The area of the region bounded by the curve y=sin(x) and the x-axis between x=0 and x=4pi is 0.
To find the area of the region bounded by the curve y=sin(x) and the x-axis between x=0 and x=4pi, we can use the following steps:
1. Determine the function: In this case, the function is y=sin(x).
2. Identify the interval: The interval is from x=0 to x=4pi.
3. Integrate the function over the given interval: We'll integrate y=sin(x) with respect to x from 0 to 4pi.
∫(sin(x) dx) from 0 to 4pi.
4. Find the antiderivative: The antiderivative of sin(x) is -cos(x).
-∫(cos(x) dx) from 0 to 4pi.
5. Apply the fundamental theorem of calculus: We'll evaluate the antiderivative at the upper limit (4pi) and subtract the antiderivative evaluated at the lower limit (0).
[-cos(4pi)] - [-cos(0)]
6. Calculate the values: cos(4pi) = 1 and cos(0) = 1.
[-1] - [-1]
7. Determine the area: The area is the difference between the values calculated in step 6.
[-1 - (-1)] = 0
The area of the region bounded by the curve y=sin(x) and the x-axis between x=0 and x=4pi is 0.
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Scientists estimate that the mass of the sun is 1. 9891 x 1030 kg. How many zeros are in this
number when it is written in standard notation?
A 26
B 30
C 35
D 25
The total number of zeros in the mass of the sun when written in standard notation is 30, which is option B.
When we write the number in standard notation, we move the decimal point to the left or right to express the number in terms of powers of 10. In this case, we can write the mass of the sun as:
1.9891 x 10^30
To count the number of zeros in this number, we only need to count the number of digits to the right of the decimal point, which is zero in this case. Then we add the exponent, which tells us the number of places we need to move the decimal point to the right to express the number in standard notation. In this case, the exponent is 30, so we need to move the decimal point 30 places to the right, which means adding 30 zeros.
Therefore, the total number of zeros in the mass of the sun when written in standard notation is 30, which is option B.
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Amal's sister is half as old as Amal. Amal's mother is 3 times amals age. Amals father is 4 times older than amals motherThe sum of all 4 ages si 94. How old was Amal's mother when amal was born
Answer:
Amal's mother was 11.4 years old when Amal was born.
Step-by-step explanation:
Let's start by using variables to represent the ages of each person:
Let A be Amal's ageLet S be Amal's sister's ageLet M be Amal's mother's ageLet F be Amal's father's ageFrom the problem, we know:
S = 0.5AM = 3AF = 4MA + S + M + F = 94Substituting the first three equations into the fourth, we get:
[tex]\sf:\implies A + 0.5A + 3A + 4(3A) = 94[/tex]
Simplifying:
[tex]\sf:\implies A + 0.5A + 3A + 12A = 94[/tex]
[tex]\sf:\implies 16.5A = 94[/tex]
[tex]\sf:\implies A = 5.7[/tex]
So Amal is 5.7 years old. To find the age of Amal's mother when Amal was born, we need to subtract Amal's age from his mother's age:
[tex]\sf:\implies M - A = 3A - A = 2A[/tex]
So Amal's mother was 2A = 2(5.7) = 11.4 years old when Amal was born.
In circle m, secants pamd and pbc are drawn from point p such that mbc = 100 and mcd = 62°. which
of the following is the measure of p?
(1) 19
(2) 22
(3) 34
(4) 40
In the circle, the measure of p is 34 (option 3).
First, we know that angle MBC is an exterior angle to triangle PBC. Therefore, the measure of angle PBC is equal to the sum of angles MBC and MCB, which is 100 + (1/2)(angle MCP) = 100 + (1/2)(angle MQP).
Similarly, angle MCD is an exterior angle to triangle PCD. Therefore, the measure of angle PDC is equal to the sum of angles MCD and MDC, which is 62 + (1/2)(angle MPQ) = 62 + (1/2)(angle MQP).
