Given the point (2, 1) on a tangent line to the curve f(x) = x² – 2x + 5 find the point(s) where the tangent touches f(x).
Answers
The two points where the tangent line touches the curve f(x) are:
(2+√3, 7+2√3) and (2-√3, 7-2√3)
How to find the point(s) where the tangent touches f(x)To find the point(s) where the tangent touches f(x), we need to first find the slope of the tangent line.
The slope of a tangent line at a point on a curve can be found by taking the derivative of the function at that point.
So, taking the derivative of f(x) = x² – 2x + 5, we get: f'(x) = 2x - 2
Now, we can find the slope of the tangent line at the point (2,1) by plugging in x=2:
f'(2) = 2(2) - 2 = 2 So the slope of the tangent line is 2.
Next, we can use the point-slope form of a line to write the equation of the tangent line: y - 1 = 2(x - 2) Expanding and simplifying, we get: y = 2x - 3
Now, to find where this tangent line touches the curve f(x), we need to solve for x when y = f(x).
So, we set: 2x - 3 = x² - 2x + 5
Rearranging, we get: x² - 4x + 8 = 0
Using the quadratic formula, we can solve for x:
x = (4 ± √(4² - 4(1)(8))) / (2) x = 2 ± √3
So the two points where the tangent line touches the curve f(x) are:
(2+√3, 7+2√3) and (2-√3, 7-2√3)
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Related Questions
divide snd answer in simplest form: 5/3 divided by 3
Answers
Answer: 8
Step-by-step explanation: I think I am right !? Hope this helps!!
Which angles!!! Need answers 40% of my grade please and thank you
Answers
Answer:
alternate interior angle
How do you find the third side of an inequality of a triangle?
Answers
To find the third side of an inequality of a triangle, you must first use the Triangle Inequality Theorem.
This theorem states that for any triangle, the sum of any two sides of the triangle must be greater than the third side. This means that in order to find the length of the third side, you must subtract the sum of the two known sides from the smaller of the two sides, then the length of the third side will be equal to the difference between these two numbers. For example, if two sides of a triangle have lengths of 4 and 3, the third side must be greater than 1 (4 + 3 = 7 and 4 - 3 = 1). Therefore, the length of the third side must be greater than 1.
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Which statement is true for all functions f(x)?
Answers
Find the volume of the solid enclosed by the paraboloid z = 2 + x2 + (y - 2)2 and the planes z = 1, x = ?2, x = 2, y = 0, and y = 3.
Answers
Main Answer:The volume of the solid enclosed by the paraboloid and the planes is 18.67 cubic units.
Supporting Question and Answer:
How do we calculate the volume of a solid bounded by surfaces using triple integration?
To calculate the volume of a solid bounded by surfaces using triple integration, we set up a triple integral with the integrand equal to 1, representing the infinitesimal volume element. The bounds of integration are determined by the equations defining the surfaces that enclose the solid. By evaluating the triple integral over the specified region, we can find the volume of the solid.
Body of the Solution: To find the volume of the solid enclosed by the paraboloid z = 2 + x^2 + (y - 2)^2 and the planes z = 1, x = -2, x = 2, y = 0, and y = 3, we can set up a triple integral in the given region.
To find the volume,using the triple integral:
V = ∫∫∫ R (1) dz dy dx
where R is the region bounded by the given planes and the paraboloid.
The bounds of integration for x are -2 to 2, for y are 0 to 3, and for z are the lower bound function z = 1 and the upper bound function z = 2 + x^2 + (y - 2)^2.
Setting up the triple integral:
V = ∫ from x = -2 to 2 ∫ from y = 0 to 3 ∫ from z = 1 to 2 + x^2 + (y - 2)^2 (1) dz dy dx
Integrating the innermost integral with respect to z:
V = ∫ from x = -2 to 2 ∫ from y = 0 to 3 [(2 + x^2 + (y - 2)^2) - 1] dy dx
Simplifying the expression inside the integral:
V = ∫ from x = -2 to 2 ∫ from y = 0 to 3 [x^2 + (y - 2)^2 + 1] dy dx
Integrating the inner integral with respect to y:
V = ∫ from x = -2 to 2 [x^2(y) + ((y - 2)^3)/3 + y] evaluated from y = 0 to 3 dx
Substituting the limits of integration for y:
V = ∫ from x = -2 to 2 [x^2(3) + (3 - 2)^3/3 + 3 - (x^2(0) + (0 - 2)^3/3 + 0)] dx
Simplifying further:
V = ∫ from x = -2 to 2 [3x^2 +2/3] dx
Integrating the final integral with respect to x:
V = [(x^3) + (2/3)x] evaluated from x = -2 to 2
Evaluating the expression at the limits:
V = [(2^3) +(2/3) 2] - [((-2)^3) + (2/3)(-2)]
V = (8 +4/3) - (-8 - 4/3)
V = 16+8/3
V =56/3
Final Answer:Therefore, the volume of the solid enclosed by the paraboloid and the given planes is 56/3 cubic units.
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The volume of the solid enclosed by the paraboloid and the planes is 18.67 cubic units.
How do we calculate the volume of a solid bounded by surfaces using triple integration?To calculate the volume of a solid bounded by surfaces using triple integration, we set up a triple integral with the integrand equal to 1, representing the infinitesimal volume element. The bounds of integration are determined by the equations defining the surfaces that enclose the solid. By evaluating the triple integral over the specified region, we can find the volume of the solid.
Body of the Solution: To find the volume of the solid enclosed by the paraboloid z = 2 + x^2 + (y - 2)^2 and the planes z = 1, x = -2, x = 2, y = 0, and y = 3, we can set up a triple integral in the given region.
To find the volume,using the triple integral:
V = ∫∫∫ R (1) dz dy dx
where R is the region bounded by the given planes and the paraboloid.
The bounds of integration for x are -2 to 2, for y are 0 to 3, and for z are the lower bound function z = 1 and the upper bound function z = 2 + x^2 + (y - 2)^2.
Setting up the triple integral:
V = ∫ from x = -2 to 2 ∫ from y = 0 to 3 ∫ from z = 1 to 2 + x^2 + (y - 2)^2 (1) dz dy dx
Integrating the innermost integral with respect to z:
V = ∫ from x = -2 to 2 ∫ from y = 0 to 3 [(2 + x^2 + (y - 2)^2) - 1] dy dx
Simplifying the expression inside the integral:
V = ∫ from x = -2 to 2 ∫ from y = 0 to 3 [x^2 + (y - 2)^2 + 1] dy dx
Integrating the inner integral with respect to y:
V = ∫ from x = -2 to 2 [x^2(y) + ((y - 2)^3)/3 + y] evaluated from y = 0 to 3 dx
Substituting the limits of integration for y:
V = ∫ from x = -2 to 2 [x^2(3) + (3 - 2)^3/3 + 3 - (x^2(0) + (0 - 2)^3/3 + 0)] dx
Simplifying further:
V = ∫ from x = -2 to 2 [3x^2 +2/3] dx
Integrating the final integral with respect to x:
V = [(x^3) + (2/3)x] evaluated from x = -2 to 2
Evaluating the expression at the limits:
V = [(2^3) +(2/3) 2] - [((-2)^3) + (2/3)(-2)]
V = (8 +4/3) - (-8 - 4/3)
V = 16+8/3
V =56/3
Therefore, the volume of the solid enclosed by the paraboloid and the given planes is 56/3 cubic units.
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An ice cream store recorded the flavors of its recent cone sales.
chocolate 10
cookie dough 6
mocha 20
vanilla 8
Considering this data, how many of the next 99 cones sold would you expect to have mocha ice cream?
Answers
The width of a rectangle is 5n−2.5 feet and the length is 2.5n+6 feet. Find the perimeter of the rectangle.
Answers
Answer:
5.0n+7.0
Step-by-step explanation:
Perimeter of a rectangle = 2(L+W)
L is the length = 5n-2.5
W is the width = 2.5n+6
Perimeter of the rectangle = 2(5n-2.5+2.5n+6)
Perimeter of the rectangle = 2(2.5n+3.5)
Perimeter of the rectangle = 5.0n+7.0
Hence the perimeter of the rectangle is 5.0n+7.0
Find the percent of change from the first value to the second. 72: 81 -
is means "From 72 to 81"*
Answers
Answer:
+12.5%
Step-by-step explanation:
This is rather simple. Subtract 72 from 81, then put the difference over 72. Then, multiply that by 100.
(81 - 72)/72 * 100
Subtract 72 from 81 to get 9
9/72 * 100
Multiply 9 by 100 to get 900
900/72
Simplify the above fraction by cancelling out 9.
100/8
Divide 100 by 8 to get 12.5%
The percent of change is +12.5%
You have at most $20.75 to spend at a fair. Rides cost $0.50 each, and games cost $2 each. Let r be numbers of rides and g be numbers of games. Write an inequality that represents the numbers of rides and games you can afford.
Do not include the dollar sign ($) in your inequality.
An inequality is _.
Answers
Answer:
0.5r+2g>=20.75
Step-by-step explanation:
You start a savings account and on the first week you deposit $2. Every
week you add $1 more to the account then the week before. So on the
second week you add $3, on the third week $4. On which week would the
account be worth $560?
Answers
Answer:
558 weeks
Step-by-step explanation:
let x = number of weeks
this equation can be derived from the question
2 + 1x = 560
collect like terms
x = 560 - 2
x = 558
Which ratio equals 224:32?
5:26
28:4
16:2
5:14
Answers
Answer: 28:4
Step-by-step explanation:
If you divide 224 by 32 you’re going to get 7. If you also divide 28 and 4 you’re going to get 7. Hope that helps!
Answer:
option 28:4 is the answer
What ordered pairs are the solutions of the
system of equations shown in the graph below?
Answers
Answer:
The solutions to the graph are (-1,1) and (4,6).
Step-by-step explanation:
Where the line and parabola intersect, or meet, are the solutions.
Points Z, L, and S are:
Answers
Points Z, L, and S are collinear points
How to determine the relationship?When 2 or more points are on a line, the points are said to be collinear.
From the figure, we have:
Points Z, L and S on the same line
This means that they are collinear points
Hence, points Z, L, and S are collinear points
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Help mee!!!!!!!!!!!!
Answers
Answer: its 8n
Step-by-step explanation:
The city of Irvine reported that approximately 75% of residents are over the age of 60. Let X be the number of Irvine residents over the age of 60.From a random sample of 500 Irvine residents, 350 were over the age of 60.What is the sampling distribution of the sample proportion for the sample size of 500?Using the distribution of X from above, what is the probability that at most 350 of the 500 Irvine residents selected will be over the age of 60?What is the probability that at least 350 of the 500 residents in the sample were over the age of 60?What is the probability that between 400 and 475 of the residents were over the age of 60?
Answers
The probability that at most 350 of the 500 Irvine residents selected will be over the age of 60 is 0.9292. The probability that at least 350 of the 500 residents in the sample were over the age of 60 is 0.0708. The probability that between 400 and 475 of the residents were over the age of 60 is 5.88.
The probability that at most 350 of the 500 Irvine residents selected will be over the age of 60 can be found by calculating the z-score for 350 and finding the corresponding probability from a normal distribution table. The z-score for 350 is (350-375)/17 = -1.47. The corresponding probability from a normal distribution table is 0.0708.
The sampling distribution of the sample proportion for the sample size of 500 is a normal distribution with a mean of 0.75 and a standard deviation of \(√[(0.75)(0.25)/500] = 0.017.\)
The probability that at least 350 of the 500 residents in the sample were over the age of 60 can be found by calculating the z-score for 350 and finding the corresponding probability from a normal distribution table. The z-score for 350 is (350-375)/17 = -1.47. The corresponding probability from a normal distribution table is 1 - 0.0708 = 0.9292.
The probability that between 400 and 475 of the residents were over the age of 60 can be found by calculating the z-scores for 400 and 475 and finding the corresponding probabilities from a normal distribution table. The z-score for 400 is (400-375)/17 = 1.47 and the z-score for 475 is (475-375)/17 = 5.88.
The corresponding probabilities from a normal distribution table are 0.9292 and 1.0000, respectively. The probability that between 400 and 475 of the residents were over the age of 60 is 1.0000 - 0.9292 = 0.0708.
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Rewrite, using the distributive
property.
16b-8b = ([?]-8)b = [?]b
![Rewrite, using the distributiveproperty.16b-8b = ([?]-8)b = [?]b](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/9Tmzv11947B9UtnbF6DBvWJp63YQcon7.png)
Answers
Answer:
8b
Step-by-step explanation:
You can factor the b-term out since b-term exists for all terms in the expression. By factoring out, you are basically dividing the factored term off and put it outside of the bracket, thus:
\(\displaystyle{16b-8b=\left(16-8\right)b}\)
Then evaluate and simplify:
\(\displaystyle{\left(16-8\right)b=8\cdot b}\\\\\displaystyle{=8b}\)
Which of the following is not a fundamental identity? A. cot θ = cos θ/sinθ. B. sec θ = 1/cosθ. C. sec^2 + 1 = tan^2θ. D. 1 + cot^2θ = csc^2θ.
Answers
A fundamental identity is an equation that relates the values of the trigonometric functions for a given angle. The equation cot θ = cos θ/sinθ is an example of a fundamental identity.
This identity states that the cotangent of an angle is equal to the cosine of the angle divided by the sine of the angle. The equation sec θ = 1/cosθ is another example of a fundamental identity. This identity states that the secant of an angle is equal to the reciprocal of the cosine of the angle. The equation sec^2 + 1 = tan^2θ is also a fundamental identity. This identity states that the square of the secant of an angle plus one is equal to the square of the tangent of the angle. The equation 1 + cot^2θ = csc^2θ is not a fundamental identity. This equation states that one plus the square of the cotangent of an angle is equal to the square of the cosecant of the angle. This equation is not a fundamental identity because it does not relate the values of the trigonometric functions for a given angle.
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Solve for x if 6(X + 3) = 36 *
Answers
Answer:
6( X + 3 ) = 36
6X + 18 = 36
6X = 36 - 18
X = 18 ÷ 6
X = 3
Thus, the value of X is 3.
Hope it helps,
Thank You.
Answer:
Step-by-step explanation:
6x +18=36
6x+18-18=36-18
6x=18
6x divide by 6 =18 divide 6
x=3
hope this helps please mark brainliest
Plot area (in acres) price (in dollars) bumper crop 222222 89{,}00089,00089, comma, 000 pay dirt 888888 312{,}000312,000312, comma, 000 the corn-er lot 249249249 978{,}000978,000978, comma, 000 which plot of farmland has the lowest price per acre?
Answers
To determine which plot of farmland has the lowest price per acre, we need to calculate the price per acre for each plot using the given area and price values. The plot with the lowest price per acre will be the one with the smallest calculated value.
To calculate the price per acre for each plot, we divide the price by the area. Let's calculate the price per acre for each plot:
For "Bumper Crop":
Price per acre = $89,000 / 222,222 acres ≈ $0.40 per acre
For "Pay Dirt":
Price per acre = $312,000 / 888,888 acres ≈ $0.35 per acre
For "The Corn-er Lot":
Price per acre = $978,000 / 249,249,249 acres ≈ $0.00392 per acre
Comparing the price per acre values, we can see that "Pay Dirt" has the lowest price per acre at approximately $0.35 per acre. Therefore, "Pay Dirt" is the plot of farmland with the lowest price per acre among the given options.
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Plot area (in acres) price (in dollars) bumper crop 222222 89{,}00089,00089, comma, 000 pay dirt 888888 312{,}000312,000312, comma, 000 the corn-er lot 249249249 978{,}000978,000978, comma, 000 which plot of farmland has the lowest price per acre?
3 times minus 4 = what
PLS EXPLAIN HOW TO DO THIS
Answers
Answer:
- 12
Step-by-step explanation:
Answer: -12 If you're trying to do 3 x negative 4.
Step-by-step explanation: I'm not sure what you're trying to do, that algebra stuff or just simply 3 x -4.
need the answer
Find (3x+7)2 .
Answers
Answer:
9x² + 42x + 49
Step-by-step explanation:
Identity
(x + a)² = x² + 2ax + a²In this case, x = 3x and a = 7, so substitute the values.
(3x + 7)²(3x)² + 2(3x)(7) + (7)²9x² + 42x + 49Answer:
\(9x^2 + 42x + 49\)
Step-by-step explanation:
Step 1: Factor out the expression
\((3x + 7)^2\)
\((3x + 7)(3x + 7)\)
\((3x * 3x) + (3x * 7) + (7 * 3x) + (7 * 7)\)
\(9x^2 + 21x + 21x + 49\)
\(9x^2 + 42x + 49\)
Answer: \(9x^2 + 42x + 49\)
Please help me ;-;
What's the next term?
0, 1/3
3, 2
6, 12
9, ?
(Above is supposed to be a table btw)
Answers
Answer:
72
Step-by-step explanation:
Based on the table, the left and the right side have a pattern. When 3 is added to the left side, the right side is multiplied by 6. Since 12 multiplied by 6 is 72, the missing number is 72.
A town with a population of 5,000 grows 3% per year. Find the population at the end of 10 years. Round to the nearest whole number.
Answers
Answer:
6500
Step-by-step explanation:
(3)1% of 5000 = (3)50= 150
150x 10= 1500
1500+5000=6500
Select each expression that is equivalent to 18x + 3.
Answers
Answer:
3(6x + 1)
Step-by-step explanation:
3(6x + 1) =
18x + 3
for a certain manufacturer, the probability of a widget is threaded at 7/12, the probability that it is flanged is 5/8, and the probability that it is both threaded and flanged is 2/9. if a widget is chosen at random, find the probability using formulas that
Answers
Probability of neither threaded nor flanged widget (complement):
P(neither T nor F) = 1 - P(T or F)
To find the probability using formulas, we can apply the principles of probability. Let's denote the events as follows:
T: Widget is threaded
F: Widget is flanged
We are given:
P(T) = 7/12 (probability of threaded widget)
P(F) = 5/8 (probability of flanged widget)
P(T and F) = 2/9 (probability of widget being both threaded and flanged)
Using the formulas for probability, we can find:
Probability of either threaded or flanged widget (union):
P(T or F) = P(T) + P(F) - P(T and F)
= 7/12 + 5/8 - 2/9
Probability of neither threaded nor flanged widget (complement):
P(neither T nor F) = 1 - P(T or F)
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5/9 (y+3)=40 I need help to solve this it’s in algebra
Answers
Answer:
= 69
Step-by-step explanation:
Combine multiplied terms into a single fraction, Distribute, then Multiply all terms by the same value to eliminate fraction denominators.
1) 5/9 ( y + 3 ) = 40 or 5(y + 3) / 9 = 40
2) 5y + 15 / 9 = 40
3) 9 ( 5y + 15 / 9) = 9 40
Find the value of x. 136° (8x + 40) (The figure is not to scale.)
Answers
Answer:
x= 12
Step-by-step explanation:
Hope u understood it
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What is the slope of the line in the graph?
Answers
Answer:
1
Step-by-step explanation:
Pick two points on the line
(0,1) and (1,2)
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 2-1)/(1-0)
= 1/1
=1
Use vector operations to draw the resultant vector. Draw u – v + w
Answers
Based on the above, the graph of the resultant vector is shown in the image attached (x-axis).
What is the graph about?In the graph construction, We need to carry out a sum of vectors and then draw the resultant vector.
Note that the resultant vector need to be <4, 0>
Hence when we view the graph attached, we can say that the vectors areas:
w = <3, 3>
u = <-3, -4>
v = <-4, -1>
So, the sum = u - v + w
Note also that in the sum of the vectors we need to add and subtract the correspondent parts and it will be:
u - v + w
= <-3, -4> - <-4, -1> + <3, 3>
= <-3 + 4 + 3, -4 + 1 + 3>
= <4, 0>
Therefore, Based on the above, the graph of the resultant vector is shown in the image attached (x-axis).
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solve the given differential equation. x^2y'' + 11xy' + 25y = 0
Answers
The general solution of the differential equation is:
y = Ax^-5 + Bx^-5ln(x)
where A and B are constants determined by the initial or boundary conditions.
To solve the differential equation x^2y'' + 11xy' + 25y = 0, we can assume the solution to be of the form y = x^r, where r is a constant.
Then, we have:
y' = rx^(r-1)
y'' = r(r-1)x^(r-2)
Substituting these into the differential equation, we get:
x^2y'' + 11xy' + 25y = x^2r(r-1)x^(r-2) + 11xrx^(r-1) + 25x^r = 0
Dividing both sides by x^2, we have:
r(r-1) + 11r + 25 = 0
Simplifying, we get:
r^2 + 10r + 25 = (r+5)^2 = 0
Therefore, r = -5.
Thus, the general solution of the differential equation is:
y = Ax^-5 + Bx^-5ln(x)
where A and B are constants determined by the initial or boundary conditions.
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