(1 point) Evaluate the following expressions. Your answer must be an angle in radians and in the interval ( (a) sin-¹ (2) = (b) sin ¹(-) = (c) sin ¹(-¹)=
Answers
The answer is given in the interval [-π/2, π/2] as sin⁻¹(x) lies in this interval.
The given expressions that need to be evaluated are:
(a) sin⁻¹(2)(b) sin⁻¹(-)(c) sin⁻¹(-¹)
To evaluate the given expressions, we need to know the definition of sin⁻¹ or arc
sine function, which is defined as follows:
sin⁻¹(x) = y, if sin(y) = x, where y lies in the interval
[-π/2, π/2]
For (a) sin⁻¹(2):
We know that the range of sinθ is [-1, 1] as it is an odd function and sin(-θ) = -sin(θ).
Therefore, sin⁻¹(x) exists only if x lies in the range [-1, 1].
Hence, sin⁻¹(2) is not defined as 2 lies outside the range of sinθ.
Therefore, the answer is undefined.
For (b) sin⁻¹(-):
We know that the range of sinθ is [-1, 1].
Therefore, sin⁻¹(x) exists only if x lies in the range [-1, 1].
Hence, sin⁻¹(-) is not defined as it is not a real number. Therefore, the answer is undefined.
For (c) sin⁻¹(-¹):
We know that -1 ≤ sinθ ≤ 1 or -1 ≤ sin⁻¹(x) ≤ 1.
Hence, sin⁻¹(-¹) = sin⁻¹(-1) = -π/2.
The required angles in radians for the given expressions are:
For (a) sin⁻¹(2), the answer is undefined.
For (b) sin⁻¹(-), the answer is undefined.
For (c) sin⁻¹(-¹), the answer is -π/2.
Therefore, the final answer is (c) sin⁻¹(-¹) = -π/2.
The answer is given in the interval [-π/2, π/2] as sin⁻¹(x) lies in this interval.
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Related Questions
What are two decimals equivalent to 3.7
Answers
Using a minimum of two sentences, describe how to write the function, f(x) = (x 2)2 - 3, in standard form.
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The function is a quadratic function, and the standard form of a quadratic function is ax^2 + bx + c
The standard form of the function \(\mathbf{f(x) = (x - 2)^2 - 3}\) is \(\mathbf{f(x) = x^2 - 4x + 1}\)
The function is given as:
\(\mathbf{f(x) = (x - 2)^2 - 3}\)
Factor out (x - 2)^2
\(\mathbf{f(x) = (x - 2)(x - 2) - 3}\)
Expand the expression
\(\mathbf{f(x) = x^2 - 2x -2x + 4 - 3}\)
Simplify the like terms i.e. add -2x and -2x
\(\mathbf{f(x) = x^2 - 4x + 4 - 3}\)
Simplify the like terms i.e. add 4 and -3
\(\mathbf{f(x) = x^2 - 4x + 1}\)
Hence, the standard form of the function \(\mathbf{f(x) = (x - 2)^2 - 3}\) is \(\mathbf{f(x) = x^2 - 4x + 1}\)
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Answer:
the one above is all right except its a positive 4x, the question was
f(x) = (x + 2)2 - 3
not
f(x) = (x - 2)2 - 3
the real answer is: f(x) = x^2+4x+1
sales of cds during the week were as follows: 14, 17, 20, 24, and 25. find the sales of cds one standard deviation from the mean.
Answers
To find the sales of CDs one standard deviation from the mean, we first need to find the mean and standard deviation of the data:
Step 1: Find the mean
mean = (14 + 17 + 20 + 24 + 25) / 5 = 20
Step 2: Find the variance
variance = [(14 - 20)² + (17 - 20)² + (20 - 20)² + (24 - 20)² + (25 - 20)²] / 5
= (36 + 9 + 0 + 16 + 25) / 5
= 17.2
Step 3: Find the standard deviation
standard deviation = sqrt(variance) = sqrt(17.2) ≈ 4.15
Now, to find the sales of CDs one standard deviation from the mean, we can add and subtract the standard deviation from the mean:
One standard deviation below the mean: 20 - 4.15 ≈ 15.85
One standard deviation above the mean: 20 + 4.15 ≈ 24.15
Therefore, the sales of CDs one standard deviation below the mean is approximately 15.85 and the sales of CDs one standard deviation above the mean is approximately 24.15.
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draw a rectangle. label the height as 5 cm and the width as 2x + 8. if the area is 80 cm^2 write an equation to find the value of x. then find the width of the rectangle
Answers
Answer:
16cm
Step-by-step explanation:
The area of a 2d figure is w x h. We know the area, a, is 80cm^2, the height, h, is 5, and the width, w, is 2x + 8.
Since we are solving for x, we want to isolate the variable.
5 x 2x + 8 = 80
80/5 = 2x + 8
We can now solve for x.
80/5 = 2x + 8
16 = 2x + 8
16 - 8 = 2x + 8 - 8
8 = 2x
8/2 = 2x/2
4 = x
We aren't done, we still need to solve for w, where we now know x = 4
w = 2x + 8
w = 2(4) + 8
w = 8 + 8
w = 16
write the coordinates
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Answer: C- 4,3 D- 9,4 E- 4,5 F- 1,4
Step-by-step explanation:
please help me on this!
Answers
Answer:
(a.) B: 8,000
(b.) C: 800
(c.) A. 10 times
Step-by-step explanation:
8762 has 3 digits after the 8. 8,000 has 3 digits after the 8
851 has 2 digits after the 8. 800 has 2 digits after the 8.
8,000 ÷ 800 = 10
Another way to do it is: 8000 has 3 zeros and 800 has 2 zeros.
3 - 2 = 1. 10 has 1 zero.
I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!
Can someone help me with this ASAP!
Answers
The following correct answer is c.
This I because when you translate using this, you first start with the point (0,0), translate that point down 3 (-3 means down three when outside parenthesis) and translate it to the right 4 units (this shown in a paraptosis, and when you move to the right you say -4, but if you move to the left you say +4)
A child should no longer use a booster seat when they reach 4’9” tall. Janet is 59 inches tall. Can she go without a booster seat? Explain?
Answers
no because 4'9 is 57 inches.Step-by-step explanation:
Answer:
Yes.
Step-by-step explanation:
Because, 4’9 is equal to 4.75, if you multiply the length value by 12, you will most likely get 57 in.
A large container holds 8 gallons of water. It begins leaking at a constant rate. After 32 minutes the container has 6 gallons left. At what rate is the water leaking. Express answer as a positive value.
Answers
Answer:
1/16 gallons per minute
Step-by-step explanation:
The water level drops from 8 gallons to 6 gallons in 32 minutes
The volume of water that has leaked is 8 - 6 = 2 gallons
Since this volume of water has leaked in 32 minutes, rate of leak
+ 2/32 = 1/16 gallons per minute
f(x) = 9x^3 + 2x^2 - 5x + 4 and g(x) = 5x^3 - 7x + 4
What is f(x) - g(x)? Show all of your steps and write final answer in factored form.
Answers
Step-by-step explanation:
f(x) - g(x)
9x³+2x²-5x+4 - (5x³-7x+4)
9x³+2x²-5x+4 - 5x³+7x-4
4x³+2x²+2x
2x(2x²+x+1)
Find the area of the shaded region.
Answers
Answer:
80
Step-by-step explanation:
multiply 10 by 8
(If it is not right... i apoligize but i don't see a shaded region)
Answer:
80 in
Step-by-step explanation:
To find the area of a rectangle, you have to multiply the length and height of the rectangle. When you do you will get 80 in
Hope this Helped
A trash bin has a capacity of 50 gallons. What percentage of its capacity is each of the following? 60% 10% 90% 200% 5 gal 30 gal 45 gal 100 gal 5 gal 30 gal 45 gal 100 gal
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Answer:
5 gallons is 1/10 of 50 gallons; this is 10%
30 gallons is 30/50 or 60%
45 gallons is 45/50 or 90%
100 gallons is 200%
Step-by-step explanation:
What is -3/2 + 5/4 - 7/4?
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Answer:
Step-by-step explanation:
COMPLETE CORRECTLY TO GET BRAINLIEST
Answers
THIS IS SO HARD HELP PLEASE
Answers
Answer:
second one: EFG NML
THIRD: 82°
(i) Let V=2xy^2z ^3+3ln(x ^2+2y ^2+3z^2)N in free space. Guduate each of the following amounts in P(3,2,−1) (a) V (b) ∣V∣ (c) E (d) ∣E∣
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The electric potential, V, is 73.63 N and the magnitude of the electric field is 12.00 V/m.
The given electric potential is,V=2xy²z³+3ln(x²+2y²+3z²) N
The components of the electric field can be found as follows,
E=-∇V=- (∂V/∂x) i - (∂V/∂y) j - (∂V/∂z) k
(a) To determine the potential at P(3, 2, -1), substitute x=3, y=2, and z=-1 in the given potential,
V=2(3)(2²)(-1)³ + 3 ln [(3)²+2(2)²+3(-1)²]= 72.32 N
(b) The magnitude of the potential is given by,
|V|= √ (Vx²+Vy²+Vz²)
The electric potential, V, is a scalar quantity. Its magnitude is always positive. Therefore,
|V|= √ [(2xy²z³)² + (3ln(x²+2y²+3z²))²]= √ [(-72)² + (16.32)²]= 73.63 N
(c) To determine the electric field E at P(3,2,-1), find the partial derivatives of V with respect to x, y, and z, and then substitute x=3, y=2, and z=-1 to obtain Ex, Ey, and Ez.
Ex = -(∂V/∂x)= -2y²z³/(x²+2y²+3z²) = -4.8 V/m
Ey = -(∂V/∂y)= -4xyz³/(x²+2y²+3z²) = -10.67 V/m
Ez = -(∂V/∂z)= -6xyz²/(x²+2y²+3z²) = 5.33 V/m
Therefore, the electric field E at P(3,2,-1) is, E=Exi+Eyj+Ezk=-4.8 i - 10.67 j + 5.33 k
(d) The magnitude of the electric field is given by,
|E|= √ (Ex²+Ey²+Ez²)= √ [(4.8)²+(10.67)²+(5.33)²]= 12.00 V/m
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The length of a triangle is 11 inches, 9.7 inches and 4.6 inches respectively. What is its area?
Answers
Answer:
Step-by-step explanation:
We can use the Heron's Formula to calculate the area of the triangle, yet first we need to calculate half the perimeter of the triangle
The sides are a= 11, b=9.7, c=4.6
Half of the perimeter is
s = (a+b+c)/ 2 = (11 +9.7 +4.6)/2 = 25.3/ 2 = 12.65 inches
Heron's Formula for calculating the area of the triangle:
A = √(s (s -a)(s -b)(s -c))
A = √(12.65* (12.65 -11)(12.65 -9.7)(12.65-4.6))
A = √(12.65* 1.65 * 2.95 *8.05)
A ≈ 22.26 inc.²
Kathleen took a total of 20 quizzes over the course of 4 weeks. After attending 7 weeks of school this quarter, how many quizzes will Kathleen have taken in total?
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To determine the number for a unit value the unitary method is used.
The number of quizzes Kathleen will take in 7 weeks is 35.
What is Unitary method ?In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method.
Given that,
Total number of quizzes in 4 weeks = 20
Total number of weeks the school is attended = 7
In order to find total number of quizzes in 7 weeks, apply unitary method to find the number of quizzes per week and then multiply it by 7 as follows,
Since, total number of quizzes in 4 weeks is 20
The number of quizzes in 1 week is 20 / 4 = 5.
Thus, the number of quizzes in 7 weeks is 5 × 7 = 35.
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In a box-and-whisker plot, the interquartile
range is a measure of the spread of the
middle half of the data. Find the interquartile
range for the data set: 10, 3, 7, 6, 9, 12, 13.
Answers
Answer:
IQR=8
Step-by-step explanation:
write numbers in ascending order
3 6 9 10 12 13
find the middle, in this case, it's two numbers (10 and 12)
3 6 are on the left, find the middle between them; 3+6/2
4.5
12 and 13 are on the right, find the middle between them;
12+13/2
12.5
IQR=12.5-4.5
For what value of k, the following system of equations kx+2y=3, 3x+6y=10 has a unique solution ?
Answers
The given system of equations to have a Unique solution, the value of k must be any real number except 1 (k ≠ 1).
The value of k for which the given system of equations has a unique solution, we can use the concept of determinants. The system of equations is as follows:
kx + 2y = 3 -- (1)
3x + 6y = 10 -- (2)
To have a unique solution, the determinant of the coefficients of x and y must not be zero.
The determinant of the coefficient matrix for the system is:
D = | k 2 |
| 3 6 |
By calculating the determinant, we have:
D = (k * 6) - (2 * 3)
D = 6k - 6
For the system to have a unique solution, the determinant D must not equal zero.
6k - 6 ≠ 0
Simplifying the inequality:
6k ≠ 6
Dividing both sides by 6:
k ≠ 1
Therefore, for the given system of equations to have a unique solution, the value of k must be any real number except 1 (k ≠ 1).
In other words, if k is not equal to 1, the system of equations will have a unique solution. If k is equal to 1, the system will either have infinitely many solutions or no solution.
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Emani has $10.00 to spend at the grocery store. So far, in her basket, she has 6 cans of soup that cost $0.47 each and a gallon of milk that costs $3.88. Approximately how much more money can Emani spend?