Since angle PBC and angle PDC are both subtended by the same arc BC, they are equal. Therefore, we can set the expressions for these angles equal to each other and solve for angle MQP:
100 + (1/2)(angle MQP) = 62 + (1/2)(angle MQP)
38 = (1/2)(angle MQP)
angle MQP = 76 degrees
Finally, we can use the fact that angles MPQ and MQP form a linear pair, so they add up to 180 degrees. Therefore, angle MPQ is 180 - 76 = 104 degrees.
Since angle MPQ is an exterior angle to triangle PAB, we can use the exterior angle theorem to find the measure of angle P, as follows:
angle P = angle MPQ + angle PAB = 104 + 100 = 204 degrees
However, angles in a circle cannot be greater than 180 degrees, so we need to subtract 180 from angle P to get the actual measure of angle P:
angle P = 214 - 180 = 34 degrees
Therefore, the answer is option (3).
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Show that the series Σα) f(n)/2n^3 - 1 n converges regardless of the rule for f.
To show that the series Σα) f(n)/2n^3 - 1 n converges regardless of the rule for f, we can use the Comparison Test. Let's choose a series that is easier to compare to, such as Σ(1/2n^3).
First, note that 0 ≤ f(n) ≤ 1 for all n, since f is a function that is not negative and bounded by 1. Thus, we have: 0 ≤ f(n)/2n^3 - 1 n ≤ 1/2n^3, Now, we can compare the given series to the series Σ(1/2n^3) using the Comparison Test. Since 0 ≤ f(n)/2n^3 - 1 n ≤ 1/2n^3 for all n, we know that: 0 ≤ Σα) f(n)/2n^3 - 1 n ≤ Σ(1/2n^3), The series Σ(1/2n^3) is a convergent p-series with p = 3 > 1, so by the Comparison Test, the given series Σα) f(n)/2n^3 - 1 n also converges. Therefore, we have shown that the series Σα) f(n)/2n^3 - 1 n converges regardless of the rule for f.
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PLEASE HELP!! Find the area of the figure.
The area of the trapezoid in this problem is given as follows:
15 square feet.
How to obtain the height of the trapezoid?The area of a trapezoid is given by half the multiplication of the height by the sum of the bases, hence:
A = 0.5 x h x (b1 + b2).
The dimensions for this problem are given as follows:
h = 3 ft, b1 = 4 ft and b2 = 6 ft.
Hence the area is given as follows:
A = 0.5 x 3 x (4 + 6)
A = 1.5 x 10
A = 15 square feet.
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hello! are these correct?
if you can not see my answers :
1. right triangle
2. isosceles triangle
3. equilateral triangle
4. acute triangle
5. isosceles triangle
6. right triangle
( if im incorrect, please tell me the correct answer )
Answer: Yes those are correct good job
Step-by-step explanation:
Chloe receives her paycheck and knows that her gross pay and federal tax are correct. using the fact that social security tax is 6.2% of gross pay, medicare tax is 1.45% of gross pay and state tax is 23% of federal tax, determine if chloe's net pay is correct. earnings deductions week ended regular fed. soc. med state with. with. care. with. net pay 9/10 $856.00 $80.00 $53.07 $12.41 $18.40 $692.12 choose the true statement below. a. the net pay is correct. b. the social security tax is not correct. c. the medicare tax is not correct. d. the state tax is not correct.
The net pay is correct.
To determine if Chloe's net pay is correct, we need to check if all the deductions are calculated correctly. Let's examine each deduction one by one:
1. Social Security tax:
Social Security tax is 6.2% of gross pay.
6.2% of $856 = 0.062 * $856 = $53.07
2. Medicare tax:
Medicare tax is 1.45% of gross pay.
1.45% of $856 = 0.0145 * $856 = $12.41
3. State tax:
State tax is 23% of federal tax.
