The Graph Of F′, The Derivative Of A Function F, Consists Of Two Line Segments And A Semicircle, As Shown In The Figure Above. If F(2)=1, Then F(−5)=
https://apcentral.collegeboard.org/media/pdf/ap-calculus-bc-practice-exam-2012.pdf?course=ap-calculus-bc question 18
Answers
The graph of the derivative, F', shows that the slope is positive until x = 2 (the right end of the semicircle) and then becomes zero.
Since the graph of F' consists of two line segments and a semicircle, we can determine the values of F using the information provided.
Let's break down the problem into different intervals based on the graph:
Interval (-∞, -5):
Since we don't have specific information about this interval, we cannot determine the exact value of F(-5).
Interval (-5, 0):
In this interval, we have a line segment. Let's assume the equation of the line segment is y = mx + b. We can find the equation of this line segment by using the slope-intercept form of a line and the given point (2, 1).
The slope of the line can be calculated using the difference in y-coordinates divided by the difference in x-coordinates:
m = (1 - F(2)) / (2 - (-5)) = (1 - 1) / 7 = 0/7 = 0
Since the slope is 0, the equation of the line becomes y = b. Plugging in the point (2, 1) into the equation, we get:
1 = b
Therefore, the equation of the line segment for the interval (-5, 0) is y = 1.
Interval (0, ∞):
In this interval, we have a semicircle. The graph of the derivative, F', shows that the slope is positive until x = 2 (the right end of the semicircle) and then becomes zero. This indicates that the original function F is increasing until x = 2 and remains constant afterward.
Since F(2) = 1, we can conclude that F(x) = 1 for x ≥ 2. Therefore, F(-5) cannot be determined based on the given information.
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Related Questions
A ) find the perimeter of the plot land
B) find the area of the plot land without the building and parking lot
Answers
The perimeter of the plot land is 78.49 units and the area of the plot land without the building and parking lot is 210 square units
Finding the perimeter of the plot landFrom the graph, the vertices of the land are
A = (0, 20), B = (25, 19), C = (20, 2) and D = (5, 0)
Calculate the distance between adjacent vertices
So, we have
AB = √[(0 - 25)² + (20 - 19)²] = 25.02
BC = √[(20 - 25)² + (2 - 19)²] = 17.72
DC = √[(20 - 5)² + (2 - 0)²] = 15.13
AD = √[(0 - 5)² + (20 - 0)²] = 20.62
The perimeter of the plot land is
P = 25.02 + 17.72 + 15.13 + 20.62
P = 78.49 units
Finding the area of the plot landThis is calculated as
Area = Plot land - Building - Parking lot
Using the vertices, we have
Area = 1/2 * |0 * 19 + 25 * 2 + 20 * 0 + 5 * 20 - (20 * 25 + 19 * 20 + 2 * 5 + 0 * 0)| - [1/2 *(15 - 7 + 17 - 7) * (15 - 10)] - [(18 - 10) * (10 - 5)]
This gives
Area = 295 - 45 - 40
So, we have
Area = 210
Hence, the area is 210 square units
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Find the area under the curve
from 1 to 2.
thank you guys sm
Answers
2.883
I used Desmos graphing calculator to find this answer.
A recent concert sold $916 worth
of tickets. Students were charged
$1.25 and adults were charged
$2.25. If 560 people attended, how
many adults attended the concert?
How many students?
Answers
Answer:
250 students and 310 adults
Step-by-step explanation:
so if students are charged 1.25 and adults are charged 2.25 and 560 people attended if you divided from it should equal
Suppose y varies inversely with x, and y = 5 when x = 15. What is the value of y when x = 25 ?
Answers
The value of y is 3 when x = 25.
When two variables, x, and y, vary inversely, it means that as one variable increases, the other decreases in a proportional manner. In other words, their product is constant.
Mathematically, this relationship can be expressed as:
y = k/x
where k is the constant of proportionality.
To solve the problem, we are given that y = 5 when x = 15, which can be rewritten as:
5 = k/15
To find the value of y when x = 25, we need to first determine the value of k. We can do this by rearranging the equation above to solve for k:
k = 5 x 15 = 75
Now that we know the constant of proportionality, we can use it to find the value of y when x = 25:
y = k/x = 75/25 = 3
Therefore, when x = 25, y = 3. This means that as x increases from 15 to 25, y decreases from 5 to 3, in accordance with the inverse variation relationship between x and y.
