10. Find the exact value of each expression. b. cos - (eln 1-4-2)
Answers
The exact value of cos⁻¹(\(e^{(1 - 1/2 \;ln 2\))) is 0.5435 radians or approximately 31.176 degrees.
To find the exact value of the expression cos⁻¹ (\(e^{1-1/2\;ln2}\)), we can use the properties of inverse trigonometric functions and logarithms.
We will perform the question in steps
1. Recall the inverse cosine function:
cos⁻¹(x) = arc cos(x), which represents the angle whose cosine is x.
2. We are given cos⁻¹(\(e^{1-1/2\;ln2}\)).
Using the properties of exponents and logarithms,
we can rewrite it as e . \(e^{1-1/2\;ln2}\).
= e (\(e^{1-1/2\;ln2}\)).
Now, \(e^{(ln x)\)= x, we can rewrite it as e (\(2^{(-1/2)\)).
= e \((\sqrt2)^{(-1)\).
= e (√2\()^{-1/2\).
Again, (√a)ⁿ = \(a^{(1/2n)\),
= e (\(2^{(-1/2)^{(1/2)\)).
= e(\(2^{-1/4\)).
Now we substitute the simplified expression into the inverse cosine function: cos⁻¹(e(\(2^{-1/4\))).
Then, the exact value to be 0.5435 radians or 31.176 degrees.
Therefore, the exact value of cos⁻¹(\(e^{(1 - 1/2 \;ln 2\))) is 0.5435 radians or approximately 31.176 degrees.
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Related Questions
please help me:) appreciated :) have a good day!!
Answers
1930 to the nearest 1000
Answers
Answer:
2000.
Step-by-step explanation:
The hundreds digit is 9 so we round up the 1 so the answer is 2000.
please help only real answers please
Answers
Answer:
D. WV
Step-by-step explanation:
A ray has one endpoint and one arrow. It goes infinitely in one direction.
D is the one that is a ray; the endpoint is on the left, the arrow is on the right.
Suppose a laboratory has a 30 g sample of polonium-210. The half-life of polonium-210 is about 138 days How many half-lives of polonium-210 occur in 1104 days? How much polonium is in the sample 1104 days later?
A. 9; 0.06 g
B. 8; 2,070 g
C. 8; 0.12 g
D. 8; 3.75 g
Answers
Answer: the amount of polonium remaining in the sample 1104 days later is approximately 0.12 g, and the answer is C
Step-by-step explanation:
To determine how many half-lives of polonium-210 occur in 1104 days, we can divide 1104 by the half-life of 138 days:
1104 / 138 ≈ 8
Therefore, there are approximately 8 half-lives of polonium-210 in 1104 days.
To determine how much polonium is in the sample 1104 days later, we can use the fact that the amount of polonium remaining after n half-lives is given by:
Amount remaining = initial amount × (1/2)^n
where n is the number of half-lives that have occurred.
In this case, we know the initial amount is 30 g and the number of half-lives is 8. So we can calculate the amount of polonium remaining as:
Amount remaining = 30 g × (1/2)^8 ≈ 0.117 g ≈ 0.12 g (rounded to two decimal places)
Therefore, the amount of polonium remaining in the sample 1104 days later is approximately 0.12 g, and the answer is C.
The radius of a circle is 10 inches. What is the area of a sector bounded by a
180° arc?
r=10 in
180°
Give the exact answer in simplest form.
square inches
Answers
Answer:
25/2pi
Step-by-step explanation:
stg that is right
Solve for g:
2g = -14
Answers
Answer:
g= -7
Step-by-step explanation:
Think about it like a blank.
2x__=-14
Traditionally, if -14 wasn't negative, we would just do 7.
But, it is negative, so we make the 7 negative.
Hope this helps!
-AxekickNebulite
HELP PLS: A store receives a shipment of 5,000 MP3 players. In a previous shipment of 5,000 MP3 players, 300 were defective.
A store clerk generates random numbers to simulate a random sample of this shipment. The clerk lets the numbers 1
through 300 represent defective MP3 players, and the numbers 301 through 5,000 represent working MP3 players.
The results are given.
13 2,195 3,873 525 900 1 67 1,094 1,472 709 5,000
Based on the sample, how many of the MP3 players might the clerk predict would be defective?
Answers
Answer: 1,000 players
Step-by-step explanation: The result has two values between 1 through 300
out of the 10 value in the sample so the clerk would predict 5,000 *\(\frac{2}{10}\)=1,000 defective players.
