How to do part b
2. Express the following in the form r sin(t + a). TI Solion. Using the as 20464. u (b) 2 sint - 3 cos t TOD +
Answers
The given expression 2 sin(t) - 3 cos(t) in the Form r sin(t + a), can be expressed as √13 sin(t - arctan(2/3)).
To express the given expression, 2 sin(t) - 3 cos(t), in the form r sin(t + a), we can use trigonometric identities to simplify and rewrite it.
Let's start by using the identity cos(a - b) = cos(a)cos(b) + sin(a)sin(b):
2 sin(t) - 3 cos(t) = r sin(t + a)
Here, r represents the magnitude or amplitude of the trigonometric function, and a represents the phase shift or the angle by which the function is shifted horizontally.
To find r and a, we need to manipulate the given expression to match the form r sin(t + a).
We can rewrite 2 sin(t) - 3 cos(t) as:
r [sin(t)cos(a) + cos(t)sin(a)]
By comparing the coefficients with the identity cos(a - b) = cos(a)cos(b) + sin(a)sin(b), we can determine that r = √(2^2 + (-3)^2) = √(4 + 9) = √13.
Next, we equate the coefficients of sin(t) and cos(t) to sin(a) and cos(a) respectively:
sin(a) = 2/√13
cos(a) = -3/√13
To find the value of a, we can use the arctan function:
a = arctan(sin(a)/cos(a)) = arctan((2/√13)/(-3/√13)) = arctan(-2/3)
Thus, we have expressed the expression 2 sin(t) - 3 cos(t) in the form r sin(t + a):
2 sin(t) - 3 cos(t) = √13 sin(t - arctan(2/3))
Note that the given value of 20464 and the letter "u" do not appear to be related to the given expression and can be ignored in this context.
In summary, the given expression 2 sin(t) - 3 cos(t) can be expressed as √13 sin(t - arctan(2/3)).
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Related Questions
What is the length of HG?
and if your able to could you explain the process? (i struggle on this topic)
Answers
Answer:
15:8
6:x
15×0.4=6
so, 8÷0.4=x=3.2 units
Please I really need help!!!
Answers
Answer:
For the line in red
The slope is 6/3 or 2
The y-intercept is negative 2
Equation is y = 2x - 2
For the line in blue
Slope is 4/2 or 2
Y-intercept is 3
Equation is y = 2x + 3
Step-by-step explanation:
I found slope by how many units you have to go up to get to the other point which is y to how many units you have to get horizontally to get to that point which is x. I found the y-intercept just by looking where the line met the x-axis. Lastly, I found the equation just by plugging everything in. This is because the equation is y = mx + b. For m you put in the slope and for b you put in the y-intercept.
Hope this helps!
what is the independent variable in this example HURRY PLEASE
Answers
Answer:
Volume
Step-by-step explanation:
x axis is always independant y axis is always dependant
my gross annual salary is $38,256. Each paycheck, I have 12% withdrawn for federal
taxes, 6.2% withdrawn for Social Security and 1.45% withdrawn for Medicare. There
are no other deductions. How much my monthly paycheck?
Answers
Answer:
$2561.56========================
GivenAnnual gross salary = $38256,Deductions = 12%, 6.2% and 1.45%.SolutionFind the monthly gross and subtract all the deductions.
Monthly gross salary is:
$38256/12 = $3188Total deductions:
12% + 6.2% + 1.45% = 19.65%Monthly paycheck is:
$3188 - 19.65% = $3188(100 - 19.65)/100 =$2561.56 (rounded to the nearest cent)Answer:
$2,561.56
Step-by-step explanation:
Income:
Gross annual salary = $38,256Deductions:
Federal tax = 12%Social Security = 6.2%Medicare = 1.45%Total deductions:
⇒ 12% + 6.2% + 1.45% = 19.65%
If 19.65% of the gross salary is deducted, the percentage remaining will be:
⇒ 100% - 19.65% = 80.35%
Find 80.35% of the gross annual salary:
⇒ 80.35% of $38,256
⇒ 0.8035 × 38256
⇒ 30738.696
Divide this by 12 to find the value of the monthly pay check:
⇒ 30738.696 ÷ 12 = 2561.558
Therefore, the monthly pay check is $2,561.56 (nearest cent).
