Verify that the following equation is an identity. (cos 2x + sin 2y)^2 = 1 + sin 4x Expand the expression on the left side, but do not apply any trigonometric identities. (cos 2x + sin 2x)^2 = Rearrange the terms and apply a Pythagorean identity, Type the new expression below.
Answers
Yes, the equation \((cos 2x + sin 2y)^2 = 1\)+ sin 4x is an identity.
What is following equation is an identity?. (cos 2x + sin 2y)^2 = 1 + sin 4xThe given equation is \((cos 2x + sin 2y)^2 = 1 +\)sin 4x. To verify that it is an identity, we need to expand the expression on the left side without applying any trigonometric identities. By using the binomial expansion, we have \((cos 2x)^2 + 2(cos 2x)(sin 2y) + (sin 2y)^2.\)
Next, we can rearrange the terms in the expression to obtain (\(cos^2 2x) + 2(cos 2x)(sin 2y) + (sin^2 2y).\) Now, applying the Pythagorean identity sin^2 θ + cos^2 θ = 1, we can replace \((cos^2 2x) and (sin^2 2y) with 1 - sin^2 2x and 1 - cos^2 2y\) respectively.
After substitution, we get 1 - \(sin^2 2x + 2(cos 2x)(sin 2y) + 1 - cos^2 2y.\)Simplifying further, we have \(2 - sin^2 2x - cos^2 2y + 2(cos 2x)(sin 2y)\). Applying the Pythagorean identity again, \(sin^2 θ + cos^2 θ = 1\), we can simplify the equation to\(2 + 2(cos 2x)(sin 2y).\)
Now, we can observe that 2 + 2(cos 2x)(sin 2y) is equivalent to 1 + sin 4x, which was the right side of the original equation. Therefore, we can conclude that the equation (c\(os 2x + sin 2y)^2 = 1 +\) sin 4x is an identity.
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Related Questions
What is the probability of picking a red balloon at random
to the nearest hundredth?
** A 0.19
**B 0.18
**C 0.17
5 of 10
-D 0.16
36.53
Answers
The probability of picking a red balloon at random is,
⇒ P = 0.18
We have to given that,
Total number of balloons = 17
And, Number of red balloons = 3
Now, We get;
The probability of picking a red balloon at random is,
⇒ P = Number of Red balloons / Total number of balloons
Substitute given values, we get;
⇒ P = 3 / 17
⇒ P = 0.1786
⇒ P = 0.18
(After rounding to the nearest hundredth.)
Thus, The probability of picking a red balloon at random is,
⇒ P = 0.18
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A 3-quart container of disinfectant costs $13.56. What is the price per cup?
Answers
Answer: The answer is $1.13.
Step-by-step explanation:
There are 12 cups inside a 3-quart container.
The sum of an integer and 3 times the next consecutive even integer is 6. Find the value of the greater integer.
Answers
The value of the greater integer according to the description in the task content is; 2.
What is the value of the greater integer as described?It follows from the task content that the value of the greater integer according to the given information.
Let the first integer be; x so that the greater integer is; x + 2.
Consequently, the equation which holds true is;
x + 3 ( x + 2 ) = 6
x + 3x + 6 = 6
4x = 6 - 6
4x = 0
x = 0.
On this note, the greater even integer as required in the task content is; 0 + 2 = 2.
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The first 300 natural numbers are written in an ascending order of sequence. Now all the numbers at the odd places of this sequence are removed and, thus a new sequence is formed. From this new sequence, all the numbers at odd places are removed once again. This process continues till only one number remains at the end. What is this number?
Answers
The final number remaining in this sequence is the number 2.
We start with the first 300 natural numbers written in ascending order. We remove the numbers at odd places, which means we remove all the numbers at positions 1, 3, 5, and so on.
After the first removal, we are left with the numbers at even positions: 2, 4, 6, and so on.
Now, we repeat the process and remove the numbers at odd positions again. We remove numbers at positions 1, 3, 5, and so on from the remaining sequence.
After the second removal, we are left with the numbers at even positions again: 4, 8, 12, and so on.
We can observe that in each removal, the sequence reduces to half its size, and we are left with the numbers at even positions.
Continuing this process, we will eventually reach a point where we have only one number left.
Since we start with 300 numbers, after the first removal, we have 150 numbers. After the second removal, we have 75 numbers. After the third removal, we have 38 numbers. After the fourth removal, we have 19 numbers. After the fifth removal, we have 10 numbers. After the sixth removal, we have 5 numbers. After the seventh removal, we have 3 numbers. After the eighth removal, we have 2 numbers. Finally, after the ninth and last removal, we are left with a single number.
Therefore, the final number remaining in this sequence is the number 2.
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You and a friend delivered 400 newpapers together. If your friend delivired 60% of the newspapers how many newspapers did you deliver
Answers
Answer:
160 newspapers (400 × .4 = 160)
you have three dice: one red (r), one green (g), and one blue (b). when all three dice are rolled at the same time, calculate the probability of the following outcome:...?
Answers
The probability of rolling a 6 with the red die, a 5 with the green die, and a 4 with the blue die at the same time is 1/216, or approximately 0.46%.
Assuming that each die is fair and that the outcome of rolling one die does not affect the outcome of rolling the others, the probability of rolling a 6 with the red die is 1/6, the probability of rolling a 5 with the green die is also 1/6, and the probability of rolling a 4 with the blue die is 1/6.
Since the three events of rolling each die are independent of each other, we can multiply their probabilities to get the probability of all three events happening at the same time, i.e., rolling a 6 with the red die, a 5 with the green die, and a 4 with the blue die:
Probability of rolling 6 with the red die = 1/6
Probability of rolling 5 with the green die = 1/6
Probability of rolling 4 with the blue die = 1/6
Probability of rolling 6 (R), 5 (G), 4 (B) at the same time = Probability of rolling R and G and B together = Probability of R × Probability of G × Probability of B
= 1/6 × 1/6 × 1/6 = 1/216
Therefore, the probability of rolling a 6 with the red die, a 5 with the green die, and a 4 with the blue die at the same time is 1/216, or approximately 0.46%.
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You have three dice: one red (R), one green (G), and one blue (B). When all three dice are rolled at the same time, calculate the probability of the following outcome: 6 (R), 5 (G), 4 (B)?
I am making two kinds of cookies: chocolate chip and lemon cookies.
(a)
Chocolate Chip Cookies
It takes 0.25 cup of sugar to make a batch of chocolate chip cookies. I have 5.50 cups of sugar. How many batches of cookies can I make?
I can make
batches of chocolate chip cookies.
You may use the scratchpad to show your work.
(b) Lemon Cookies
It takes 0.75 cups of sugar to make a batch of lemon cookies. I have 5.5 cups of sugar. How many batches can I make?
I can make
batches of lemon cookies.
You may use the scratchpad to show your work
Enter your answer as a fraction
Uhh sorry to bother again I’ve had no motivation haven’t been paying attention so uh yea
Answers
22 chocolate cookies can be made from 5.50 cups of sugar and 7 lemon cookies can be made from 5.50 cups of sugar
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The chocolate cookies is given as:
Number of chocolate cookies = 5.50 cups / 0.25 cup per cookie = 22
The lemon cookies is given as:
Number of lemon cookies = 5.50 cups / 0.75 cup per cookie = 7
22 chocolate cookies can be made from 5.50 cups of sugar and 7 lemon cookies can be made from 5.50 cups of sugar
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\(\sqrt{25} =5\)
Answers
A poll agency reports that 33% of teenagers aged 12-17 own smartphones. A random sample of 103 teenagers is drawn.
Would it be unusual if less than 25% of the sampled teenagers owned smartphones?
Answers
To answer this question, we need to calculate the expected number of teenagers in the sample who own smartphones. We know that the poll agency reported that 33% of all teenagers aged 12-17 own smartphones.
Therefore, we can expect that around 33% of the 103 teenagers in the sample, or 33/100 * 103 = 34. However, we also need to take into account the fact that we are dealing with a sample, and there will be some variability in the results.
To determine whether it would be unusual for less than 25% of the sampled teenagers to own smartphones, we can use the concept of standard deviation. The standard deviation of a sample proportion is given by the formula:
sqrt(p(1-p)/n)
where p is the expected proportion (33%), and n is the sample size (103). Plugging in the values, we get:
sqrt(0.33*0.67/103) = 0.051
This means that we can expect the actual proportion of teenagers in the sample who own smartphones to be within plus or minus 5.1 percentage points of the expected proportion (33%). So, a proportion of less than 25% would be more than two standard deviations below the expected proportion, which is quite unusual. In fact, it would be less than 5% likely to occur by chance alone. Therefore, we can conclude that it would be unusual if less than 25% of the sampled teenagers owned smartphones.
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In ⊙P, QR≅ST. Which statement must be true? Select all that apply.
A circle with center point P and four points Q,R,S,T on the circumference. Line segments join the points to make three chords QR,RS and ST. All the four points are connected to center point P making three triangles QPR,RPS and SPT.
A. △QRP ≅ △STP
B. QR¯¯¯¯¯¯¯¯ ≅ RS¯¯¯¯¯¯¯
C. ∠QPS ≅ ∠RPT
D. △RPS ≅ △SPT
E. QR¯¯¯¯¯¯¯¯ ≅ ST¯¯¯¯¯¯¯Which is the length of PQ expressed in terms of π?
A circle with center point N and radius 1. It has a minor arc PQ whose angle measures 99 degree
A. 1140π
B. 2940π
C. 1120π
D. 2920π
Answers
The true statement about the circle with center P is that triangles QRP and STP are congruent, and the length of the minor arc is 11/20π
The circle with center PGiven that the circle has a center P
It means that lengths PQ, PR, PS and PT
From the question, we understand that QR = ST.
This implies that triangles QRP and STP are congruent.
i.e. △QRP ≅ △STP is true
The length of the minor arcThe given parameters are:
Angle, Ф = 99
Radius, r = 1
The length of the arc is:
L = Ф/360 * 2πr
So, we have:
L = 99/360 * 2π * 1
Evaluate
L = 198/360π
Divide
L = 11/20π
Hence, the length of the minor arc is 11/20π
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2) A cone has a volume of 87 cm, and a height of 4 cm. What is the radius, to the
nearest centimeter?
Answers
Answer:
5cm
Step-by-step explanation:
radius of cone using volume:
v = (r)^2 (h/3)
1. Plug in:
87 = (3.14) (r)^2 (4/3)
2. Divide
87 = (3.14) (r)^2 (1.33333333333)
3. Multiply
87 = 4.18666666667 (r)^2
4. Divide to get r alone:
87 / 4.18666666667 = 4.18666666667 / 4.18666666667 (r)^2
20.7802547771 = r^2
5. Square root
The principal, real, root of:
20.7802547771
√220.78025477712 = 4.55853647 = r
So the radius is 4.55853647 or 5 cm
Nearest centimeter means rounding the value to the closest whole number in centimeters. In this case, the radius of the cone is approximately 4.55853647 cm. Rounding this value to the nearest centimeter gives 5 cm.
Added pictures to help.
Hope this helped!!
S=(1,2,3,4,5,6); A=(1,2,3,4); B= (3,4,5) c = (6). Solve P (A U C)
Answers
Finding the union of the sets A and C is the first step in solving P(A U C). Since set C only contains the number 6, the union of A and C has the elements 1, 2, 3, 4, and 6. A U C thus equals 1, 2, 3, 4, and 6.
The power set of A U C, which comprises all conceivable subsets of 1, 2, 3, 4, and 6, must then be located. If all conceivable subsets are listed, the power set of A U C, designated as P(A U C), will be discovered.
P(A U C) = { {}, {1}, {2}, {3}, {4}, {6}, {1,2}, {1,3}, {1,4}, {1,6}, {2,3}, {2,4}, {2,6}, {3,4}, {3,6}, {4,6}, {1,2,3}, {1,2,4}, {1,2,6}, {1,3,4}, {1,3,6}, {1,4,6}, {2,3,4}, {2,3,6}, {2,4,6}, {3,4,6}, {1,2,3,4}, {1,2,3,6}, {1,2,4,6}, {1,3,4,6}, {2,3,4,6}, {1,2,3,4,6}}.
There are 31 subsets in the power set P(A U C) that result from the union of sets A and C.
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In the figure below, the segments ST and SU are tangent to the circle centered at O. Given that OT=8 and OS=17, find SU.
Answers
The measure of length of SU is 18.7
Since a tangent to a circle makes a 90º angle to the origin, we can trace radius, and state that this is 13 units long. Therefore we have here two congruent triangles.
Given that OT=8 and OS=17,
We need to find SU.
To write a property that relates a tangent and a secant from one point
So, ST = SU
SU^2 = GF^2 + OG^2
SU^2 = 8^2 + 17^2
SU^2 = 289+ 64
SU^2 = 353
SU= 18.7
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i will mark brainliest!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Find the value of each variable
Answers
Answer:
1. a=90; b=110
2. a=140
3. b=105
4. c=60
5. d=50
Step-by-step explanation:
For Problem 1, A can be found by adding up all the exterior angles and minus the final number by 360. The final number is 270, and 360-270=90, so a=90. To find b, you need to do 180-70=110, so b=110 Another way you could do it is get the original number as 360 and minus all the angles until you get the variable's angle.
For problem 2, you can do the same thing you did to find A in problem 1, which is 140.(360-120-100=140)
For problem 3, we can do the same as the problems before us, so b would be 105. (360-95-70-90=105)
For problem 4, we get c as 60 (360-55-55-90-100=60)
Problem 5 would be d=50 (360-70-70-70-60-40=50)
The larger of two integers is 4 more than 9 times the smaller. The sum of the two integers is greater than or equal to 26. Find the smaller possible integer values for both of these integers.
Answers
We are given 2 statements.
We translate them to algebraic statements.
Let
smaller integer be s, and
larger integer be l
"The larger of two integers is 4 more than 9 times the smaller."
We can write this as:
\(l=9s+4\)Then, we are given sum of 2 integers is greater than or equal to 26, we can write:
\(l+s\geq26\)We put 1st equation in 2nd:
\(\begin{gathered} l+s\geq26 \\ 9s+4+s\geq26 \\ 10s\geq22 \\ s\geq2.2 \end{gathered}\)The next integer value (smallest of them all) of s is "3".
Now, if s is 3, l would be:
l = 9s + 4
l = 9(3) + 4
l = 27 + 4
l = 31
smaller of the both integers:
Smaller Number: 3
Larger Number: 31
Calculate the composite functions f∘g and g∘f. f(x)=10x,g(x)=x^10 f(g(x))=g(f(x))=
Answers
Composite function f∘g is 10x¹⁰ and composite function g∘f is 10000000000x¹⁰.
The composite functions f∘g and g∘f can be calculated as follows:
Function f(x) = 10x
Function g(x) = x¹⁰
Let's begin with the composite function f∘g
(f∘g)(x) = f(g(x)) = 10(g(x))
= 10(x¹⁰)
= 10x¹⁰
The composite function f∘g is therefore 10x¹⁰.
Let's now calculate the composite function g∘f
(g∘f)(x) = g(f(x))
= (f(x))¹⁰
= (10x)¹⁰
= 10¹⁰x¹⁰
= 10000000000x¹⁰
Therefore, the composite function g∘f is 10000000000x¹⁰. Composite function f∘g is 10x¹⁰ and composite function g∘f is 10000000000x¹⁰.
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Which line is the correct graph for y = -3/4x
A/ blue line
B/ purple line
C/ green line
D/ red line
Answers
Answer:D
Step-by-step explanation:
Suppose that you are rolling a six sided dice. Let A-get a 3 What is P(A^C)? 2/6
4/6 5/6 1/6 3/6
Answers
Answer:
5/6 (option 3)
Step-by-step explanation:
\(P(A^C)\) is asking what the complement of A is. This means we are asking what the probability of NOT getting A is. This would be 1 - P(A).
P(A) = The probability of getting a 3 = 1/6
We can solve for the probability of the complement of the A and get:\(P(A^C) = 1 - P(A) = 1 - \frac{1}{6} = \frac{5}{6}\)
Thus, the answer is 5/6 (which I believe is the 3rd option you are given)
12Find the total surface area of a cylinder that has a radius of 6 m and a height of 2 m.User = 3.14 and round your answer to the nearest hundredth.Total surface area =m2
Answers
The total surface area of a cylinder is calculated with the formula
\(\text{Acylinder}=2\times base\text{ area}\times curved\text{ surface area}\)\(\begin{gathered} \text{base area= }\pi r^2 \\ \text{curved surface area=2}\pi rh \end{gathered}\)\(\begin{gathered} A_{\text{cylinder}}=2\times\pi r^2+2\pi rh \\ \pi=3.14;r=6m;h=2m \end{gathered}\)\(A_{\text{cylinder}}=2\times3.14\times6^2+2\times3.14\times6\times2\)\(\begin{gathered} A_{\text{Cylinder}}=6.28\times36+6.28\times12 \\ =226.08+75.36 \\ =301.44m^2(\text{nearest hundredth)} \end{gathered}\)Hence, the area of the total surface area of the cylinder is 301.44m²
Which of the following expressions will have a product greater than 4?
four times ninety-nine hundredths
four times eight-eighths
three-fourths times four
one hundred and one-one hundredths times four
Answers
The Expression that have a product greater than 4 is one hundred and one hundredths times four , the correct option is (d).
In the question ,
four expressions are given as
(a) four times ninety-nine hundredths
= 4 × 99/100
= 4 × 0.99
= 3.96
(b) four times eight-eighths
= 4 × 8/8
= 4 × 1
= 4
(c) three-fourths times four
= 3/4 × 4
= 3
(d) one hundred and one hundredths times four
= 1.01 × 4
= 4.04
Therefore , The Expression that have a product greater than 4 is one hundred and one hundredths times four .
The given question is incomplete , the complete question is
Which of the following expressions will have a product greater than 4?
(a) four times ninety-nine hundredths
(b) four times eight-eighths
(c) three-fourths times four
(d) one hundred and one hundredths times four
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I need to show the work. Please help
Answers
Answer:
x = 7
Both angles are 134°
Step-by-step explanation:
Congruent because they are alternate exterior angles
16x +22 = 134
16x = 112
x = 7
7 pengiuns for $188.88
Answers
Answer:
1 penguin = $26.97
Step-by-step explanation:
188.88/7=
26.971429 which approximately equals 26.97
if the average speed of a light plane had been 40 km/h less, the plane would have taken one hour longer to fly the 1200 km route. what was the average speed of the plane?
Answers
The average speed of the plane is 240 km/h
Average speed is the ratio of total distance travelled to total time taken. It is given by:
Average speed = total distance / total time
Let S represent the average speed of the plane.
S = 1200/t
When driving 40 km/h less, the total time = t + 1 hour, hence:
S - 40 = 1200 / (t + 1)
1200/t - 40 = 1200/(t+ 1)
1200 - 40t + 1200/t - 40 = 1200
- 40t + 1200/t - 40 = 0
Multiply through by t:
- 40t² + 1200 - 40t = 0
This gives t = 5 and t = -6
Since the time cannot be negative, hence the total time is 5 hours. Hence:
S = 1200/t = 1200 / 5 = 240 km/h
Hence the average speed of the plane is 240 km/h.
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Speed is a scalar quantity, we will ignore the negative sign.
The average speed of the plane is 240 km/h
The Parameters to work with in this question are :
Speed, Time and distance. Where
distance S = 1200 km and the formula for speed is
Speed V = distance S / Time T
The assumed equation for this assumption will be:
(V - 40) = 1200/ (T + 1 )
Cross multiply and open the bracket
(V - 40)(T + 1) = 1200 ............. Equation 1
The real equation for the real scenario will be
V = 1200/ t
Where V is the average speed of the plane.
Make t the subject of the formula
t = 1200/V
Substitute the above t in equation 1 since we are looking for V
(V - 40)(1200/V + 1) = 1200
Open the bracket
1200 + V - 48000/V - 40 = 1200
Rearrange
V - 48000/V + 1160 = 1200
V - 48000/V = 1200 - 1160
\(V^{2}\) - 48000 = 40V
\(V^{2}\) - 40V - 48000
The two numbers to multiply together to give -48000 and add together to give -40 are -240 and 200
\(V^{2}\) - 240V + 200V - 48000
V - 240 = 0 or V + 200 = 0
V = 240 or - 200
Since the speed is a scalar quantity, we will ignore the negative sign.
Therefore, the average speed of the plane is 240 km/h
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Suppose A and B are a set of integers in the range 0 to 10n for
some integer n, and the goal is to find A + B = {x + y|x ∈ A, y ∈
B}. Give an O(n log n) algorithm for the problem using polynomial
Answers
The O(n log n) algorithm for finding A + B can be implemented using polynomial interpolation.
To find A + B, we can utilize polynomial interpolation. First, we construct two polynomials, P(x) and Q(x), where the coefficients of P(x) represent the frequencies of the integers in set A, and the coefficients of Q(x) represent the frequencies of the integers in set B.
We can construct these polynomials in O(n) time by iterating through sets A and B and counting the occurrences of each integer. The coefficients of the polynomials can be stored in arrays of size 10n+1, where the index represents the integer and the value represents the frequency.
Next, we multiply the two polynomials, P(x) and Q(x), using fast Fourier transform (FFT) in O(n log n) time. The resulting polynomial, R(x), represents the frequencies of the sums of all possible pairs of integers from sets A and B.
Finally, we can extract the coefficients of R(x) and construct the set A + B by iterating through the coefficients and adding the corresponding integers to the result set.
By utilizing polynomial interpolation and FFT, we can achieve an O(n log n) time complexity for finding A + B, making it an efficient algorithm for large values of n.
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solve the equation x^2=6
Answers
PLEASE HELP I REALLY NEED THIS ANSWERED, I NEED THE VOLUME OF BOTH CYLINDERS PLZ DONT USE AN ONLINE CALCULATOR THEY GIVE THE WRONG ANSWER
Answers
Answer:
\(\large\fbox{\green{\underline{Cylinder P :- \blue{ 794.0275 in ³}}}}\)
\(\large\fbox{\green{\underline{Cylinder Q :- \blue{1,307.81 in³}}}}\)
Step-by-step explanation:
Volume of cylinder = π × ( radius ) ² × h
1.) Here, radius = 4.25 in and height = 14 in.
Volume of cylinder = π × ( radius ) ² × height
substitute the values
Volume of cylinder P = 3.14 × ( 4.25 in ) ²×14 in.
now, simplify
= 3.14 × 18.0625 in²× 14 in.
= 3.14 × 252.875 in³
multiplying the value
= 794.0275 in³
\( \small \: \: \sf \: \fbox{ cirumference \: of \: cylinder \: P \: = {794.0275 in³}}\)
2.) Here, radius = 7 in. and height = 8.5 in.
Volume of cylinder Q = π × ( radius ) ² × height
substitute the values
Volume of cylinder Q = 3.14 × ( 7 in )² × 8.5 in.
Simplify
= 3.14 × 49 in² × 8.5 in.
multiply the values
= 3.14 × 416.5 in³
\( \small \sf \fbox{Volume of cylinder Q = 1,307.81 in ³}\)
Suppose you leave your house and travel 13 mi due west. then you travel 3 mi due south. how far are you from your house?
Answers
13.34 mi
from question,
perpendicular (p) = 3mi
base(b) = 13 mi
hypotenuse (h) = ?
from Pythagoras theorem,
h^2 = p^2 + b^2
h = √(3^2 + 13^2)
h = √(9+169)
h= √(178)
h= 13.34 mi
Answer:
≈ 13.3 miles
Step-by-step explanation:
a line due west and a line due south form a right triangle with the hypotenuse being the direct distance x from the house.
using Pythagoras' identity in the right triangle , then
x² = 13² + 3² = 169 + 9 = 178 ( take square root of both sides )
x = \(\sqrt{178}\) ≈ 13.3
distance from house ≈ 13.3 miles ( to the nearest tenth )
which of the following method returns the sine of 90 degree?
Answers
The correct method to return the sine of 90 degrees is Math.sin(90). The Math.sin() method accepts the angle in radians as its parameter and returns the sine value of that angle. Thus, option B is correct.
In Java, the Math class provides various mathematical functions, including trigonometric functions like sine (sin). Option A, Math.sine(90), is incorrect because there is no method named "sine" in the Math class. The correct name is "sin".
Option C, Math.sin(PI), is incorrect because the constant PI is the value of pi in radians, not in degrees. Since the parameter of the Math.sin() method should be in radians, passing PI as the argument will give the sine of pi radians, not 90 degrees.
Option D, Math.sin(Math.toRadians(90)), is incorrect because the radians () method converts an angle in degrees to radians. So, Math.toRadians(90) would give the value of pi/2 in radians, not 90 degrees.
Option E, Math.sin(Math.PI), is also incorrect for the same reason as option C. Math.PI represents the value of pi in radians, not in degrees.
In conclusion, the correct method to return the sine of 90 degrees in Java is Math.sin(90), which takes the angle in degrees as its parameter. Thus, option B is correct.
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Complete Question:
Which of the following method returns the sine of 90 degree?
A. Math.sine(90)
B. Math.sin(90)
C. Math.sin(PI)
D. Math.sin(Math.toRadian(90))
E. Math.sin(Math.PI)
Prove this equation
I'll give brianliest!!
Answers
\((\frac{1}{sin\alpha } -sin\alpha )(\frac{1}{cos\alpha } -cos\alpha )=cos\alpha *sin\alpha \\\\\\(\frac{1}{sin\alpha } -\frac{(sin\alpha)^2}{sin\alpha} )(\frac{1}{cos\alpha } -\frac{(cos\alpha)^2}{cos\alpha } )=cos\alpha *sin\alpha \\\\\\(\frac{1-(sin\alpha )^2}{sin\alpha } )(\frac{1-(cos\alpha)^2 }{cos\alpha } ) = cos\alpha *sin\alpha\\\\\\(\frac{(cos\alpha)^2 }{sin\alpha } )(\frac{(sin\alpha )^2}{cos\alpha } )=cos\alpha *sin\alpha\\\\\\cos\alpha *sin\alpha = cos\alpha *sin\alpha\)
Identities used
\((sin\alpha )^2+(cos\alpha)^2=1\)the second to last step to the last step was just a matter of simplificationHope it helped!
p.s. If you can give me a brainly, it would help a lot since the formatting of these equations were a lot of work
Barb had $55 in her checking account. She spent $12 on makeup and $13 on
socks. How much is in her checking account now?
Answers
Answer: Barb now has 30$ left.
Step-by-step explanation:
55-12=43 43-13=30