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19. What is the tangent of ?
5√/11
11
O 5√11
O 6√11
√11
5
Answers
Hello,
tan = opposite/ adjacent
[tex]tan0 = \frac{5}{\sqrt{11} } = \frac{5\sqrt{11} }{11}[/tex]
it's the first answer
My sallary was first increased by 10% and then decreased by 10%.find the net change in my salary.
Answers
Hello,
x = departure's sallary
increasing a value by 10% means multiplying it by 1,1decreasing a value by 10% means multiplying it by 0,9x*1,1*0,9 = 0,99x
multiplying by 0,99 is equivalent to decreasing by 1%the net change in my salary is 1%
What is the value of x?
Answers
Answer:
Step-by-step explanation:
help please Find the base angles of the figure below.
A) 130°
B) 65°
C) 25°
D) 50°
Answers
Answer:
c
Step-by-step explanation:
The two angles on the bottom are equal.
All 3 angles equal 180 degrees.
We know one angle is 130.
The other two are 180-130= 50 combined.
Since those angles are equal, divide by two.
50/2= 25 degrees each.
URGENT
A box contains 18 large marbles and 16 small marbles. Each marble is either green or white. 7 of the large marbles are green, and 7 of the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is large or green? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answers
Answer:
p(large or green) = 0.794
Step-by-step explanation:
A box contains 18 large marbles and 16 small marblesEach marble is either green or white7 of the large marbles are green, and 7 of the small marbles are whiteIf a marble is randomly selected from the box, we need to find the
probability that it is small or green
1. Find P(large) ⇒ P(l)
2.Find P(green) ⇒ P(g)
3. Find P(large and green) ⇒ P(l and g)
4. Use the rule P(large or green) = P(l) + P(g) - P(l and g)
∵ The box contains 18 large marbles and 16 small marbles
∴ The total number of marbles = 18 + 16 = 34
∴ P(l) = 18/34
∵ There are 7 large green marbles
∵ There are 18 large marbles
∴ P(l and g) = 7/34
7 large green marbles9 small green marblesnumber of green marbles = 7+9 = 16∴ P(g) = 16/34
∵ P(large or green) = P(l) + P(g) - P(l and g)
∴ P(large or green) = 18/34 + 16/34 - 7/34
∴ P(large or green) = 27/34
= 0.7941176471
If a marble is randomly selected from the box, then the probability that it is large or green is 0.794
help me find an answer?
Answers
Answer:
The solution is (-2, 0).
If anyone can help me on this please
Answers
true or false if two squares have equal side length then they are congruent
How many combinations are possible? Assume the items are distinct.
7 items chosen 2 at a time
____ combinations
Answers
Answer:
21 combinations-----------------------
Find the combination of 2 out of 7:
7C2 = 7!/[(7-2)! * 2!] = 7! / (5! * 2!) = 6*7/2 = 21There are 21 combinations.
Find the area of the shaded region.
f(x)=x4-12x³ +48x², g(x) = 44x+105
340-
(-1,61)
(5,325)
co.
8
Q
Polestarp
Answers
Answer:
To find the area of the shaded region, we need to first find the x-coordinates of the points where the two functions intersect. We can set f(x) = g(x) and solve for x:
x^4 - 12x^3 + 48x^2 = 44x + 105
x^4 - 12x^3 + 48x^2 - 44x - 105 = 0
We can use a numerical method, such as the Newton-Raphson method, to approximate the roots of this equation. Using a graphing calculator or computer algebra system, we can find that the roots are approximately:
x = -1.932, x = 0.695, x = 4.149
Note that the root x = -1.932 is outside the given interval [3, 4], so we can ignore it.
The shaded region is bounded by the x-axis, the line y = 340, and the graphs of f(x) and g(x) between x = 3 and x = 4. To find the area of this region, we can integrate the difference between the two functions over this interval:
A = ∫3^4 [g(x) - f(x)] dx
A = ∫3^4 [44x + 105 - (x^4 - 12x^3 + 48x^2)] dx
A = ∫3^4 [-x^4 + 12x^3 - 48x^2 + 44x + 105] dx
We can integrate term by term using the power rule:
A = [-x^5/5 + 3x^4 - 16x^3 + 22x^2 + 105x]3^4
A = [-1024/5 + 192 - 192 + 22 + 105] - [-81/5 + 108 - 192 + 66 + 105]
A = 347.2
Therefore, the area of the shaded region is approximately 347.2 square units.
A 30-year-old earns an average income and plans to retire in 35 years. The employee plans to begin making $6,000 annual contributions into an IRA.
Which type of IRA is best for the employee, and why?
The Roth IRA is the best choice because the employee will pay less in taxes during employment than in retirement.
The Traditional IRA is the best choice because the employee will pay less in taxes during employment than in retirement.
The Roth IRA is the best choice because the employee will pay more in taxes during employment than in retirement.
The Traditional IRA is the best choice because the employee will pay more in taxes during employment than in retirement.
Answers
The IRA that is best is C. The Roth IRA is the best choice because the employee will pay more in taxes during employment than in retirement.
Why is the Roth IRA best ?When contributing to a Roth IRA, one must use after-tax dollars, resulting in taxes being paid on the money prior to it being deposited into the account. Withdrawals made from a Roth IRA that meet the necessary qualifications are completely exempt from taxation, thus employees will not be required to pay any taxes on the amount withdrawn during their retirement period.
It is probable that an employee's retirement income tax bracket will be higher than their current bracket, given the anticipated increase in their income and tax rate.
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A cross section is taken from a sphere.Which of the following is true?
Answers
Option A is correct: the cross-section of a sphere must be a circle.
When a sphere is cut by a plane, the resulting cross-section will always be a circle, regardless of the orientation or angle of the cut. This is because all cross-sections of a sphere have the same shape and size as a great circle, which is a circle that passes through the center of the sphere and divides it into two equal halves.
Option B is not correct because an ellipse is not a possible cross-section of a sphere.
Option C is not correct because the cross-section of a sphere can only be a circle, not an ellipse.
Option D is not correct because a line is not a possible cross-section of a sphere. A line can only be a cross-section of a cylinder or a cone, but not a sphere.
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Juanita is an accident reconstruction expert. She measured a 70-foot chord from the outer rim of the yaw mark on the road surface. The middle ordinate measured 9 feet in length. The drag factor of the road surface was determined to be 1.13. What is the minimum speed that the car was traveling when the skid occurred? Record your answer to the nearest tenth.
Answers
The minimum speed at which the car was traveling is 52.9 miles per hour.
To find the minimum speed at which the car was traveling during the skid, we can use the formula for calculating skid speed:
Skid speed = (Chord length x Chord length x Drag factor) / (2 x Middle ordinate)
Plugging in the given values:
Chord length = 70 feet
Middle ordinate = 9 feet
Drag factor = 1.13
Skid speed = (70 x 70 x 1.13) / (2 x 9)
Skid speed = 1391 / 18
Skid speed ≈ 77.3 feet per second
To convert the speed to miles per hour, we can multiply it by 3600/5280
= 77.3 x (3600/5280)
≈ 52.9 miles per hour
Therefore, the minimum speed at which the car was traveling is 52.9 miles per hour.
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Guests are filling out RSVP cards for Maria's wedding. They must choose which type of entree they would prefer for dinner. The choices are chicken, beef, or vegetarian dinners. Abigail chooses an entree; on the other side of town, Zeke also chooses. Are these two events dependent or independent?
Answers
These two events are independent because the outcome of both doesn't affect each other.
What is an independent and dependent events?An independent event is the type of event that occurs when the outcome of one event does not affect the outcome of the second event it is compared with.
A dependent event is the type of event that it's outcome affects the outcome of the second event it is compared with.
That Abigail chose an entree in a town different from Zeke doesn't affect her ability to attend the wedding.
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100 people questioned, 37 say they eat fruits, 33 say they eat vegetables, 9 say they eat cheese and fruits, 12 eat cheese and vegetables, 10 eat fruits and vegetables, 12 eat only cheese, and 3 report they eat all three offerings. How many people surveyed eat cheese? How many do not eat any of the offerings?
Answers
Answer:
Done
Step-by-step explanation:
To solve the problem, we can use a Venn diagram to visualize the information provided in the question.
Let's draw three overlapping circles to represent the three groups of people: those who eat fruits, those who eat vegetables, and those who eat cheese.
We know that:
- 37 people eat fruits, so we write "37" in the circle representing fruits.
- 33 people eat vegetables, so we write "33" in the circle representing vegetables.
- 9 people eat both cheese and fruits, so we write "9" in the overlap between the cheese and fruits circles.
- 12 people eat both cheese and vegetables, so we write "12" in the overlap between the cheese and vegetables circles.
- 10 people eat both fruits and vegetables, so we write "10" in the overlap between the fruits and vegetables circles.
- 12 people eat only cheese, so we write "12" in the part of the cheese circle that does not overlap with the other circles.
- 3 people eat all three offerings, so we write "3" in the intersection of all three circles.
Here's what the Venn diagram looks like:
```
Cheese
+----9----+----3----+----12---+
| | Cheese | | |
| Fruits +----6----+--4 | |
| | | | |
+----10---+----3----+----8---+---+
| Vegetables |
+------------+
9 24 15
```
To find out how many people eat cheese, we add up the numbers in the cheese circle: 9 + 3 + 12 = 24. So, 24 people eat cheese.
To find out how many people do not eat any of the offerings, we need to add up the numbers in the regions that are not part of any circle: the region outside of all circles, and the region in the center of the Venn diagram. These regions add up to 9 + 15 = 24. So, 100 - 24 = 76 people do eat at least one of the offerings.
Find the surface area of
the prism.
The surface area isin.²
8 in.
15 in.
5 in.
Answers
Answer: A = 470 in²
Step-by-step explanation:
If the given prism is a rectangular prism, we can use the given formula to solve for the surface area of a rectangular prism.
A = 2((8 in)(15 in) + (5 in)(15 in) + (5 in)(8 in))
A = 2(120 in² + 75 in² + 40 in²)
A = 2(235 in²)
A = 470 in²
ABCD is a square and AB = 5cm. What is the perimeter and the area of rectangle EFGH if AE=AH=FC=GC = 2cm square
Answers
The perimeter and the area of rectangle EFGH are 24 cm and 35 square cm
Calculating the perimeter and the area of rectangle EFGHFrom the question, we have the following parameters that can be used in our computation:
Side length, AB = 5 cm
Extension AE=AH=FC=GC = 2cm
Using the above as a guide, we have the following:
Dimension of the rectangle = 5 cm By (5 + 2) cm
So, we have
Dimension of the rectangle = 5 cm By 7 cm
The perimeter is then calculated as
P = 2 * (5 + 7) = 24 cm
The area is calculated as
A = 5 * 7 = 35 square cm
Hence, the perimeter and the area of rectangle EFGH are 24 cm and 35 square cm
See attachment for figure
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In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 36 and a standard deviation of 3. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 33 and 39? Do not enter the percent symbol. ans = %
Answers
Answer:
According to the empirical rule (also known as the 68-95-99.7 rule), for a bell-shaped distribution, approximately:
- 68% of the data falls within one standard deviation of the mean.
- 95% falls within two standard deviations of the mean.
- 99.7% falls within three standard deviations of the mean.
In this case, the mean number of phone calls answered by each receptionist is 36, and the standard deviation is 3.
To calculate the percentage of daily phone calls numbering between 33 and 39, we need to find the proportion of data within one standard deviation of the mean in either direction.
The range of interest (33 to 39) is within one standard deviation of the mean, so approximately 68% of the data will fall within this range.
Therefore, the approximate percentage of daily phone calls numbering between 33 and 39 is 68%.
The sum of my digits is 14. their difference is 4. I am less than 60. What number am I?
Answers
From the first clue, we know that:
x + y = 14
From the second clue, we know that:
x - y = 4
We can use these two equations to solve for x and y.
If we add the two equations together, the y terms will cancel out:
2x = 18
x = 9
Now we can substitute 9 for x in either equation to solve for y:
9 + y = 14
y = 5
So the number we are looking for is 59.
C) John, a meteorologist, recorded the temperatures from Monday to Frida and the mean temperature of five days was 40°F. The temperatures recorded on four consecutive days were 40°F, 39°F, 44°F, and 40°F. What temperature was recorded on the fifth day?
Answers
Average is the total sum of the given values divided by the number of values.
The average low temperature for the week is -3°F.
We have,
It is the total sum of the given values divided by the number of values.
We have,
Temperatures for one week:
Day Temperature
Sunday −5 °F
Monday −8 °F
Tuesday −6°F
Wednesday −8°F
Thursday −3 °F
Friday 2° F
Saturday 7° F
The average of the low temperature:
= [ -5 + (-8) + (-6) + (-8) + (-3) + 2 + 7 ] / 7
= (-5 - 8 - 6 - 8 - 3 + 2 + 7) / 7
= -30 + 9 / 7
= -21 / 7
= -3
Thus,
The average low temperature for the week is -3°F.
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complete question:
Christopher recorded the low temperature each day for 1 week and recorded his results in this table.
Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday
Low −5 °F −8 °F −6 °F −8°F −3 °F 2° F 7° F
What is the average low temperature for the week?
write the alhebraic expression for each graph
Answers
Answer:
[tex]y = 1- |x + 1| [/tex]
Overnight, a pipe cracked and started to leak into a basement. The graph shows the depth of the water in relation to time.
Answers
The water rises 10 inches each hour. The water is 4 inches deep is the water after four hours. It will take 8 hours for the water to reach a depth of 80 inches.
A pipe cracked overnight and started to leak into a basement.
The graph represents the depth (d) of the water over time (t).
As per the given graph, the required solution would be as:
Take two points (1, 10) and (5, 50) in the given graph
The linear function will be :
d - 10 = (50-10)/(5-1)(t - 1)
d - 10 = (40/4)(t - 1)
d = 10(t - 1) + 10
d = 10t - 10 + 10
d = 10t
Here slope of the given function is 10, which means 10 inches the water rise each hour.
The value of time (t) = 4 hr corresponds to the depth of water (d) is
d = 10(4) = 40
So, the water is 40 inches deep is the water after four hours
The value of depth of water (d) = 80 in corresponds to the time (t) is
80 = 10t
t = 80/10 = 8
So, It will take 8 hours for the water to reach a depth of 80 inches
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got the answer but said that it was wrong still?
Answers
Find the surface area of the triangular prism.
3,360 m2
1,662 m2
6,720 m2
1,872 m2
Answers
The total surface area of the triangular prism is is 1872 square meters
Finding the surface area of the triangular prismFrom the question, we have the following parameters that can be used in our computation:
The triangular prism
The surface area of the triangular prism from the net is calculated as
Surface area = sum of areas of individual shapes that make up the of the triangular prism
Using the above as a guide, we have the following:
Area = 1/2 * 12 * 16 * 2 + 35 * (20 + 16 + 12)
Evaluate
Area = 1872
Hence, the surface area is 1872 square meters
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How many times does 12 go into 72
Answers
Answer:
6 times with a remainder of 0
how do u not know this
skipped basic math have u?
Question 7 (5 points)
Graph f(x)=(x-4) (x+4)
x²-8x+12
Answers
A graph that represent the system of quadratic equations is shown in the image attached below.
What is the graph of a quadratic function?In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the given quadratic function, we can logically deduce that the graph would be an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).
By expanding the bracket, we have:
f(x) = (x - 4)(x + 4)
f(x) = x² - 4x + 4x - 16
f(x) = x² - 16
Since the leading coefficient (value of a) in the given quadratic function y = x² - 8x + 12 is positive 1, we can logically deduce that the parabola would open upward and the y-intercept is given by the ordered pair (0, 12).
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solve this exercise using the fact that the sum of the measures of the three angles of a triangle is 180 degrees in a triangle the measures of three angles are x x + 18 + x - 15 what is the measure of each angle
Answers
The measure of the first Angle is 59 degrees, the second angle is x + 18 = 77 degrees, and the third angle is x - 15 = 44 degrees
In any triangle, the sum of the measures of the three angles is always 180 degrees.
Let x be the measure of the first angle.
The second angle is x + 18 because it is given that the second angle is 18 more than the first angle.
The third angle is x - 15 because it is given that the third angle is 15 less than the first angle.
So, we have:
x + x + 18 + x - 15 = 180
Simplifying and solving for x, we get:
3x + 3 = 180
3x = 177
x = 59
Therefore, the measure of the first angle is 59 degrees, the second angle is x + 18 = 77 degrees, and the third angle is x - 15 = 44 degrees.
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