t)
12
0.09
3000 = 1500 ( 1 + ------- ) ^(12)(t)
÷1500 ÷1500 12
0.09
2 = ( 1 + ------- ) ^(12)(t)
12
Change into logs and divide
log 2
---------------------- = 12t
0.09
log (1 + ----------)
12
multiply both sides by (1/12)
log 2
(1/12) ---------------------- = 12t (1/12)
0.09
log (1 + ----------)
12
7.7304805 = t
7.7 ≈ t
I hope this helps!
-2x^3(3x^2-4x+7)
?????
Answers
Answer:
\(-6x^5+8x^4-14x^3\)
Step-by-step explanation:
\(-2x^3(3x^2-4x+7)\) Use distributive property
\(-2x^3\) · \(3x^2\) = \(-6x^5\)
\(-2x^3\) · \(-4x\) = \(8x^4\) Product becomes positive because of two negatives
\(-2x^3\) · \(7\) = \(-14x^3\)
Group all of those numbers together (in order)
\(-6x^5+8x^4-14x^3\)
The number of messages that arrive at a Web site is a Poisson distributed random variable with a mean of 5 messages per hour. Round your answers to four decimal places.(a) What is the probability that 5 messages are received in 1 hour?(b) What is the probability that 10 messages are received in 1.5 hours?(c) What is the probability that less than 2 messages are received in 1/2 hour?
Answers
The probability that 5 messages are received in 1 hour is is 0.1755 ,the probability that 10 messages are received in 1.5 hours is 0.0858 and the probability that less than 2 messages are received in 1/2 hour is 0.2873
Let X shows the number of messages received per hour. The pdf of X is
\(P(X=x)=\) \(\frac{e^{-5}\cdot 5^{x}}{x!},x=0,1,2,3,....\)
Therefore, the probability that 5 messages are received in a single hour is
\(P(X=5)=\frac{e^{-5}\cdot 5^{5}}{5!}=0.1755\)
(b) Number of message received in 1 hour is 5 so number of message received in 1.5 hour is 7.5. So the probability that 10 messages are received in 1.5 hours is
\(P(X=10)=\frac{e^{-7.5}\cdot 7.5^{10}}{10!}=0.0858\)
(c) Number of message received in 1 hour is 5 so number of message received in 1/2 hour is 2.5. So the probability that less than 2 messages are received in 1/2 hour is
\(P(X < 2)=\frac{e^{-2.5}\cdot 2.5^{0}}{0!}+\frac{e^{-2.5}\cdot 2.5^{1}}{1!}=0.2873\)
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Hannah spends $4.50 each day to buy lunch at her school. After school each day, she buys the same snack. Hannah spends $28.75 for lunch and snacks each week. The equation and solution model the situation.
5 (4.50 + x) = 28.75; x = 1.25
What does the solution, x = 1.25, represent?
the total cost of snacks for the week
the cost of each snack
the total amount of lunch for the week
the amount she spends each day for lunch and snack
Answers
Answer:
The cost of each snack
Step-by-step explanation:
Because if we are using what makes sense and what doesnt it would not be that much for lunch each week and it wouldnt be for the day so it must be the cost of each snack
Answer:
Step-by-step explanation:
B, the cost of each snack
How many degrees did the minute hand turn from the beginning of Cameron’s bike ride until the end?
Answers
Answer: I believe it is 6 degrees or 5
Step-by-step explanation: just like a clock has 360 degrees *cause its a circle* and has 60 minutes and each minutes = 6 or 5
Segment-Part of a ____ (line,point,plane) bounded by two_____ (line,point,plane)
Answers
8% of us adults have blood type b-positive. suppose we take a random sample of 38 us adults. let x represent the number of adults (out of the sample of 38) with blood type b- positive. this situation can be modeled with a binomial random variable x. 4. calculate the mean of x. show all work and round your answer to two decimal places.
Answers
Mean of the number of adults (out of the sample of 38) with blood type b- positive (x) is 3.04
Let x be the number of adults out of 38 with blood type b-positive
Probability, p of adults with blood type b-positive=8%=0.08
Sample size, n=38
Using binomial random variable x binomial(n=38, p=0.08)
p(X=x)=\(\left \ ({{n} \atop {x}}) \right. p^{x} q^{n-x}\), where x=0,1,2,3,.....n
Mean of x:
Mean of x=(probability of adults with blood type b-positive*sample size)
So, mean of x=p*n, where n=38, p=0.08
=0.08*38
=3.04
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The measure of an angle is 10 degrees more than its supplement. What is the measure of
the smaller angle?
Answers
Supplementary angles are angles that add up to 180 degrees.
Angle 1 = x
Angle 2 = x + 10
Since they are supplementary, we can set then equal to 180
x + x + 10 = 180
Combine like terms
2x + 10 = 180
Subtract 10 from both sides
2x = 170
Divide both sides by 2
x = 85
Angle 1 = 85 degrees
Angle 2 = 85 + 10 = 95 degrees
Charlette reads 8 1/3 pages of a book in 10 minutes. What is her average reading rate in pages per minute?
Answers
Answer:
Step-by-step explanation:
8 1/3 pages/10 minutes = 25/3 pages / 10 minutes = 25/30 pages/minute = 5/6 page/minute
Find the value of x if the perimeter is 20
Answers
Answer:
x = 3Step-by-step explanation:
Find the value of x if the perimeter is 20
20 = X + 4X - 6 + X + 8
20 + 6 - 8 = 6X
18 = 6X
x = 18 : 6
x = 3
-----------------
check
20 = 3 + 3 * 4 - 6 + 3 + 8
20 = 20
the answer is good
Answer:
Value of x is 3
Step-by-step explanation:
Given perimeter of figure = 20
x + (x+8) + (4x-6) = 20
x + x + 8 + 4x - 6 = 20
6x + 2 = 20
6x = 20 - 2
6x = 18
x = 18 / 6
x = 3
Find the values of a and b that make the following piecewise defined function both continuous and differentiable everywhere. f(x) = 3x + 4, X<-3
2x2 + ax + b. X>-3
Answers
The values of a and b that make the piecewise defined function f(x) = 3x + 4, for x < -3, and f(x) = 2x^2 + ax + b, for x > -3, both continuous and differentiable everywhere are a = 6 and b = 9.
To ensure that the piecewise defined function is continuous at the point where x = -3, we need the left-hand limit and right-hand limit to be equal. The left-hand limit is given by the expression 3x + 4 as x approaches -3, which evaluates to 3(-3) + 4 = -5.
On the right-hand side of the function, when x > -3, we have the expression 2x^2 + ax + b. To find the value of a, we need the derivative of this expression to be continuous at x = -3. Taking the derivative, we get 4x + a. Evaluating it at x = -3, we have 4(-3) + a = -12 + a. To make this expression continuous, a must be equal to 6.
Next, we find the value of b by considering the right-hand limit of the piecewise function as x approaches -3. Substituting x = -3 into the expression 2x^2 + ax + b, we get 2(-3)^2 + 6(-3) + b = 18 - 18 + b = b. To make the function continuous, b must equal 9.
Therefore, the values of a and b that make the piecewise defined function both continuous and differentiable everywhere are a = 6 and b = 9.
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Graph y = x -- 5. Complete the table of values by solving for the values of y given the values of x then graph the equation.
x|1|0|-1
y| | |
Answers
Answer:
Y-X= 5
Step-by-step explanation:
I think.... i dont know
What is the answer to this?