Let w = { 9:,ber) with the standard operations in M22. Which of the following statements is true? W is not a subspace of Mzxz because it does not contain the zero matrix the above is true The 2x2 identity matrix is in W W is a subspace of M2x2. the above is true None of the mentioned
Answers
The correct statement is : W is a subspace of M2x2.
TO show that W is a subspace of M2x2, we need to verify that it satisfies the three properties of a subspace:
1. W contains the zero matrix:
The zero matrix in M2x2 is the 2x2 matrix with all entries equal to zero, which is not in W . However , we can see that the matrix {0,0;0,0} can be obtained as the difference between two matrices in W: {9,0;0,0} -{0,ber;0,0} = {0,0;0,0}. So , W does contain the zero matrix.
2. W is closed under addition:
Let A and B be two matrices in W. Then, A ={9,0;0,0} + {0,ber;0,0} and B = {9,0;0,0} + {0,ber;0,0}, which is also in W. Therefore, W is closed under addition.
3. W is closed under scalar multiplication:
Let A be a matrix in W and c be a scalar. Then ,A = {9,0;0,0} + {0,ber;0,0}, and c A = c {9,0;0,0} + c{0,ber;0,0}.
Since {9,0;0,0} and {0,ber;0,0} are both scalar multiples of A, c {9,0;0,0} and c{0,ber;0,0} are also in W . Therefore , W is closed under scalar multiplication.
Since W satisfies all three properties of a subspace, we can conclude that W is a subspace of M2x2.
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3+ (-8)
Someone please answer this
Answers
Answer:
The answer is - 5
Step-by-step explanation:
3+-8=-5
Answer:
-5
Step-by-step explanation: because i know that answer hope i helped!
Consider a sample of 45 football games, where 28 of them were won by the home team. Use a significance level to test the claim that the probability that the home team wins is greater than one-half
Answers
Based on the given sample, there is sufficient evidence to suggest that the home team has a higher probability of winning in football games.
To test the claim that the probability of the home team winning is greater than one-half, a significance test can be conducted using the given sample of 45 football games, where 28 were won by the home team. The test will determine if the observed proportion of home team wins is statistically significant enough to support the claim.
To test the claim, we can use a hypothesis test with the following null and alternative hypotheses:
Null Hypothesis (H0): The probability of the home team winning is equal to one-half or less (p <= 0.5).
Alternative Hypothesis (Ha): The probability of the home team winning is greater than one-half (p > 0.5).
To conduct the test, we can use the z-test for proportions since we have a large sample size (n = 45). The test statistic, z, can be calculated using the formula:
z = (p - p0) / sqrt[(p0 * (1 - p0)) / n],
where p is the sample proportion, p0 is the hypothesized proportion under the null hypothesis, and n is the sample size.
In this case, p is the observed proportion of home team wins, which is 28/45, or approximately 0.622. Since the null hypothesis states that p <= 0.5, we use p0 = 0.5 in the calculation.
Using the formula, the calculated z-value is:
z = (0.622 - 0.5) / sqrt[(0.5 * (1 - 0.5)) / 45] = 1.911.
Next, we compare the calculated z-value to the critical z-value at the chosen significance level. Let's assume a significance level of α = 0.05 for a one-tailed test.
Looking up the critical z-value for a one-tailed test with α = 0.05, we find it to be approximately 1.645.
Since the calculated z-value (1.911) is greater than the critical z-value (1.645), we have evidence to reject the null hypothesis. This means that the observed proportion of home team wins (0.622) is statistically significant and supports the claim that the probability of the home team winning is greater than one-half.
Therefore, based on the given sample, there is sufficient evidence to suggest that the home team has a higher probability of winning in football games.
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IT RAINS 15 DAYS IN JANURAY WRite the ratio of rainiy days to dry days
Answers
Answer:
3:9 6:15 14:21 15:35 all of these should work
A transportation problem with four sources and five destinations will have nine decision variables. True/False
Answers
False. A transportation problem with four sources and five destinations would have 20 decision variables, not nine.
In a transportation problem with four sources and five destinations, the number of decision variables is determined by the number of possible routes from sources to destinations. Each route represents a decision variable, indicating how much flow is sent from a specific source to a specific destination.
For this problem, there would be a maximum of 4 sources and 5 destinations, resulting in a total of (4 * 5) = 20 possible routes. Each route would correspond to a decision variable, indicating the flow from a particular source to a specific destination.