Answers
Answer:
$3.30
Step-by-step explanation:
6×0.47=2.82 (money spent on soup)
2.82+3.88=6.70 (total money spent on soup and milk)
10.00-6.70=3.30 (money she has left after buying soup and milk)
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Answers
Answer: bro this ez 1.5 for the first one second should be 22 correct me if im wrong.
Step-by-step explanation:
Suppose you buy one contract for september 2019 delivery. if the contract closes in september at a level of 4.10, what will your profit be?
Answers
If you buy one contract for September 2019 delivery and the contract closes in September at a level of 4.10, your profit will be $100.
A futures contract is an agreement to buy or sell a certain underlying asset at a predetermined price on a predetermined date. In this case, you are buying a futures contract for corn with a delivery date of September 2019. The contract price is currently 4.00. If the contract closes in September at a level of 4.10, you will be able to buy the corn at the lower price of 4.00 and then sell it at the higher price of 4.10, resulting in a profit of $0.10 per bushel. Since each contract is for 5,000 bushels, your total profit will be $100.
Here is a table showing the steps involved in calculating your profit:
| Step | Calculation | Result |
|---|---|---|
| Contract price | 4.00 | |
| Market price | 4.10 | |
| Profit per bushel | 4.10 - 4.00 | $0.10 |
| Total profit | $0.10/bushel * 5,000 bushels | $100 |
As you can see, your profit will be $100 if the contract closes in September at a level of 4.10.
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What are the y-intercept and the horizontal asymptote of g(x) = 7x + 2?
(0, 3) ; y = 2
(0, 4) ; y = 7
(0, 7) ; y = 2
(0, 9) ; y = 7
Answers
The y-intercept and the horizontal asymptote of g(x) = 7ˣ + 2 is (a) (0, 3) ; y = 2
How to determine the y-intercept?The equation of the function is given as
g(x) = 7ˣ + 2
To calculate the y-intercept, we set x = 0
So, we have
g(0) = 7⁰ + 2
Evaluate the exponent
g(0) = 1 + 2
Evaluate the sum
g(0) = 3
So, we have
(x, y) = (0, 3)
How to determine the horizontal asymptote?The equation of the function is given as
g(x) = 7ˣ + 2
To calculate the horizontal asymptote, we set 7ˣ
So, we have
y = 0 + 2
Evaluate the sum
y = 2
Hence, the solution is (a) (0, 3) ; y = 2
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The required y-intercept of the given function is (0,3) and the horizontal asymptote is y = 2.
What is an asymptote?Asymptote is the line on the curve that does not intersect the curve but passes as near to the maximum and minimum of the graph.
Here,
The y-intercept of the given function is evaluated as put the x coordinate to zero,
So,
g(0) = 1 + 2
g(0) = 3
Now, the horizontal asymptote is a line that passes near to the line but does not intersect with the curve,
So,
Terminating the x compositon of the function 7ˣ = 0 the rest will be the horizontal asymptote,
y = 7ˣ + 2
y = 0 + 2
y = 2
Thus, the required y-intercept of the given function is (0,3) and the horizontal asymptote is y = 2.
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Can somebody plz help me out:)))
Answers
Answer:28 possibly? I know that you connect it with the angles use across from the angle I hope I helped a little
Step-by-step explanation:
Answer:
Sin 30°
= 0.5 appromaxit
15 of the students in a English class passed a English test. If these students are 75% of
all the studerts in the class, howmary students are in this English dess? Round your
answer to the nearest whole number if necessary.
Answers
Answer:
20
Step-by-step explanation:
15=75%
15=3/4
3/4÷15=60/3=20
Write an expression for the phrase 5 times the quantity x squared subtracted from 7
Answers
Answer: 5 * \(x^{2}\) - 7
If you can walk 3 miles in an hour, how many miles can you walk in 30 minutes, given the
3
same pace?
A. 1 1/6 miles
B. 1 2/3miles
C. 6 2/3miles
D. 1 1/3 miles
Answers
60 minutes divided by 3 equals 20 minutes.
Construct a difference table to predict the next term of the sequence.
1, 8, 18, 31, 47, 66, . . .
Answers
Answer:
88
Step-by-step explanation:
8-1=7
+3
18-8=10
+3
31-18=13
+3
47-31=16
+3
66-47 = 19
+3
x - 66 = 22
+66 +66
x= 88
dc vvvvsiujhjcxhieh;wdbc
Answers
Answer:
I don't understand the question
Answer:
Oh cool!
Step-by-step explanation: