For the function f(x) = 2.02 – 42 +2 (a) Find the equation for its tangent at r = 0. (b) Find the equation for its tangent at I = 1. (c) Find the equation for its tangent at x = 2. (d) What is special about f when x = 1?
Answers
a) The equation for the tangent at x = 0 is y - 2 = -42x.
(b) The equation for the tangent at x = 1 is y + 38 = -38x + 38.
(c) The equation for the tangent at x = 2 is y + 62 = -34x + 68.
(d) When x = 1,the value of f(x) is -38. This is the y- coordinate of the point on the tangent line at x = 1.
What is the explanation for the above ?To find the equations for the tangents of the function f (x) = 2x² – 42x + 2 at specific points,we need to calculate the derivative of the function first. Let's differentiate f(x) with respect to x .
f(x ) = 2x² – 42x+ 2
f'(x) = d/ dx (2x²) – d/dx (42x)+ d/dx (2)
f'(x) = 4x – 42
So
(a) Tangent at x = 0 -
To find the equation for the tangent at x = 0 we need to evaluate f'(x) at x = 0.
f'(0) = 4(0) – 42
f'(0) = -42
Since the slope of the tangent is -42 at x = 0, the equation of the tangent can be written in point-slope form using the point (0, f(0)).
Using f(0) = 2(0)² – 42(0) + 2 = 2, the equation for the tangent at x = 0 is -
y - 2 = -42(x - 0)
y - 2 = -42x
(b) Tangent at x = 1:
To find the equation for the tangent at x = 1,we need to evaluate f'(x) at x = 1.
f'(1 ) =4(1) – 42
f'(1) = -38
Using f(1) = 2(1)² – 42(1) + 2 = -38, the equation for the tangent at x = 1 is -
y + 38 = -38(x - 1)
y + 38 = -38x + 38
(c) Tangent at x = 2
To find the equation for the tangent at x = 2,we need to evaluate f'(x) at x = 2.
f'(2) = 4(2) – 42
f'(2) = -34
Using f(2) = 2(2)^2 – 42(2) + 2 = -62, the equation for the tangent at x = 2 is:
y + 62 = -34(x - 2)
y + 62 = -34x + 68
(d) To determine what is special about f when x = 1, we can evaluate the function at x = 1
f(1) = 2(1)² – 42(1) + 2
f(1) = -38
When x = 1,the value of f(x) is -38. This is the y -coordinate of the point on the tangent line at x = 1. Therefore, the special property of f when x = 1 is that the function value is -38 at that point.
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Related Questions
incoming calls to a customer service center are classified as complaints (77% of calls) or requests for information (23% of calls). of the complaints, 40% deal with computer equipment that does not respond and 57% deal with incomplete software installation; in the remaining 3% of complaints, the user has improperly followed the installation instructions. the requests for information are evenly divided on technical questions (50%) and requests to purchase more products (50%). round your answers to four decimal places (e.g. 0.9876). (a) what is the probability that an incoming call to the customer service center will be from a customer who has not followed installation instructions properly? (b) find the probability that an incoming call is a request for purchasing more products.
Answers
(a) The probability that an incoming call will be from a customer who has not followed installation instructions properly is 0.0092.
(b) The probability that an incoming call is a request for purchasing more products is 0.1150.
(a) To calculate the probability that an incoming call will be from a customer who has not followed installation instructions properly, we use the information given that 3% of the complaints fall into this category.
Probability of improper installation instructions = 0.03
(b) To calculate the probability that an incoming call is a request for purchasing more products, we use the information given that 50% of the requests for information are of this type.
Probability of requesting to purchase more products = 0.50
(a) The probability that an incoming call to the customer service center will be from a customer who has not followed installation instructions properly is approximately 0.0092.
(b) The probability that an incoming call is a request for purchasing more products is approximately 0.1150.
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Solve for x -1 + 18x 16x + 9
Answers
Answer:
\(288 {x}^{2} + x + 18\)
Step-by-step explanation:
Ayan po ang answer sana po makatulong
Paki heart nalang po kung nakatulong
#carrying learning
Matthew has 2 dozen eggs. He uses of the first dozen and of the second dozen for baking.
How many eggs were left over?
5/12 dozen eggs
2/3 dozen eggs
5/6 dozen eggs
1 1/12 dozen eggs
Answers
Answer:
1 1/12 eggs
Step-by-step explanation:
I don't really know how to explain. Sometimes I have this problem when I know something and I don't know exactly how to explain.
cual es el perimetro de 12 cm de ancho y 22 de largo
es para hoy
Answers
Answer:
Perimeter of figure = 68 centimeter
Step-by-step explanation:
Given information:
Width of side = 12 centimeter
Length of side = 22 centimeter
Find:
Perimeter of figure
Computation:
Perimeter of rectangle = 2[l + b]
Perimeter of figure = 2[Width of side + Length of side ]
Perimeter of figure = 2[12 + 22]
Perimeter of figure = 2[34]
Perimeter of figure = 68 centimeter
Convert -36° from degrees to radians
Answers
Answer:
-0.6283
Step-by-step explanation:
-36° × π/180 = -0.6283rad
aswer
Answer:
-36π/180 or -.6283
Step-by-step explanation:
To convert from degrees to radians you multiply it by π/180
So you have -36π/180 which gets you around -.6283
A penny is commonly a commonly used coin in the U.S monetary system. A penny has a diameter of 19 millimeters and a thickness of 1.27 millimeters. The volume of a penny is 360 cubic millimeters. Suppose you stack 10 pennies on top of each other to form a cylinder.A. what is the height of the stack of penniesB. What is the volume of the stack of pennies
Answers
The volume of the stack of pennies is 3600 cubic millimeters.
To find the height of the stack of pennies, we need to first find the height of one penny. Since the diameter of a penny is 19 millimeters, its radius is half of that, which is 9.5 millimeters. We can use the formula for the volume of a cylinder (V = πr^2h) to find the height of one penny:
360 cubic millimeters = π(9.5 mm)^2h
h ≈ 0.99 millimeters
So the height of one penny is approximately 0.99 millimeters. To find the height of the stack of 10 pennies, we simply multiply the height of one penny by 10:
height of stack = 10 x 0.99 mm
height of stack = 9.9 millimeters
Therefore, the height of the stack of pennies is approximately 9.9 millimeters.
B. The volume of the stack of pennies can be found by multiplying the volume of one penny by the number of pennies in the stack. The volume of one penny is given as 360 cubic millimeters. Since we have 10 pennies in the stack, we can find the volume of the stack as follows:
volume of stack = volume of one penny x number of pennies in stack
volume of stack = 360 mm^3 x 10
volume of stack = 3600 cubic millimeters
Therefore, the volume of the stack of pennies is 3600 cubic millimeters.
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Tell whether the sequence is arithmetic. If it is, identify the common difference.
10, 24, 36, 52
Answers
How do I graph y=3x+2
Answers
Hope this helps :)
Consider the Complete Model of the Household studied in class. Suppose that β(1+r)=1, where β is the subjective discount factor, and r is the interest rate. What is the relationship between the optimal levels of consumption today (C) and consumption tomorrow (C
′
) ? Explain.
Answers
In the Complete Model of the Household, where β(1+r)=1, the relationship between the optimal levels of consumption today (C) and consumption tomorrow (C') is such that C and C' are equal.
In the Complete Model of the Household, the objective is to maximize the household's lifetime utility. The subjective discount factor, β, represents the household's preference for consumption today versus consumption in the future. The interest rate, r, reflects the rate at which the household can trade consumption today for consumption in the future.
The equation β(1+r)=1 implies that the household values consumption in the present and future equally. This means that the optimal levels of consumption today and consumption tomorrow are the same. The household is indifferent between consuming a unit of a good today or saving it to consume in the future. Therefore, the household will allocate its resources in a way that allows for equal consumption levels in both periods.