Therefore, a transportation problem with four sources and five destinations would have 20 decision variables, not nine.
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A bank is currently offering a savings account paying an interest rate of 9.4 percent compounded quarterly. Interest is paid once per month at the end of each month. It would like to offer another account, with the same effective annual rate, but compounded monthly. What is the equivalent rate compounded monthly? (Round answer to 4 decimal places, e.g. 25.1254%.)
Please show steps im trying to understand. Thanks
Answers
The equivalent rate of the other account, with the same effective annual rate, compounded is 9.5156%.
First, we can use the formula for effective annual interest rate (EAR):
EAR = (1 + r/n)^n - 1
where r is the nominal annual interest rate and n is the number of compounding periods per year. Since the given rate is compounded quarterly, we have:
r = 9.4% / 4 = 0.094 / 4 = 0.0235
n = 4
Using these values, we can find the EAR of the given rate:
EAR = (1 + 0.0235/4)⁴ - 1
EAR ≈ 0.0961 = 9.61%
Now we need to find the equivalent rate compounded monthly. Let's call this rate r'. To find r', we can use the EAR formula again, but with n = 12 (since there are 12 months in a year):
EAR = (1 + r'/12)¹² - 1
Since we want the same EAR, we can set this equal to 0.0961 and solve for r':
0.0961 = (1 + r'/12)¹² - 1
1.0961 = (1 + r'/12)¹²
1.0961^(1/12) = 1 + r'/12
r'/12 = 1.007930 - 1
r' = 0.095156 or 9.5156% (rounded to 4 decimal places)
Therefore, the equivalent rate compounded monthly is 9.5156%.
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PLEASE help me need solution please
Answers
Answer:
The answer is letter B
Step-by-step explanation:
-5x^2+3x+10
-25x+3x(-5)+10
-25x-15+10
-40+10
30
9514 1404 393
Answer:
A. f(x) = x^2 -3x -10
Step-by-step explanation:
You can easily determine the correct equation by looking at a couple of table values.
The y-value for x=0 is -10, which is the constant in the quadratic formula. (eliminates choices B and C)
The y-value for x=1 is -12, which is the sum of coefficients in the quadratic formula. For choice A, the sum of coefficients is 1 -3 -10 = -12. For choice D, the sum of coefficients is 1 +3 -10 = -6. The value for choice D does not match the table, but the value for choice A does.
The function that represents the table is ...
f(x) = x^2 -3x -10
_____
Additional comments
If you don't have equations to test, and you want to write your own equation, there are a couple of ways to do that. One is to look at the differences of y-values, and the differences of those.
The sequence of y-values shown is ...
30, 18, 8, 0, -6, -10, -12
The sequence of differences of these numbers, starting with 18-30 = -12 is ...
-12, -10, -8, -6, -4, -2
The sequence of differences of these numbers is ...
2, 2, 2, 2, 2
The fact that they are constant tells you a quadratic (degree = 2) will describe the table.
We can find the coefficients a, b, c in the quadratic formula f(x) = ax^2 +bx +c as follows. First, we define d1 as the first of the sequence of differences (-12), and d2 as the value of the second differences (2). And we'll let x0 and y0 be defined as the first of the x-values (-5) and y-values (30).
The formulas for the coefficients (a, b, c) can be found from ...
a = (d2)/2 = 2/2 = 1
b = (d1) -a(2·(x0) +1) = -12 -1(2·(-5) +1) = -12 +9 = -3
c = y0 -x0(a·x0 +b) = 30 -(-5)(1·(-5) +(-3) = 30 -40 = -10
As we noted above, the y-value corresponding to x=0 is also this c value. When the table includes x=0 and x=1, those can be used to simplify the finding of the formula coefficients.
These computations tell us f(x) = x^2 -3x -10, as above.
__
If you have to do this again, it might be useful to make a note of the expressions for 'a', 'b', and 'c' that we showed here, along with the definitions of the variables we used in them.
__
Another way to find the formula for f(x) is to make use of a calculator or spreadsheet capable of quadratic regression. Give it three (x, y) pairs from the table, and it can tell you the formula coefficients. This is illustrated by the attachment.
Select all the statements that are true about rhombus MNPQ.
Answers
Answer:
your answer will be option A and B
Step-by-step explanation:
hope it helps u
have a wonderful day/night
What is the range of 10,13,14,15,17,18,20,30,35
Answers
Given
The data is given
10,13,14,15,17,18,20,30,35
A baker has 2 1/4 cups of blueberries to make three batches of muffins. How many cups of blueberries should the baker put into each batch?
Answers
Answer:
0.75
Step-by-step explanation:
To answer this question you need to divide 2 1/4 by 3. To make it easier turn 2 1/4 to 2.25 because .25 = 1/4.
simplify (-4x+4)(4x\(x^{2}\)+2)
Answers
Answer:
−16x3+16x2−8x+8
solve by factorizing x² + 8x + 15 + 0
Answers
Download
GET
Algebra
Factor
Factor the polynomial.
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(
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Tap to view FREE steps...
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Factor
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Factor
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using the AC method.
Tap for fewer steps...
Consider the form
x
2
+
b
x
+
c
. Find a pair of integers whose product is
c
and whose sum is
b
. In this case, whose product is
15
and whose sum is
8
.
3
,
5
Write the factored form using these integers.
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x
+
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Answer:
(x+3)(x+5)
Step-by-step explanation:
How to answer linear measure with mixed numbers problem
Answers
Answer:
1. Change the mixed number to an improper fraction; 1 1/2 as 3/1
2. Multiply both sides with the reciprocal of the improper fraction
3. Simplifly your answer if possible
Can someone help ???????? Thanks
Answers
I think this is correct, but sorry if not.
Hope this helps x
11) Ms. Ripa's family is planning to come visiting her from New York. She hopes to take
them to some of the National Parks in Utah while they are here, but she needs to save up to
buy their tickets. Adult tickets are $12 each, and child tickets are $7 each. If she has 5 adults
and 4 children coming to visit, how much money will she need to save up to buy all of their
tickets?
Answers
Explanation:
Adults $12x5 = 60
Child $7x 4=28
60+28=88
how many frequent flyer program members are reported in newspaper quintile v? remember to report your answer with regards to the (000) format!
Answers
The number of frequent flyer program members in newspaper quintile V.
The information related to that specific quintile.
Unfortunately, you didn't provide the required data to calculate the number of frequent flyer program members in newspaper quintile V.
To understand what the given data represents.
Since the question is asking for the number of frequent flyer program members in newspaper quintile V.
The data is provided, I will guide you through a step-by-step process to find the answer and ensure that it is reported in the (000) format, as you requested.
Please provide the relevant data, and I'll be more than happy to help you calculate the answer.
Once the information is given, I will walk you through a step-by-step procedure to identify the solution and make sure it is presented in the (000) format, as you asked, when I have the data.
Comprehend what the provided data means.
Given that the number of frequent flyers programmed members in newspaper quintile V is the subject of the issue.
Information pertinent to that particular percentile.
Unfortunately, you didn't supply the information needed to determine how many people in newspaper quintile V are members of frequent flyer programmed.
The pertinent information, and I'll be pleased to assist you in coming up with the solution.
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is so eassy 2 puls 2
Answers
Answer:
4
Step-by-step explanation:
Answer:
22
Step-by-step explanation:
A triangle on the coordinate plane has points located at A (2,5), B (5,9), and C (8,5). What is the area of the triangle? O A 10 square units O B. 24 square units O C 12 square units O D. 8 square units
Answers
HELP! which label goes the correct place ?
Answers
Answer:
Step-by-step explanation:
Hey there! I hope this helps:
If you have a graphing calculator, go to y=, then enter, and plug each equation in then graph. The graph should show you which equation belongs to which line. You can search "graphing calculator" and plug the equation in and it'll graph it for you
9514 1404 393
Answer:
clockwise from top left, coefficients are ... 5, 1, 1/3, -5, -1, -1/3
Step-by-step explanation:
In the form ...
y = ax²
the coefficient 'a' is a vertical scale factor. When it is greater than 1, the parent function is vertically stretched, so it gets farther away from the x-axis for smaller values of x. (Parabola closest to the y-axis.)
The 'a' is less than 1, the parent function is vertically compressed, so the graph stays closer to the x-axis for larger values of x. (Parabola farthest from the y-axis.)
__
To answer this correctly, you only need to look to see if the coefficient is more than 1, equal to 1, or less than 1. If it is negative, the curve opens downward. Otherwise the vertical scaling is the same.
It looks like you're given coefficients of ±5, ±1, ±1/3. The negative coefficients apply to the graphs at the bottom of the figure. The positive ones apply to the top. Working to the left from the extreme right, the graphs are compressed (a=1/3), unaffected (a=1), and stretched (a=5).
Nate borrows $300 to buy a smartphone. He is charged 5% simple interest per year.
How much interest, in dollars, will Nate pay after 2 years?
Answers
Answer:
He is charged 5% simple interest per year. How much interest, in dollars, will Nate pay after 2 years? The interest after 2 years will be 0.05*300*2 = 30 dollars.
If t = 2 hours, s = 0.72 km/h then d = _____ m.
Answers
Answer:
we know that distance = speed *time
hence d= t*s
=2*0.72{ no need to convert into second and meter because both are given in km and hr}
=1.44 m
How to form a polynomial with given zeros and degree calculator.
Answers
The polynomial with zeros 2, -3, and 5 and degree 3 is P(x) = x^3 - 4x^2 - 11x + 30.
To form a polynomial with given zeros and degree, you can use the following steps:
Start with the given zeros: Let's say you have the zeros a, b, c, ..., up to the degree of the polynomial.
Use the zero-factor property: The zero-factor property states that if a polynomial has a zero at a certain value, then the corresponding factor of the polynomial is (x - zero).
Write down the factors: Write down the factors based on the zeros you have. For example, if you have zeros a, b, and c, the corresponding factors would be (x - a), (x - b), and (x - c).
Multiply the factors: Multiply all the factors together to obtain the polynomial expression.
Simplify the polynomial: Simplify the polynomial by expanding and combining like terms.
Here's an example to illustrate the process:
Let's say you want to form a polynomial with the zeros 2, -3, and 5, and the degree is 3.
The corresponding factors would be (x - 2), (x + 3), and (x - 5).
Multiplying these factors together, we get:
P(x) = (x - 2)(x + 3)(x - 5)
Expanding and simplifying:
P(x) = (x^2 + 3x - 2x - 6)(x - 5)
= (x^2 + x - 6)(x - 5)
= x^3 - 5x^2 + x^2 - 5x - 6x + 30
= x^3 - 4x^2 - 11x + 30
So, the polynomial with zeros 2, -3, and 5 and degree 3 is P(x) = x^3 - 4x^2 - 11x + 30.
By following these steps, you can form a polynomial with given zeros and degree.
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Simplify the expression.
4.8x - 4.6 + 3.9x
Answers
Answer:
8.7x - 4.6
Step-by-step explanation:
4.8x - 4.6 + 3.9x
Group like terms
4.8x + 3.9x - 4.6
Add similar elements: 4.8x + 3.9x = 8.7x
Then you get your answer:
8.7x - 4.6
A circular running track is 1/3 miles long. Zoe runs on this track, completing each lap in 1/21 of an hour. What is Zoe's running speed?
a) 7 hours per lap
b) 3 miles per hour
c) 7 miles per hour
d) 1/7 lap per hour
Answers
Answer:
b
Step-by-step explanation:
1 mile = 3 laps.
3x7=21
21=hour
21/7=3
4. [-/1 Points] DETAILS LARCALC11 15.2.003. Find a piecewise smooth parametrization of the path C. (ti + tj Ostsi r(t) ists 2 y = VX (1,1) 1 y=x Need Help? Read It
Answers
A piecewise smooth parametrization of the path C can be found by dividing the given curve into different segments and assigning appropriate parameterizations to each segment. This allows for a continuous and smooth representation of the path.
To find a piecewise smooth parametrization of the path C, we can divide the given curve into different segments based on its characteristics. In this case, the curve is defined as y = Vx and represents a line passing through the points (1,1) and (1,1).
First, let's consider the segment of the curve where x is less than or equal to 1. We can parameterize this segment using t as the parameter and assign the coordinates (t, t) to represent the points on the curve. This ensures that the curve passes through the point (1,1) at t=1.
Next, for the segment where x is greater than 1, we can also use t as the parameter and assign the coordinates (t, t) to represent the points on the curve. This ensures that the curve remains continuous and smooth. By combining these two parameterizations, we obtain a piecewise smooth parametrization of the path C.
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is 9 a prime number ples help
Answers
Answer:
no
Step-by-step explanation: