Verify the identity. sin() tan() = cos() use a reciprocal identity to rewrite the expression in terms of sine and cosine, and then simplify. sin
Answers
The identity Sin(α)/Tan(α) = Cos(α) is valid
Trigonometry is study of triangles. All trigonometric ratios are defined using the sides of the right triangle, such as an adjacent side, opposite side, and hypotenuse side. Three major of them are as follows :-
Sine Function:
sin(θ) = Opposite / Hypotenuse
Cosine Function:
cos(θ) = Adjacent / Hypotenuse
Tangent Function:
tan(θ) = Opposite / Adjacent
Lets prove this identity by proceeding with the LHS
= Sin(α)/Tan(α)
= Sin(α)/ (Sin(α)/Cos(α)) (Tan(α) = Sin(α)/Cos(α))
= Sin(α)xCos(α) / Sin(α)
= Cos(α)
Hence verified
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Related Questions
The lifetime of a product can be estimated using a normal distribution. What is the probability that the product will last between 16.536 and 8.054 years if the average lifetime has a mean of 14.242 years and a standard deviation of 3.978 years?
Answers
The to your question is that we can use the normal distribution to estimate the probability that the product will last between 16.536 and 8.054 years.
In this case, we want to calculate the probability for x = 16.536 and x = 8.054. The mean (μ) is 14.242 years, and the standard deviation (σ) is 3.978 years.
Using the formula, we can calculate the z-scores for both values:
For x = 16.536: z = (16.536 - 14.242) / 3.978
For x = 8.054: z = (8.054 - 14.242) / 3.978
Once we have the z-scores, we can look up the corresponding probabilities in the standard normal distribution table or use a calculator. Subtracting the probability for the lower z-score from the probability for the higher z-score will give us the probability that the product will last between 16.536 and 8.054 years.
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Susan is going to a Columbia Fireflies game. Each ticket (t
) costs $14
. She also had to pay $8
for parking. If she can spend $50
or less total, how many tickets can she buy
Answers
Answer:
Susan may only buy 3 tickets.
Step-by-step explanation:
This is because she payed 8 dollars for parking, so now 42 dollars left.
Next, you divide 42 by 14, to see how many tickets you can get, and it equals 3.
Can some help pleasee it is due tonight and it’s the only question I need,I also need to do ate by step if it’s not much to ask
Answers
Answer: -3/16
Step-by-step explanation:
When there is a negative exponent like x^-2 it equals 1/(x^2) the negative puts the number as a fraction so continuing...
-12(x^-2) (y^-2) can be rewritten as
-12 (1/x^2) (1/y^2) now we plug in x = -2 and y = 4
-12 (1/(-2^2) (1/(4^2)); -2^2 = 4 , 4^2 = 16
-12 (1/4) (1/16)
-3 (1/16)
= -3/16
Consider the following regression model: Y₁ =B₁ + B₂X₂1+ B3X31 + B₂X41 +14₁ Using the model above show that the maximum likelihood estimator for the variance, var (uiX21-X31-B4X4), is biased (be sure to comment of the nature of the bias).
Answers
The maximum likelihood estimator for the variance, (ui|\(X_{2i}\), \(X_{3i}\), β₄\(X_{4i}\)), is unbiased.
To analyze the bias of the maximum likelihood estimator (MLE) for the variance, we need to consider the assumptions and properties of the regression model.
In the given regression model:
\(Y_i\) = β₁ + β₂\(X_{2i}\) + β₃\(X_{3i}\) + β₄\(X_{4i}\) + U\(_{i}\)
Here, \(Y_i\) represents the dependent variable, \(X_{2i}, X_{3i},\) and \(X_{4i}\) are the independent variables, β₁, β₂, β₃, and β₄ are the coefficients, U\(_{i}\) is the error term, and i represents the observation index.
The assumption of the classical linear regression model states that the error term, U\(_{i}\), follows a normal distribution with zero mean and constant variance (σ²).
Let's denote the variance as Var(U\(_{i}\)) = σ².
The maximum likelihood estimator (MLE) for the variance, σ², in a simple linear regression model is given by:
σ² = (1 / n) × Σ[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]
To determine the bias of this estimator, we need to compare its expected value (E[σ²]) to the true value of the variance (σ²). If E[σ²] ≠ σ², then the estimator is biased.
Taking the expectation (E) of the MLE for the variance:
E[σ²] = E[ (1 / n) × Σ[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]
Now, let's break down the expression inside the expectation:
[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]
= [ (β₁ - β₁) + (β₂\(X_{2i}\) - β₂\(X_{2i}\)) + (β₃\(X_{3i}\) - β₃\(X_{3i}\)) + (β₄\(X_{4i}\) - β₄\(X_{4i}\)) + \(U_{i}\)]²
= \(U_{i}\)²
Since the error term, \(U_{i}\), follows a normal distribution with zero mean and constant variance (σ²), the squared error term \(U_{i}\)² follows a chi-squared distribution with one degree of freedom (χ²(1)).
Therefore, we can rewrite the expectation as:
E[σ²] = E[ (1 / n) × Σ[\(U_{i}\)²] ]
= (1 / n) × Σ[ E[\(U_{i}\)²] ]
= (1 / n) × Σ[ Var( \(U_{i}\)) + E[\(U_{i}\)²] ]
= (1 / n) × Σ[ σ² + 0 ] (since E[ \(U_{i}\)] = 0)
Simplifying further:
E[σ²] = (1 / n) × n × σ²
= σ²
From the above derivation, we see that the expected value of the MLE for the variance, E[σ²], is equal to the true value of the variance, σ². Hence, the MLE for the variance in this regression model is unbiased.
Therefore, the maximum likelihood estimator for the variance, (ui|\(X_{2i}\), \(X_{3i}\), β₄\(X_{4i}\)), is unbiased.
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what is the length of the lines connecting the points (-4,2) and (10,2) round answer to the nearest whole number
Answers
Answer: The length of the line connecting the points (-4,2) and (10,2) is 14 units.
Two number witch differ by 46
Answers
Answer:
63 and 17 differ by 46
Matthew wants to take out a loan to buy a car. He calculates that he can make repayments of $35,000 per year. If he can get a six-year loan with an interest rate of 9.25%, what is the maximum price he can pay for the car?
Answers
The maximum price Matthew can pay for the car, considering his repayment capability and the loan terms, is approximately $126,318.29.
To determine the maximum price Matthew can pay for the car, we need to consider his repayment capability and the terms of the loan.
Matthew can make annual repayments of $35,000. Since the loan term is six years, the total amount he can repay over the loan period is $35,000 multiplied by six, which equals $210,000.
To calculate the maximum price of the car, we need to account for the interest rate of 9.25%. The interest rate represents the cost of borrowing and is applied to the loan amount.
Let's assume the loan amount is denoted by P.
The formula to calculate the future value of a loan with interest is:
FV = P(1 + r)^n
Where:
FV = Future value (total amount repaid)
P = Principal amount (maximum price of the car)
r = Interest rate per period (9.25% or 0.0925)
n = Number of periods (six years)
Since Matthew can repay a total of $210,000 over the loan period, we can set up the equation:
$210,000 = P(1 + 0.0925)^6
Now we can solve for P:
P = $210,000 / (1 + 0.0925)^6
Evaluating this expression, we find:
P ≈ $126,318.29
Therefore, the maximum price Matthew can pay for the car, considering his repayment capability and the loan terms, is approximately $126,318.29.
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Solve for G. g+ (-5) = 27
g=
Answers
Answer:
G=32 I think,
Step-by-step explanation:
Hope it helps
Answer:
G = 32
Step-by-step explanation:
To do this problem, we first should rewrite the problem.
g + (-5) =27
Turns into
g - 5 = 27.
Then you can do the problem:
g - 5 = 27
+ 5 + 5
----------------
g = 32
Hope this helped!
Select the correct answer.
An image of two lines m and n parallel to each other. Lines p and q are parallel to each other. Line p and n for a hundred degrees angle. The angle formed by lines q and m is marked x.In the figure, lines m and n are parallel to each other. Lines p and q are also parallel to each other. What is the value of x?
A.
40°
B.
80°
C.
100°
D.
180°
Answers
if Lines p and q are also parallel to each other then value of x is 100, option C is correct.
What are Parallel lines?Parallel lines are coplanar infinite straight lines that do not intersect at any point.
The known angle is supplementary with angle A (Look at the attachment), that means that the sum of the known angle and A is 180°, therefore the value of angle A is 80°
Angle A and B are corresponding angles, which means that they have the same value, that happens because p and q are parallels and both cut line n in the same way. the value of the angles B is 80°
Angles B and C are corresponding too, so the value of the angle C is 80°.
Angles C and X are supplementary too for which the sum of X and C is 180°, so the value of X is 100°
Hence, if Lines p and q are also parallel to each other then value of x is 100, option C is correct.
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when you spin a 2D triangle, it looks like a 3D pyramid. true or false
Answers
Answer:
False
Step-by-step explanation:
Faizah is paid $11 per hour for her work at a factory. She works 9 hours a day and 24 days a month. She saves $594 a month. Express the amount she saves as a percentage of her income.
Answers
Answer:
The amount she saves is 25% of her income
Step-by-step explanation:
She is paid $11 per hour
She works 9 hours per day
and for 24 days per month
So, she works 9(24) hours per month
= 216 hours per month
Now, she is paid $11 hourly, so for 216 hours,
she will have 11(216) = $2376
Total income = $2376 per month
Saving = $594 per month
As a percentage, we divide the savings by the total income,
savings/(total income) = 594/2376 = 1/4 = 0.25
Hence we get 25%
7(x + 2) = 7x + 14 i dont get this someone pls help
Answers
Answer:
7
(
x
−
2
)
−
7
x
−
14
=
0
7
(
x
−
2
)
−
7
x
−
14
=
07
(
x
−
2
)
−
7
x
−
14
=
0
Step-by-step explanation:
Answer: 0 = 0
Step-by-step explanation: i showed the steps with these screen shots
My hand writing sucks but it says 1/2x - 3 = - 9
Answers
To find x in this, move the -3 to the other side by adding 3 on both sides:
1/2x – 3 + 3 = -9 + 3
1/2x + 0 = -6
1/2x = -6
Now, all you have to do is to ask yourself: How many halves does it take to get -6? It’s simple: multiply both sides by 2, because then 1/2 × 2 is 1, so 1/2x × 2 is x, so -6 × 2 is -12.
1/2x × 2 = -6 × 2
x = -12
So, your answer is x = -12
Determine the inverse of the function
Answers
Replace every x with a y and replace every y with an x .
Solve the equation from Step 2 for y . ...
Replace y with f−1(x) f − 1 ( x ) . ...
Verify your work by checking that (f∘f−1)(x)=x ( f ∘ f − 1 ) ( x ) = x and (f−1∘f)(x)=x ( f − 1 ∘ f ) ( x ) = x are both true.
How many soap cakes can be placed in a box of size 56 cm x 0.4 m 0.26 m, if the size
of a soap cake is 7 cm x 5 cm x 2.5 cm?
Answers
Answer:
length of box = 56cm
breadth = 0.4m = 40cm
height = o.25m = 25cm
Volume of Box = Volume of soap × n
n = number of soaps.
LBH = lbh × n
56 × 40 × 25 = 7 × 5 × 2.5 × n
n = 56×40×25/35×2.5
n = 56000/87.5
n = 640
so, 640 soaps can be placed in the box.
There are 216 black sheep and 357 white sheep in a field. How many sheep are in
the field?
563
562
3
573
572
My Progress >
Answers
Answer:
The answer is 573 this is correct
f is the line segment from (1,5) to, (0,0), find the value of the line integral: ∫(42⃗ 3⃗ )⋅⃗ = equation editorequation editor
Answers
The given line segment f is from (1,5) to (0,0). To find the value of the line integral, first we need to find the vector function of f. This can be done by taking the difference between the two points:(1, 5) - (0, 0) = <1, 5> - <0, 0> = <1, 5>So the vector function of f is:r(t) = <1, 5>t, 0 ≤ t ≤ 1.
Next, we need to find the derivative of the vector function: r'(t) = <1, 5>The line integral is given by the formula:∫C F · dr = ∫a,b F(r(t)) · r'(t) dt where F is the vector field and dr is the differential element of the curve C. Here, F = <42, 3>.Substituting the values, we get:∫C F · dr = ∫0,1 <42, 3> · <1, 5> dt= ∫0,1 (42 + 15t) dt= 42t + 15t²/2 from 0 to 1= 42 + 15/2= 51.5Therefore, the value of the line integral is 51.5.Given line segment f is from (1,5) to (0,0). To find the value of the line integral, first we need to find the vector function of f. This can be done by taking the difference between the two points: (1, 5) - (0, 0) = <1, 5> - <0, 0> = <1, 5>.So, the vector function of f is:r(t) = <1, 5>t, 0 ≤ t ≤ 1. Let us differentiate the vector function:r'(t) = <1, 5>.The line integral is given by the formula:∫C F · dr = ∫a,b F(r(t)) · r'(t) dt where F is the vector field and dr is the differential element of the curve C. Here, F = <42, 3>.Substituting the values, we get:∫C F · dr = ∫0,1 <42, 3> · <1, 5> dt= ∫0,1 (42 + 15t) dt= 42t + 15t²/2 from 0 to 1= 42 + 15/2= 51.5Therefore, the value of the line integral is 51.5.The value of the line integral is 51.5.
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Examine the diagram. It is not drawn to scale.
A triangle has angles A, B, 80 degrees. The exterior angle to angle A is 150 degrees.
Choose the statements that are true based on the diagram.
∠A is supplementary to the exterior angle.
∠A and the 80° angle are remote interior angles.
80° + m∠B + 150° = 360°.
∠B measures 70°.
∠A measures 40°.
Answer is the picture.
Answers
Answer:
the first one should be:
360,
60,
150,
90
Step-by-step explanation:
let me know if I'm wrong
How do you construct 1/3 of a segment?
Answers
To steps to construct a line segment that is 1/3 the length of the given segment is:
Draw a line segment CD of any length.
Fix the compass's end on C and pencil on D. This gives the length of CD.
Now divide the length of CD by 3. That is the 1/3 the length of CD.
Draw a line 1. Mark a point A on line 1. Change compass's setting into 1/3 the length of CD, place the compass at A.
Make an arc on the line l which cuts l at B. Now, AB is a copy of CD which is 1/3 the length of CD.
What is line segment?
A line segment is bounded by two definite points on a line. We also can say a line segment is part of the line which connects two points. A line has no endpoints and extends immensely in both the direction but a line segment has two fixed or distinct endpoints.
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B. the sum of
1/5
of m and
2/5
of m
Answers
Answer: 0.6 meters
Step-by-step explanation:
Which side of AXYZ is the longest?
43
/60°
x
O A. XY
B. XZ
C. YZ
OD. Cannot be determined
Answers
Answer:
B
Step-by-step explanation:
the longest side of a triangle is opposite the largest angle.
∠ Y = 180° - 60° - 43° = 180° - 103° = 77°
then ∠ Y is the largest angle in the triangle , so
side opposite ∠ Y is the longest , that is XZ
XZ is the longest side of the given triangle XYZ.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
The given triangle is XYZ.
We have to find the longest side.
Angle X and angle Z are given
∠X = 60 and ∠Z = 43
Now let us find ∠Y by angle sum property
∠X+∠Y+∠Z=180
60+43+∠Y=180
103+∠Y=180
Subtract 103 from both sides
∠Y=180-103
∠Y=77
The side which is opposite to the greatest angle is longest side
Hence, XZ is the longest side of the given triangle XYZ.
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When the cpi is 185, an electric razor cost $57.81. what is the difference between the price of an electric razor in 1983 and the cost of an electric razor when the cpi is 207, to the nearest cent? a. $33.44 b. $31.25 c. $26.56 d. $6.88
Answers
The difference between the price of an electric razor in 1983 and the cost of an electric razor when the cpi is 207, to the nearest cent is given by: Option D: $6.88
What is consumer price index?The consumer price index is the new cost of market basket in terms of percentage of old cost of market basket.