A. Factor: 5m2 40m + 5
B. Expand: 72(x – 3)
Answers
Answer:
A = \(200m^{3} + 5\)
B = 72x − 216
Step-by-step explanation:
Mark me Brainllest
Whats 6x-5+2x=3x-2x+9?
Answers
Answer:
X=2
Step-by-step explanation:
first combine like terms
subtract the x
add 5
lastly divide by 7
draining 15 gallons of water from a fish tank
(Write your answer as an integer)
Answers
Answer:
-15
Step-by-step explanation:
if its just asking for what number would represent a loss of 15 it would be negative 15
i dont know if there's more to the problem or not
Answer:
-15
Step-by-step explanation:
This is because whatever much water was in the tank is now decreasing by 15, therefore, you can write it as -15,
hope this helps!
Kevin Horn is the national sales manager for National Textbooks Inc. He has a sales staff of 4040 who visit college professors all over the United States. Each Saturday morning he requires his sales staff to send him a report. This report includes, among other things, the number of professors visited during the previous week. Listed below, ordered from smallest to largest, are the number of visits last week.
38 40 41 45 48 48 50 50 51 51 52 52 53 54 55 55 55 56 56 57
59 59 59 62 62 62 63 64 65 66 66 67 67 69 69 71 77 78 79 79
a. Determine the median number of calls.
b. Determine the first and third quartiles. (Round Q1 to 2 decimal places and Q3 to nearest whole number.)
c. Determine the first decile and the ninth decile. (Round your answer to 1 decimal place.)
d. Determine the 33rd percentile. (Round your answer to 2 decimal places.)
Answers
a. The median number of calls = 55
b. The first and third quartiles, Q1 = 48 and Q3 = 66
c. The first decile and the ninth decile, D1 = 45 and D9 = 71.
d. The 33rd percentile = 52.5
To answer the questions, let's first organize the data in ascending order:
38 40 41 45 48 48 50 50 51 51 52 52 53 54 55 55 55 56 56 57 59 59 59 62 62 62 63 64 65 66 66 67 67 69 69 71 77 78 79 79
(a) The median is the middle value of a dataset when arranged in ascending order.
Since we have 40 observations, the median is the value at the 20th position.
In this case, the median is the 55th visit.
(b) The quartiles divide the data into four equal parts.
To find the first quartile (Q1), we need to locate the position of the 25th percentile, which is 40 * (25/100) = 10.
The first quartile is the value at the 10th position, which is 48.
To find the third quartile (Q3), we need to locate the position of the 75th percentile, which is 40 * (75/100) = 30.
The third quartile is the value at the 30th position, which is 66.
Therefore, Q1 = 48 and Q3 = 66.
(c) The deciles divide the data into ten equal parts.
To find the first decile (D1), we need to locate the position of the 10th percentile, which is 40 * (10/100) = 4.
The first decile is the value at the 4th position, which is 45.
To find the ninth decile (D9), we need to locate the position of the 90th percentile, which is 40 * (90/100) = 36.
The ninth decile is the value at the 36th position, which is 71.
Therefore, D1 = 45 and D9 = 71.
(d) To find the 33rd percentile, we need to locate the position of the 33rd percentile, which is 40 * (33/100) = 13.2 (rounded to 13). The 33rd percentile is the value at the 13th position.
Since the value at the 13th position is between 52 and 53, we can calculate the percentile using interpolation:
Lower value: 52
Upper value: 53
Position: 13
Percentage: (13 - 12) / (13 - 12 + 1) = 1 / 2 = 0.5
33rd percentile = Lower value + (Percentage * (Upper value - Lower value))
= 52 + (0.5 * (53 - 52))
= 52.5
Therefore, the 33rd percentile is 52.5.
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Is the following a fixed or a variable expense?
Car Gas
Question 1 options:
A) Fixed Expense
B) Variable Expense
Answers
Answer:
A Because It's Called *Fixed*
Step-by-step explanation:
Sorry If it's Wrong
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The Correct choice is ~
Variable ExpenseA man is 40 years old and his son is 5years old. In how many years will the father be 3 times the age of his son.
Answers
12 1/2 years
Step-by-step explanation:
Let the unknown be n. Then 40+n = 3(5+n).
Performing the multiplication:
40+n = 15+3n
Isolate n and combine the constant terms:
25=2n, so n= 25/2 years
at the time 2:58 p.m., the digits displayed on a clock form an arithmetic sequence in the order in which they appear. how many minutes later will the digits displayed next form an arithmetic sequence?
Answers
It will take forty seven minute (i.e., 47 minute later) for the digits displayed next to form an arithmetic sequence again.
What is Arithmetic Progression?
An arithmetic progression is a sequence of numbers where each term is the sum of the previous term and a constant difference. It is also known as an arithmetic sequence.
At 2:58 p.m., the digits displayed on the clock are 2, 5, and 8, and they form an arithmetic sequence with a common difference of 3.
The next time the digits will form an arithmetic sequence is when the time is 3:45 p.m.
At 3:45 p.m., the digits displayed on the clock are 3, 4, and 5, and they also form an arithmetic sequence with a common difference of 1.
Therefore, it will take forty seven minute (i.e., 47 minute later) for the digits displayed next to form an arithmetic sequence again.
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Rational Exponents Practice- Practice (1-10)
4. Write the expression in rational form. (1 point)
t^-3/4
A. ^4√t^3
B. 1/^4√t^3
C. -^4√t^3
D. -^3√t^4
Answers
Therefore, the expression \(t^{(-3/4)}\) in rational form is:
\(B. 1/^4 \sqrt {t^3}\)
What is the exponential function?
An exponential function is a mathematical function of the form:
f(x) = aˣ
where "a" is a constant called the base, and "x" is a variable. Exponential functions can be defined for any base "a", but the most common base is the mathematical constant "e" (approximately 2.71828), known as the natural exponential function.
To write the expression \(t^{(-3/4)}\) in rational form, we need to eliminate the negative exponent.
Recall that a negative exponent can be rewritten as the reciprocal of the positive exponent. In this case, \(t^{(-3/4)}\) can be written as 1/ \(t^{(-3/4)}\).
Therefore, the expression \(t^{(-3/4)}\)in rational form is:
\(B. 1/^4 \sqrt {t^3}\)
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What is 7% of 100%?
Answer and you will get B R A I N L I E S T
Answers
7 % of 100 %
Formula :
\( \frac{x \%}{y \%} × 100 \)
Lets , solve it :
\( \frac{7\%}{100\%}× 100 \)
\(7\)
What is the domain and range of d(x)=|x|-4
Answers
Answer:
Domain = (-∞,∞) { x|x∈R}
Range = { -4 , ∞} , { y|y≥-4}
Step-by-step explanation:
4 x what gets us close to 38? (How many groups of 4 can we take out?)
Answers
Answer:
4 x 9 = 36
Step-by-step explanation:
Suppose y is a positive integer. If x – (–y) = z, will z be greater than or less than x?
Answers
Hope my answer helped u :)
Answer:
Z would be greater than X because suppose (-y) is 8 and X is 5, you add them up and the sum will be 13 aka X and 13 is bigger than 8 so that is your answer.
Hope it helped
Step-by-step explanation:
how many integers are there in between 10.5 and 31.2?
Answers
Answer:
original recipe
Step-by-step explanation:
Carlisle Transport had $4,520 cash at the beginning of the period. During the period, the firm collected $1,654 in receivables, paid $1,961 to supplier, had credit sales of $6,916, and incurred cash expenses of $500. What was the cash balance at the end of the period?
Answers
To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.
Starting cash balance: $4,520
Cash inflows: $1,654 (receivables collected)
Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)
Total cash inflows: $1,654
Total cash outflows: $1,961 + $500 = $2,461
To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:
Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows
Cash balance at the end of the period = $4,520 + $1,654 - $2,461
Cash balance at the end of the period = $4,520 - $807
Cash balance at the end of the period = $3,713
Therefore, the cash balance at the end of the period is $3,713.
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You and your brother go to the same store to buy fruit. You purchase a large watermelon for $7.71 and 2.4 pounds of red grapes. Your brother buys a platter of pre-cut fruit for $9.95 and 1.6 pounds of red grapes. The two of you spend the same amount of money. How much do the grapes cost per pound
Answers
The cost of red grapes per pound is $2.8.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, cost of a large watermelon and 2.4 pounds of red grapes is $7.71.
Let the cost of red grapes be x.
So, the total cost = 7.71+2.4x
Cost of a platter of pre-cut fruit and 1.6 pounds of red grapes is $9.95.
The total cost = 9.95+1.6x
Person and his brother spent same amount of money.
So, 7.71+2.4x=9.95+1.6x
2.4x-1.6x=9.95-7.71
0.8x=2.24
x=2.24/0.8
x=$2.8
Therefore, the grapes cost per pound is $2.8.
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One hundred people in your neighborhood always drive to work between 7:30 and 8:00 A.M. and arrive 30 minutes later. Why must two people always arrive at work at the same time, within a minute
Answers
Answer: Pigeonhole Principle
Step-by-step explanation:
The Pigeonhole Principle espouses that if there are more objects than the places the objects are supposed to fit into, some of those places will have more than one object. For instance, if there are 20 pigeons and only 19 pigeonholes, one pigeonhole will have more than one pigeon.