23% of $80 = 0.23 * $80 = $18.40
Now let's calculate the net pay by subtracting all deductions from the gross pay:
Net pay = Gross pay - (Federal tax + Social Security tax + Medicare tax + State tax)
Net pay = $856 - ($80 + $53.07 + $12.41 + $18.40) = $856 - $163.88 = $692.12
Since all deductions are correct, and the calculated net pay matches the given net pay, the correct answer is:
a. The net pay is correct.
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For what primary reason have many present-day African nations struggled to unite their people?
F.
Because many African peoples have strong tribal ties
G.
Because much of the African population remains loyal to former colonial powers
'H.
Because the African people refuse to accept centralized authority
J. Because many Africans seek to migrate from the continent
The primary reason many present-day African nations struggled to unite their people is F. Because many African peoples have strong tribal ties.
The strong tribal identities and loyalties that exist among various ethnic groups inside African states today are one of the main causes of the effort to bring people together. Through colonisation, many African nations were developed, and many of them contained numerous groups with various cultural, linguistic, and ethnic origins.
Therefore, as a result, it has been challenging to forge a strong sense of national identity among many individuals who still identify primarily with their own tribe or ethnic group. This has occasionally resulted in disputes and hostilities amongst various diverse groups, impeding efforts to create a community that is more unified.
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Obtain the equation of the line that passes through the point (4 , 6) and is parallel to the line y= -2x+4.
Answer:
y = -2x + 14
Step-by-step explanation:
OK so first u have to do y = -2x + b cuz its parallel
then u gotta just plug in the ordered pair so
6 = -2(4)+b
6 = -8 +b
14 = b
So now u have to do
y = -2x + 14
anyone know the dba questions for unit 8 algebra 1 honors
a) The distance the ball rebounds on the fifth bounce is approximately 7.59 ft.
b) The total distance the ball has traveled after the fifth bounce is approximately 52.61 ft.
What is the explanation for the above response?Let's denote the height of the ball after its nth bounce by h_n. Then we can express the relationship between the height of the ball after each bounce in terms of a recursive formula:
h_0 = 16 (initial height)
h_1 = (3/4) * h_0 (rebound distance after the first fall)
h_2 = (3/4) * h_1 (rebound distance after the second fall)
h_3 = (3/4) * h_2 (rebound distance after the third fall)
h_4 = (3/4) * h_3 (rebound distance after the fourth fall)
h_5 = (3/4) * h_4 (rebound distance after the fifth fall)
a) To find the distance the ball rebounds on the fifth bounce, we need to calculate h_5:
h_5 = (3/4) * h_4
= (3/4) * ((3/4) * ((3/4) * ((3/4) * 16)))
= (3/4)^5 * 16
= 7.59375 ft
Therefore, the ball rebounds approximately 7.59 ft on the fifth bounce.
b) To find the total distance the ball has traveled after the fifth bounce, we need to add up all of the distances traveled during the falls and rebounds:
total distance = distance of first fall + rebound distance after first fall + rebound distance after second fall + rebound distance after third fall + rebound distance after fourth fall + rebound distance after fifth fall
total distance = 16 + (3/4) * 16 + (3/4)^2 * 16 + (3/4)^3 * 16 + (3/4)^4 * 16 + (3/4)^5 * 16
total distance = 16 + 12 + 9 + 6.75 + 5.0625 + 3.7969
total distance = 52.6094 ft
Therefore, the ball travels approximately 52.61 ft after the fifth bounce.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
Be sure to show and explain all work using mathematical formulas and terminology. A bouncy ball is dropped from a height of 16ft and always rebounds ¼ of the distance of the previous fall.
a) What distance does it rebound the 5th time?
b) What is the total distance the ball has travelled after this time?
Dr. jackson is interested in the daily activities of a group of 4th graders. she asks the children to indicate the amount of time per day they spend watching television, playing video games, and studying. this type of data gathering technique would be an example of a(n) _____ approach.
The data gathering technique used by Dr. Jackson in her study of the daily activities of 4th graders is an example of a quantitative approach. This approach involves the collection of numerical data that can be analyzed using statistical methods to identify patterns and relationships.
By asking the children to indicate the amount of time they spend on different activities, Dr. Jackson is collecting quantitative data that can be used to compare and contrast the daily routines of different children. This approach is particularly useful for identifying trends and patterns in the data, such as the amount of time spent watching television or playing video games.
Quantitative data gathering techniques are commonly used in social sciences research, including education, psychology, and sociology. They are useful for identifying patterns and trends in large data sets, and can be used to make predictions about future behavior or outcomes.
Overall, Dr. Jackson's study of the daily activities of 4th graders is an example of the quantitative approach to data gathering. By collecting numerical data on the amount of time spent on different activities, Dr. Jackson can analyze the data using statistical methods to identify patterns and trends, and make predictions about future behavior or outcomes.
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An athletic Beld is a 50 yd-by-100 yd rectangle, with a semicircle at each of the short sides. Arunning track 10 yd wide surrounds the field. If the track is divided into eight lanes of equal width, with lane 1 being the inner-most and lane 8 being the outer-most lane, what is the distance around the along the inside edge of each lane?
The distance along the inside edge of each lane is 170 yards, 180 yards, 190 yards, 200 yards, 210 yards, 220 yards, 230 yards, and 240 yards.
Length of the Beld = 100 yd
Width of the Beld = 50 yd
The radius of the lane = 50/2 = 25 yards
To calculate the length of the overall length of the lane including semicircles is:
100 yards + 2 × 25 yards = 150 yards
The length of the innermost lane is:
150 yards + 2 × 10 yards = 170 yards
To calculate the length of the other lanes is:
170 yards + 10 yards = 180 yards
The length of lane 3 is:
180 yards + 10 yards = 190 yards
The distance between the two lanes is 10 yards. Then the remaining lengths of the lanes will be 200 yards, 210 yards, 220 yards, 230 yards, and 240 yards
Therefore, we can conclude that the distance between the two lanes along the inside edge of each lane is 10 yards.
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The equation y = –1.25x + 13.5
represents the gallons of water
y left in an inflatable pool after
x minutes. Select all the true
statements.
A. When the time starts, there
are 13.5 gallons of water in
the pool.
B. The tub is being filled at a rate
of 1.25 gallons per minute.
C. The water is draining at a rate
of 1.25 gallons per minute.
D. When the time starts, there
are 1.25 gallons of water in
the pool.
E. The water is draining at a rate
of 13.5 gallons per minute.
F. When the time starts, there
are 12.25 gallons of water in
the pool.
The two true statements are:
A "When the time starts, there are 13.5 gallons of water in the pool."
C "The water is draining at a rate of 1.25 gallons per minute."
Which statements are true?Here we have the linaer equation y = –1.25x + 13.5 that represents the gallons of water y left in an inflatable pool after x minutes.
And we want to see which of the given statements are true.
We can see that the slope is -1.25, this means that the volume of water is reducing (due to the negative sign) then the statement C is true.
We also can see that the y-intercept is 13.5, that would be the initial volume of water in the pool, then the statement A "When the time starts, there are 13.5 gallons of water in the pool." is also true.
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Suppose that in 1682, a man bought a diamond for $32. Suppose that the man had instead put the $32 in the bank at 3% interest compounded continuously. What would that $32 have been worth in 2003? In 2003, the $32 would have been worth $ (Do not round until the final answer. Then round to the nearest dollar as needed.)
If a man bought a diamond for $32 in 1682 and the man had instead put the $32 in the bank at 3% interest compounded continuously, then the value of the diamond in 2003 would be $554,311.
The given problem is related to exponential growth. In this problem, the continuous compounding formula will be used to find the value of $32 in 2003.
The formula for continuous compounding is given by:
A = Pert Where,
P is the principal amount,
r is the annual interest rate,
e is the Euler's number which is approximately 2.71828, and
t is the time in years.
Using the formula, we get:
A = 32e^(0.03 x 321)
A = 32e^9.63
A = 32 x 17322.23
A = $ 554311.36
Thus, $32 invested at 3% compounded continuously from 1682 to 2003 would be worth $554,311.
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AC B Round your answer to the nearest hundredth.
Answer:
4.28
Step-by-step explanation:
To find what the length of AC is, we can use the tangent of angle A, which is 35°. Here's the equation:
tan(35)=3/x
multiply both sides by x
x·tan(35)=3
divide both sides by the tangent of 35
x=4.28 (rounded to the nearest hundredth)
This means that AC=4.28
Hope this helps! :)
Two weeks ago i bought 20 cupcakes last week I bought 13 help me continue the pattern
Answer:
If the pattern is to continue, the next value would be a decrease of 7 from the previous value because 20-13=7. Therefore, the value for this week would be:
13 - 7 = 6
So, if you were to continue the pattern, you would have bought 6 cupcakes this week.
PLEASE HELP SERIOUSLY!
A. Determine whether the following statements are true or false.
1. The higher the percentile rank of a score, the greater the percent of scores above that score.
2. A mark of 75% always has a percentile rank of 75.
3. A mark of 75% might have a percentile rank of 75.
4. It is possible to have a mark of 95% and a percentile rank of 40.
5. The higher the percentile rank, the better that score is compared to other scores.
6.A percentile rank of 80, indicates that 80% of the scores are above that score.
7. PR50 is the median.
8. Two equal scores will have the same percentile rank.
Answer:
**Statement | True or False**
---|---
**1. The higher the percentile rank of a score, the greater the percent of scores above that score.** | True
**2. A mark of 75% always has a percentile rank of 75.** | False. A mark of 75% could have a percentile rank of 75 if it is the median score. However, it could also have a percentile rank of 60, 65, 80, or any other percentile rank, depending on the distribution of scores.
**3. A mark of 75% might have a percentile rank of 75.** | True. See above.
**4. It is possible to have a mark of 95% and a percentile rank of 40.** | True. For example, if there are 100 students in a class, and 95 of them get 100% on a test, then the student who gets 95% will have a percentile rank of 40.
**5. The higher the percentile rank, the better that score is compared to other scores.** | True. A higher percentile rank indicates that a score is better than more of the other scores.
**6.A percentile rank of 80, indicates that 80% of the scores are above that score.** | False. A percentile rank of 80 indicates that 80% of the scores are **at or below** that score.
**7. PR50 is the median.** | True. The median is the middle score in a distribution. By definition, half of the scores will be at or below the median, and half of the scores will be at or above the median. Therefore, the percentile rank of the median is 50.
**8. Two equal scores will have the same percentile rank.** | True. Two equal scores will always have the same percentile rank.
Step-by-step explanation:
URGENT !Tricia has 10 quarters, 17 dimes, 40 nickels, and 15 pennies.
How much money does Tricia have in all?
O A. $5. 15
B. $5. 85
OC. $6. 20
D. $6. 35
Tricia has a total of $6.35. The answer is D.
Tricia has 10 quarters, which is equivalent to $2.50 (since 1 quarter is $0.25).
She also has 17 dimes, which is equivalent to $1.70 (since 1 dime is $0.10).
Tricia has 40 nickels, which is equivalent to $2.00 (since 1 nickel is $0.05).
Finally, she has 15 pennies, which is equivalent to $0.15 (since 1 penny is $0.01).
To find the total amount of money Tricia has, we can add up the values of each coin:
$2.50 + $1.70 + $2.00 + $0.15 = $6.35
Therefore, Tricia has a total of $6.35. The answer is option D.
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Americans consume on average 32. 3 lbs of cheese per year with a standard deviation of 8. 7 lbs. Assume that the amount of cheese consumed each year by an American is normally distributed. An American in the middle 70% of cheese consumption consumes per year how much cheese?
An American in the middle 70% of cheese consumption consumes between 23.1 lbs and 41.5 lbs of cheese per year.
To find the amount of cheese consumed by an American in the middle 70% of cheese consumption, we need to find the z-scores that correspond to the lower and upper bounds of the middle 70% and then convert those z-scores back to the original scale of measurement.
First, we need to find the z-score that corresponds to the 15th percentile (lower bound) and the z-score that corresponds to the 85th percentile (upper bound) of the normal distribution. We can use a standard normal table or a calculator to find these values. Using a calculator, we get:
z_15 = invNorm(0.15) = -1.036
z_85 = invNorm(0.85) = 1.036
Next, we can use the formula:
z = (x - mu) / sigma
where x is the amount of cheese consumed by an American, mu is the mean amount of cheese consumed (32.3 lbs), and sigma is the standard deviation (8.7 lbs), to convert the z-scores back to the original scale of measurement:
For the lower bound:
-1.036 = (x - 32.3) / 8.7
x = -1.036 * 8.7 + 32.3 = 23.1 lbs
For the upper bound:
1.036 = (x - 32.3) / 8.7
x = 1.036 * 8.7 + 32.3 = 41.5 lbs
Therefore, an American in the middle 70% of cheese consumption consumes between 23.1 lbs and 41.5 lbs of cheese per year.
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The pattern of a soccer ball contains regular hexagons and regular pentagons. The figure below shows what a section of the pattern would look like on a flat surface. What is the measure of each gap between the hexagons in degrees?
Answer:
In this pattern, there are 12 regular pentagons and 20 regular hexagons. Each hexagon shares a vertex with three pentagons and each pentagon shares a vertex with five hexagons.
To find the measure of each gap between the hexagons, we can use the fact that the sum of the angles around any vertex in a regular polygon is always 360 degrees. Let x be the measure of the angle between two adjacent pentagons, and y be the measure of each angle at the center of a hexagon.
At each vertex of the pattern, there are three pentagons and three hexagons meeting. Thus, we have:
3(108) + 3y = 360
Simplifying, we get:
324 + 3y = 360
3y = 36
y = 12
Therefore, each angle at the center of a hexagon measures 12 degrees. Since there are six angles around the center of a hexagon, the total angle around the center of a hexagon is 6(12) = 72 degrees.
To find the measure of each gap between the hexagons, we need to subtract the angle of the hexagon from 180 degrees (since the sum of the angles of a triangle is 180 degrees). Thus, the measure of each gap between the hexagons is:
180 - 72 = 108 degrees
Step-by-step explanation:
Michae
all your steps.
2x 3x
problem a 60 x
miss chang ordered a pizza to share with some grade 8 students. miss chang
gave michael some slices of pizza. miss chang gave amy twice as many slices of
pizza as michael. miss chang gave mr. au three times the sum of what she gave
to michael and amy. miss chang gave 60 slices of pizza to michael, amy and mr.
au in total. how many slices of pizza miss chang give to each person?
Amy received 10 slices of pizza and Mr. Au received 45 slices of pizza.
Let's start by using variables to represent the unknown quantities in the problem. Let m be the number of slices of pizza Michael received, a be the number of slices Amy received, and au be the number of slices Mr. Au received.
We know that Miss Chang gave Michael 60 slices of pizza in total, so we can write:
m = 60
We also know that Amy received twice as many slices of pizza as Michael, so we can write:
a = 2m
Finally, we know that Mr. Au received three times the sum of what Miss Chang gave to Michael and Amy, so we can write:
au = 3(m + a)
We also know that Miss Chang gave 60 slices of pizza in total, so we can write:
m + a + au = 60
Now we can substitute the expressions we found for a and au into the last equation to get:
m + 2m + 3(m + 2m) = 60
Simplifying this equation, we get:
m + 2m + 3m + 6m = 60
12m = 60
m = 5
So Michael received 5 slices of pizza, and we can use the equations we found for a and au to determine how many slices Amy and Mr. Au received:
a = 2m = 2(5) = 10
au = 3(m + a) = 3(5 + 10) = 45
Therefore, Amy received 10 slices of pizza and Mr. Au received 45 slices of pizza.
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Question 13 of 13 > Attempt 6 Find an equation of the plane passing through the three points given P = (1,7,4), Q = (3,12,12). R = (8,11,7) (Use symbolic notation and fractions where needed. Give you answer in the form ax + by + cz = d.)
The equation of the plane passing through the three points P, Q, and R is -29x + 50y - 23z = 229
To find the equation of the plane passing through the three points P, Q, and R, we need to first find two vectors in the plane. We can do this by subtracting P from Q and R to get:
Q - P = (3-1, 12-7, 12-4) = (2, 5, 8)
R - P = (8-1, 11-7, 7-4) = (7, 4, 3)
Next, we can take the cross product of these two vectors to get a vector that is perpendicular to the plane:
(2, 5, 8) x (7, 4, 3) = (-29, 50, -23)
Now we have the equation of the plane in the form ax + by + cz = d, where (a, b, c) is the normal vector we just found and (x, y, z) is any point on the plane (we can use one of the three given points):
-29x + 50y - 23z = d (equation of plane)
To find the value of d, we can substitute one of the points, say P:
-29(1) + 50(7) - 23(4) = d
-29 + 350 - 92 = d
d = 229
Therefore, the equation of the plane passing through the three points P, Q, and R is:
-29x + 50y - 23z = 229
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A car can be rented for $75 per week plus $0. 15 per mile. How many miles can be driven if you have at most $180 to spend for weekly transportation
You can drive at most 700 miles within the $180 budget for weekly transportation.
To determine how many miles can be driven with a budget of $180 for weekly transportation, we'll use the given information: $75 per week for car rental and $0.15 per mile driven. First, subtract the weekly rental cost from the total budget:
$180 - $75 = $105
Now, divide the remaining budget by the cost per mile to find the maximum number of miles that can be driven:
$105 ÷ $0.15 ≈ 700 miles
So, you can drive at most 700 miles within the $180 budget for weekly transportation.
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Help a man out. Its due tomorrow need to get it done.
Answer:
A≈166.28
Step-by-step explanation:
Answer:
A≈166.28
Step-by-step explanation:
Evaluate the following indefinite integral (1 / 2 +e^x + e^-x ) dx
We can rewrite the integrand as follows:
1 / (2 + e^x + e^(-x))
To evaluate this integral, we use the substitution u = e^x:
du/dx = e^x
dx = du/u
Substituting u and dx in terms of u into the integral, we get:
∫ (1 / (2 + u + 1/u)) du
Multiplying the numerator and denominator by u, we get:
∫ (u / (2u + u^2 + 1)) du
Next, we complete the square in the denominator:
u^2 + 2u + 1 = (u + 1)^2
So, we can write:
∫ (u / ((u + 1)^2 + 1)) du
Now, we use the substitution v = u + 1:
dv/du = 1
du = dv
Substituting v and du in terms of v into the integral, we get:
∫ ((v - 1) / (v^2 + 1)) dv
Using partial fractions, we can write:
(v - 1) / (v^2 + 1) = A(v - i) + B(v + i)
where A and B are constants to be determined, and i = sqrt(-1).
Multiplying both sides by v^2 + 1 and simplifying, we get:
v - 1 = A(v - i)(v^2 + 1) + B(v + i)(v^2 + 1)
Substituting v = i, we get:
-i - 1 = A(0) + B(2i)
B = -(i + 1)/2i = (1 - i)/2
Substituting v = -i, we get:
i - 1 = A(-2i) + B(0)
A = (1 - i)/2i = (i - 1)/2
Therefore, we have:
(v - 1) / (v^2 + 1) = [(i - 1)/(2i)](v + i) - [(1 - i)/(2i)](v - i)
Substituting back for v, we get:
(u / ((u + 1)^2 + 1)) = [(i - 1)/(2i)][(u + 1) + ie^x] - [(1 - i)/(2i)][(u + 1) - ie^x]
Substituting this expression back into the integral and simplifying, we get:
∫ (1 / (2 + e^x + e^(-x))) dx = [(i - 1)/(2i)]*ln(e^x + e^(-x) + 2) - [(1 - i)/(2i)]*ln(e^x - i) + C
where C is the constant of integration.
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if 2x + 3y = 6x - 5y, find the value of x/y.
Answer: 2
Step-by-step explanation:
Answer:
[tex] \frac{dy}{dx} = \frac{4}{9} [/tex]
Step-by-step explanation:
sol,
2x+3y-6x+6y=0
f(x,y)=2x+3y-6x+6y
f(X,-y)=2x+3y-6y,fx=?
f(x-y)=2x+3y-6y,fy=?
fx=-4
fy=9
[tex] \frac{d}{y} = \frac{ - 4}{9} [/tex]
now,
[tex] \frac{dy}{dx} = \frac{4}{9} [/tex]
y’all please answer quick!!! :)
The mountain man ascends to the summit and then descends on the opposite side in a curved path, considering the route as a curve of a quadratic function Complete the following :
The man's path in pieces:
• Track direction "cutting hole":
•Route starting point: x=
• Path end point: x=
• The highest point reached by the man is the "head": (,)
• Maximum value:
• Y section:
•Axis of Symmetry Equation: x=
• the field:
• term:
Considering the route as a curve of a quadratic function, the information should be completed as follows;
Track direction "cutting hole": negative.Route starting point: x = -5.Path end point: x = 2.The highest point reached by the man is the "head": (-1, 4)Maximum value: 4Y section: distance or height.Axis of Symmetry Equation: x = -1The field: Area covered by the man's path.Term: x, y, a, h, and k.What is the vertex form of a quadratic equation?In Mathematics and Geometry, the vertex form of a quadratic function is represented by the following mathematical equation (formula):
y = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided about this quadratic function, we can logically deduce that a mathematical equation which quickly reveals the vertex of the quadratic function is given by:
y = a(x - h)² + k
0 = a(2.9 - (-1))² + 4
3.9a = -4
a = -4/3.9
a = -1.03
Therefore, the required quadratic function is given by:
y = a(x - h)² + k
y = -1.03(x - (-1))² + 4
y = -1.03(x + 1)² + 4
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
2 Decide if each statement about r = 6 is true or false. Choose True or False for each statement. a. The equation has the same solution as fr = 3. True False
Answer:
Step-by-step explanation:
True
Write an inequality and a word sentence that represent the graph. Let x represent the unknown number.
A number line. The number line is shaded left of an open circle at 1.
Inequality:
The word sentence for the given number line represents the X is greater than zero. The inequality is the X is not less than or equal to zero.
In the given number line the values are from negative infinity to positive infinity. Though the number line is having all values, there is some part that is shaded only on certain parts of the number line. The part is from number 1 to positive infinity marking zero as a circle.
The circle represents the value starts counting from the next step. In the given number line circle is shaded at number zero and the value started from the next value which is number 1 onwards to positive infinity.
So, the given number line represents X is greater than zero and X is not less than or equal to zero.
In mathematical words,
X < 0 and X≠0
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Given question is not having enough information to solve, for better understanding attaching the number line image below.
ldentify the relationship between the angles. y : x
Answer:
there both symmetrical
Answer:
Congruent
Step-by-step explanation:
When visualizing how two angles are related, try squashing the two parallel lines into each other. When you do that with these angles, they go from appearing like =\= to appearing like -\-, with x and y being catty-corner from each other.
Because the parallel lines are straight, x and y are both half of a pair that adds up to 180. However, x and y aren't sharing a straight line, so they cannot add up to 180 with each other. That leaves only one possibility, that x and y have the same angle measure.