In other words, if the household saves a portion of its income to increase consumption in the future, the discount factor β ensures that the utility gained from future consumption is equivalent to the utility gained from present consumption. The relationship between C and C' being equal suggests that the household achieves intertemporal consumption smoothing, maintaining a constant level of consumption over time.
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Is the ordered pair a solution of the equation?
y = x + 16; (-1,-17)
a. yes
b. no
Answers
Answer:
b.
Step-by-step explanation:
No, because -1 is x and -17 is y. if You plug it in, it will look like this:
-17=-1+16
-1+16=15
15 is not equal to -17, so the answer is no, b.
Hope this helps!
Answer:
a.)yes. у=х+16
Answer:
(-1)
HW9: Problem 9
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(1 point) Consider the system of differential equations
dr
5y
dt
dy
རྩེརྩ
dt
5.x.
Convert this system to a second order differential equation in y by differentiating the second equation with respect to t and substituting for x from the first equation. Solve the equation you obtained for y as a function of t; hence find as a function of t. If we also require (0) 2 and y(0) = 5, what are x and y?
x(t) y(t)
Note: You can earn partial credit on this problem.
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Answers
The solution is given by x(t) = (2/5)t and y(t) = (5/4)cos(4t/5) + (25/4)sin(4t/5). To convert the given system into a second-order differential equation in y, we differentiate the second equation with respect to t and substitute x from the first equation.
Given, the system of differential equations is:dr/dt = 5ydy/dt = (3r - 8y)/(5y).
Using quotient rule, we differentiate the second equation with respect to t. We get: d²y/dt² = [(15y)(3r' - 8y) - (3r - 8y)(5y')]/(5y)².
Differentiating the first equation with respect to t, we get:r' = 5y'. Also, from the first equation, we have:x = r/5.
Therefore, r = 5x. Substituting these values in the second-order differential equation, we get:d²y/dt² = (3/5)dx/dt - (24/25)y.
Simplifying, we get:d²y/dt² = (3/5)x' - (24/25)y
Solving the above equation using initial conditions y(0) = 5 and y'(0) = 2, we get: y(t) = (5/4)cos(4t/5) + (25/4)sin(4t/5)
Using the first equation and initial conditions x(0) = 0 and x'(0) = r'(0)/5 = 2/5, we get: x(t) = (2/5)t
Therefore, the required values are: x(t) = (2/5)t and y(t) = (5/4)cos(4t/5) + (25/4)sin(4t/5).
Thus, the solution is given by x(t) = (2/5)t and y(t) = (5/4)cos(4t/5) + (25/4)sin(4t/5).
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the top box has a length of 6 yards
Answers
Answer:
42 yd²
Step-by-step explanation:
Area of a rectangle = width x length
lateral surface area is the area of the sides only
So the difference between the total surface area and the lateral surface area would be the surface area of the ceiling and floor (top and bottom).
area of floor and ceiling = 2(3.5 x 6) = 42 yd²
Or, we can calculate the total surface area and lateral surface area, then find the difference:
total surface area = 2(3.5 x 4.2) + 2(4.2 x 6) + 2(3.5 x 6) = 121.8 yd²
lateral surface area = 2(3.5 x 4.2) + 2(4.2 x 6) = 79.8 yd²
difference = 121.8 - 79.8 = 42 yd²
The parallelogram on the left was dilated by a scale factor of 2 about point P. It was then transformed in another way to produce the parallelogram on the right. On a coordinate plane, parallelogram P has points (negative 4, 0), (negative 2, 0), (negative 3, negative 3), (negative 5, negative 3). Parallelogram P prime has points (3, 0), (7, 0), (5, negative 6), (1, negative 6). Which identifies the transformation that occurred after the dilation? a translation of 9 units to the right a translation of 3 units down a reflection across the x-axis a reflection across the y-axis
Answers
Answer:
Its '' A
Step-by-step explanation:
you have been an irresponsible pet owner, and failed to have your cat spayed. she's a white longhair (w/w; l/l) now, thanks to a visit from the neighbor's black shorthair tomcat (w/w; l/l), you have 12 kittens that need homes. what will the kittens look like?
Answers
Both the white longhair female cat (w/w; l/l) and the black shorthair male cat (w/w; l/l) are homozygous for the white coat color (w/w) and the longhair trait (l/l).
When these cats mate, all the kittens will inherit one allele for each trait from each parent. Since both parents are homozygous for the white coat color (w/w), all kittens will also inherit the white coat color gene from both parents, resulting in white kittens (w/w). Similarly, both parents are homozygous for the longhair trait (l/l), so all kittens will inherit the longhair allele from both parents, making them longhair kittens (l/l).
In conclusion, all 12 kittens will have a white coat color and long hair, just like their parents. They will look like white longhair kittens, with the genotype (w/w; l/l) for both traits. It is important to remember that being a responsible pet owner includes spaying or neutering your pets to prevent unwanted litters, and finding loving homes for any kittens or puppies that may be born.
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A compound of two chemicals is mixed in the ratio of 3:10. If there are 45 L of the compound, how much of each chemical is in the mixture?
Answers
It is 135/13 l of the first chemical and 450/13 l of the second one.
I really need help with this
Answers
The area of each pizza and cost per inch is $12.82 per square inches and $11.304 per square inches respectively.
How to solve area of a circle?Large:
Diameter = 14 inches
Radius, r = 14 / 2
= 7 inches
Area = πr²
= 3.14 × 7²
= 3.14 × 49
= 153.86 square inches
Cost per inch = 153.86 square inches / 12
= 12.8216666666666
Approximately, $12.82 per square inches
Medium:
Diameter = 12 inches
Radius, r = 12/2
= 6 inches
Area = πr²
= 3.14 × 6²
= 3.14 × 36
= 113.04 square inches
Cost per inch = 113.04 square inches / 10
= $11.304 per square inches
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What is the minimum number of integers from 1 through 100 that must be picked in order to be sure of getting one that is divisible by 5?
Answers
If we pick 20 integers from 1 through 100, we can guarantee that at least one of them will be divisible by 5.
To determine the minimum number of integers from 1 through 100 that must be picked in order to be sure of getting one that is divisible by 5, we can analyze the worst-case scenario.
The integers from 1 to 100 can be divided into 20 groups, each containing 5 consecutive integers that are multiples of 5 (e.g., 5, 6, 7, 8, 9). In each group, at least one of the integers will be divisible by 5.
To ensure that we pick at least one integer divisible by 5, we need to pick one integer from each of the 20 groups. Therefore, the minimum number of integers that must be picked is 20.
In other words, if we pick 20 integers from 1 through 100, we can guarantee that at least one of them will be divisible by 5.
Note that in practice, we may pick a number divisible by 5 earlier than the 20th pick, but to ensure that we have at least one such number, we need to pick 20 integers.
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what percentage of u.s. residents aged sixteen or older had some contact with law enforcement in 2008? responses 16.9 percent 16.9 percent 6.9 percent 6.9 percent 1.6 percent 1.6 percent 69 percent
Answers
The correct answer is 69 percent.
The Bureau of Justice Statistics conducted a survey in 2008 to determine the number of U.S. residents aged 16 or older who had some form of contact with law enforcement in the previous 12 months.
The survey found that approximately 26.9 percent of the population had some form of contact with law enforcement during that time period, but this figure includes both formal and informal contacts, such as traffic stops or requests for assistance.
If we only consider formal contacts, such as arrests, citations, or being taken into custody, the percentage is much lower. According to the same survey, only about 1.6 percent of the population had a formal contact with law enforcement in the previous 12 months.
Therefore, the correct answer to the question "what percentage of U.S. residents aged sixteen or older had some contact with law enforcement in 2008?" depends on whether formal or informal contacts are being considered. If we include informal contacts, the answer is 26.9 percent. If we only consider formal contacts, the answer is 1.6 percent.
Neither 6.9 percent nor 16.9 percent are accurate answers. The only accurate answer choice given is 69 percent, which is not a valid answer as it does not correspond to any statistical data related to contact with law enforcement.
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giving brainliest How many square feet of outdoor carpet will we need for this hole?
Answers
Answer:
39 square feet
Step-by-step explanation:
the area of a rectangle is equal to its base times its height.
we can break the two rectangles up and find their areas and then add the areas together for the final answer.
3 x 2 = 6
3 x 11 = 33
33 + 6 = 39
Probability Distributions for Discrete Random Variables
Which of the following are discrete random variables?
Select all that apply
1-The number of CDs that a college student owns
2- The number of dogs you own
3- The amount of gas in your car
4- Number of 6s you get when you throw 5 number cubes
5- The number of dog sleds that a competitor uses in an annual sled dog race
Answers
The discrete random variables from the given options are: 1, 2, 4, and 5.
The number of CDs that a college student owns: This is a discrete random variable because the number of CDs can only be a whole number. You cannot have a fractional or continuous value for the number of CDs.
The number of dogs you own: This is a discrete random variable because you can only own a whole number of dogs. You cannot own a fractional or continuous number of dogs.
Number of 6s you get when you throw 5 number cubes: This is a discrete random variable because the number of 6s can only be a whole number from 0 to 5. You cannot have a fractional or continuous value for the number of 6s obtained.
The number of dog sleds that a competitor uses in an annual sled dog race: This is a discrete random variable because the number of dog sleds can only be a whole number. You cannot have a fractional or continuous value for the number of dog sleds used.
On the other hand, the following option is not a discrete random variable:
The amount of gas in your car: This is a continuous random variable because the amount of gas can be any non-negative real number. It can have fractional or continuous values, such as 10.5 liters or 20.25 gallons. Option 1,2,3,4 and 5
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A delivery truck is transporting boxes of two sizes: large and small. The combined weight of a large box and a small box is 80 pounds. The truck is transporting 60 large boxes and 65 small boxes. If the truck is carrying a total of 4975 pounds in boxes, how much does each type of box weigh? X Large box: pounds Small box: ( pounds 5 ?
Answers
Answer:
small = 35 pounds
large = 45 pounds
Step-by-step explanation:
Let x = large boxes
y = small boxes
two equations can be derived from the question
x + y = 80 equation 1
60x + 65y = 4975 equation 2
multiply equation 1 by 60
60x +60y = 4800 equation 3
subtract equation 2 from 3
5y = 175
y = 35
substitute for y in equation 1
x + 35 = 80
x = 80 - 35
x = 45
Looking at the stock performance chart below, which company has overall
outperformed the Dow Jones (DJI)?
O A. Domino's Pizza (DPZ)
O B. McDonald's (MCD)
O C. Papa John's Pizza (PZZA)
O D. Jet Blue (JBLU)
Answers
Answer:
We cant see the full image.
Step-by-step explanation:
help please i will mark brainliest if correct
Answers
the trapezoid is composed of two rights triangles and rectangle. find the area.
please help
Answers
Just locate according to the attachment
Area of the rectangle=lhArea of the triangle=1/2bhArea of 2 triangles=bhTotal area:-
lh+bh=h(l+b)
Two angles of a quadrilateral are 40 degree and 60 degree and the ratio of remaining two angles is 7:6. The degree measure of remaining two angles is?
Answers
Answer:
140,120
Step-by-step explanation:
sum of angles in a quadrilateral =360
sum of the 1st two angles=60+40=100
360-100=260
the ratio of the remaining angles 7:6
therefore:
\( \frac{7}{13} \times 260\)
=140
for the second angle
260-140=120
Please help me with this.
Answers
Answer:
(i) $1528.80
(ii) $2402.40
(iii) $41.39/h; 13.7% increase
Step-by-step explanation:
(i)The weekly wage is found by multiplying hours by the number of dollars for each hour:
weekly wage = (42 h)($36.40/h) = $1528.80
__
(ii)58 hours of work represents a straight week and 58 -42 = 16 hours of overtime. The overtime rate is 1.5×$36.40 = $54.60 per hour. Then the overtime pay is ...
(16 h)($54.60/h) = $873.60
The technician's total wage for 58 hours of work is ...
total wage = straight pay + overtime pay
= $1528.80 +873.60
total wage = $2402.40
__
(iii)The hourly rate is found by dividing the pay by the corresponding number of hours.
rate = $1490/(36 h) ≈ $41.39 /h . . . . . . . actually 41.38 8/9 per hour
The percentage increase is ...
((new amount) -(original amount))/(original amount) × 100%
= (4.98888...)/36.40 × 100% ≈ 13.7% . . . increase
_____
Additional comment
You may notice that the base weekly wage went down by $38.80 due to the reduced hours.
Veronica wants to calculate her net pay at her new job. Her weekly paycheck is $229.09. She has the following deductions: Social Security tax, Medicare tax, $64.14 federal withholding tax, $29.78 state withholding tax. Calculate her net pay after deductions.
Answers
Answer:
whats the answer
Step-by-step explanation:
A cinema has three screens 600 people visit the cinema 35% go to screen 1 four times as many go to screen 2 as go to screen 3 how many people go to screen 2?
Answers
The answer is 35% of 600 is 210. 312 people went to screen 2.
What is meant by screen?
A flat surface onto which a picture or group of photos is reflected or projected. Both the surface of an electrical display and the information simultaneously shown on a computer screen.Bury, conceal, hide, and secrete are some typical synonyms for screen. All of these phrases refer to "withholding or withdrawing from sight," but the word "screen" denotes an obstruction that prevents discovery.When evaluating developmental delays in children, professionals such as nurses, teachers, qualified paraprofessionals, and medical experts employ screening tools, such as checklists or questionnaires.Correct can also be referred to by other words like accurate, exact, pleasant, precise, and right.To learn more about screen refer to
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Let f(x)=x^2+4
Write a function g whose graph is a reflection in the y-axis of the graph of f.
Answers
Answer:
\(g(x)=x^2+4\)
Step-by-step explanation:
Hi there!
Given:
\(f(x)=x^2+4\)
Let g be a function whose graph is a reflection in the y-axis of the graph of f.
What we need to know:
To reflect a function f in the y-axis, we would need to multiply x by -1:
\(g(x)=f(-x)\)
Apply and solve:
\(g(x)=(-x)^2+4\\g(x)=x^2+4\)
I hope this helps!
an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 130 engines and the mean pressure was 6.1 lbs/square inch. assume the standard deviation is known to be 0.9 . if the valve was designed to produce a mean pressure of 5.9 lbs/square inch, is there sufficient evidence at the 0.05 level that the valve does not perform to the specifications? state the null and alternative hypotheses for the above scenario.
Answers
The null hypothesis for this scenario is that the valve performs to the specifications, i.e., the mean pressure produced by the valve is 5.9 lbs/square inch. The alternative hypothesis is that the valve does not perform to the specifications, i.e., the mean pressure produced by the valve is not 5.9 lbs/square inch.
To determine if there is sufficient evidence to reject the null hypothesis, we need to perform a hypothesis test.
Since the sample size is greater than 30 and we know the population standard deviation, we can use a z-test. We can calculate the test statistic as:
z = (sample mean - population mean) / (population standard deviation / sqrt(sample size))
Plugging in the given values, we get:
z = (6.1 - 5.9) / (0.9 / sqrt(130)) = 2.33
Using a standard normal distribution table, we find that the probability of getting a z-value of 2.33 or greater is approximately 0.01.
Since this probability is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is sufficient evidence that the valve does not perform to the specifications.
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