If one hundred people in your neighbourhood leave between 7:30 and 8:00 A.M. and arrive 30 minutes later that means they will arrive between 8:00 and 8:30 A.M. This means that 100 people will have to arrive in 30 minutes.
We would have to fit 100 people in 30 minutes. The minutes are the pigeonholes and the people are the pigeons. There will therefore be a situation where at least 2 people will arrive at the same minute because there are many more people than minutes for them to arrive in.
What is the area of the entire rectangle?
triangles?
square units
6.2 in.
8 in.
square units What is the area of one of t
Answers
Answer:
Step-by-step explanation:
Area of the triangle is:
A = 1/2 * (Base * Height)
A = 1/2 * (b * h)
A = 1/2 * (8 * 6.2)
A = 1/2 * 49.6
A = 24.8
Area of the rectangle is
A = Base * Height
A = b * h
A = 8 * 6.2
A = 49.6
shape created when a rectangle is rotated about the y-axis
Answers
When a rectangle is rotated about the y-axis, it creates a solid shape known as a cylindrical shell or a hollow cylinder.
When a rectangle is rotated about the y-axis, each point on the rectangle traces a circular path.
The resulting shape is a solid formed by the collection of these circular paths, creating a cylindrical shell or a hollow cylinder.
The height of the cylinder corresponds to the length of the rectangle, while the circumference of the cylinder corresponds to the width of the rectangle. The rotation about the y-axis gives the shape a cylindrical appearance, with the y-axis running through the center.
This shape is often used in calculus and geometry to calculate volumes and solve related problems. It is important to note that the rotation about the y-axis assumes that the longer side of the rectangle is aligned parallel to the y-axis.
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When a rectangle is rotated about the y-axis, it creates a solid shape known as a cylindrical shell or a hollow cylinder.
When a rectangle is rotated about the y-axis, each point on the rectangle traces a circular path.
The resulting shape is a solid formed by the collection of these circular paths, creating a cylindrical shell or a hollow cylinder.
The height of the cylinder corresponds to the length of the rectangle, while the circumference of the cylinder corresponds to the width of the rectangle. The rotation about the y-axis gives the shape a cylindrical appearance, with the y-axis running through the center.
This shape is often used in calculus and geometry to calculate volumes and solve related problems. It is important to note that the rotation about the y-axis assumes that the longer side of the rectangle is aligned parallel to the y-axis.
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PLEASE HELP!!
just look at the picture
Answers
Answer:
its the math that solve
Step-by-step explanation:
QUESTION 1
Last week a painter painted 2 houses in 7 days. What is the
productivity of the painter? Calculate your answer to 2 decimal
places.
QUESTION 2
A company that makes kitchen chairs wants t
Answers
The productivity of the painter is 0.29 houses per day.
How many houses can the painter paint in a single day?Last week, the painter successfully completed the task of painting 2 houses within a span of 7 days. To calculate the productivity of the painter, we need to determine the number of houses painted per day. By dividing the total number of houses painted (2) by the number of days taken (7), we can find the average productivity. Therefore, the painter's productivity is calculated as 0.29 houses per day.
In the case of the painter, the productivity metric allows us to gauge how many houses can be painted per day, providing valuable insights into the speed and efficiency of their work. It's important to note that productivity is not solely limited to the number of houses completed but also takes into account the time taken to accomplish the task.
Factors such as the size and complexity of the houses, the availability of resources, and the painter's skill level can influence productivity. By analyzing the productivity rate, one can assess the painter's capacity to meet deadlines, allocate resources effectively, and optimize their workflow. Additionally, comparing the productivity of different painters can help in selecting the most efficient professional for a specific project.
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Write a+b as a difference.
Answers
Answer:
I think a-b.
Step-by-step explanation:
Hope it's help you ✨
List 3 actions you can take to protect yourself online.
Answers
Answer:
don't show your face. don't give out your name, use an alias. don't
be bored.
Find the value of y (2y+5) (5x - 17) (3x-11)
Answers
Answer:
Hope it help, please give me BRAINLEST!
Step-by-step explanation:
2y + 5= |3y| + 3 = 3
x - 3= 2
\(\sqrt{x} + 2 = 2\)
5x - 17= -3x = 2
3^(x )= 4
3 cos^(2)(x) + 2 cos(x)- 1 = 0
3x-11= \(\sqrt{x}\) +3 = 8
2 = |3x|
x - 5= -3