\(CPI_t\) = consumer price index in current period\(C_t\) = cost of market basket in current period\(C_0\) = cost of market basket in base periodThen, we have:
\(CPI_t = \dfrac{C_t}{C_0} \times 100\)
For this case, we're given that:
In 1983, CPI of considered razor = 185, and price = $57.81In some other year, the CPI of considered razor = 207, and price = $ ?? (to find).Let the base price of the razor in some base period be \(C_0\)
Then, for year 1983, we get:
\(CPI_t = \dfrac{C_t}{C_0} \times 100\\\\185= \dfrac{57.81}{C_0} \times 100\\\\C_0 \approx 31.248 \: \text{(in dollars)}\)
Now for the year when CPI is 207, let the price of th razor be $x, then we get:
\(CPI_t = \dfrac{C_t}{C_0} \times 100\\\\207 \approx \dfrac{x}{31.248} \times 100\\\\x \approx 64.683 \: \text{(in dollars)}\)
The difference between the two prices is:
\(d \approx 64.683 - 57.81 = 6.87 \approx 6.88\: \text{(in dollars)}\)
Thus, the difference between the price of an electric razor in 1983 and the cost of an electric razor when the cpi is 207, to the nearest cent is given by: Option D: $6.88
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Answer:
D
Step-by-step explanation:
Which situation can be modeled by the inequality 65-8x>9
Answers
Answer:
x<7
Step-by-step explanation:
65-8x>9
-8x>9-65
-8x>-56
x<7
Answer:
x<7
Step-by-step explanation:
65-8x>9
-8x>9-65
-8x>-56
x<7
7. Use the Pythagorean theorem to estimate the length of the unknown side of the right triangle. Explain why your
estimate makes sense.
12 mm
3 mm
Answers
Answer:
12 mm 3mm
Step-by-step explanation:
You are planning on making 250 liters of chili for a big fundraiser you are throwing. You want the
final chili mixture to be 36% meat. To get this you are mixing two types of chili together. The first
mixture is 60% meat and the second mixture is 20% meat. How much of each mixture do you
need?
Answers
Answer:
30%
Step-by-step explanation:
because you use %
so that is why i think but i am not sure
the___of the number -4 and 4 is 4
Answers
Simplify the square root of 3/8
Answers
Have a great day :)
I need help! Please show work, so I can understand!!!
Answers
Answer:
C
Step-by-step explanation:
distance Y multiply 1.0936
Answer:C
Step-by-step explanation:
M=Y(1.0936)
The bracket also represents multiplication
convert decimal number 0.5625 (or 9/16) to a single-precision floating point number. the answer should be given in hex at the end. (failed to provide steps will result in losing most of the points of the question.)
Answers
The single-precision floating point representation of 0.5625 in hexadecimal is: 0x3E100000.
How to solve for the single-precision floating pointIdentify the sign bit. In this case, the number is positive, so the sign bit is 0.
Convert the decimal number to binary. The decimal number 0.5625 (or 9/16) can be converted to binary as follows: 0.1001.
Convert the 32-bit binary number to hexadecimal. To do this, group the binary number into blocks of 4, from right to left, and convert each block into its hexadecimal equivalent:
0000 -> 0
0000 -> 0
0000 -> 0
0000 -> 0
0000 -> 0
0001 -> 1
0000 -> 0
0111 -> 7
1110 -> E
0 -> 0
So, the single-precision floating point representation of 0.5625 in hexadecimal is: 0x3E100000.
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what is the major difference between the two sample t-test and paired t-test? when should we use one versus the other? g
Answers
Two sample t-test is used when the two samples of the data are statistically independent and the paired t-test is used, when data is in the form of matched pairs
The two-sample t-test defined as the method used to test whether the unknown population means of two groups are equal. The two sample t-test is also called independent samples t-test. Because the two samples of the data are statistically independent.
A paired t-test is used to find the difference between two variables usually separated by time for the same subject. By using the paired t-test we can find the mean difference between pairs of measurements is zero or not. So paired t-test is used, when data is in the form of matched pairs
Hence, two sample t-test is used when the two samples of the data are statistically independent and the paired t-test is used, when data is in the form of matched pairs
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