find the curve in the xy plane that passes through the point (4,7) and whose slope at each point is
Answers
The equation of the curve is y = x² - 4x + 3
How to calculate the curve in xy plane?Since we are given the slope of the curve at each point, we can use integration to find the equation of the curve. Let's denote the equation of the curve as y = f(x).
The slope of the curve is given by dy/dx = 2x - 4. We can integrate this expression with respect to x to obtain an expression for f(x):
∫dy = ∫(2x - 4)dx
y = x² - 4x + C
where C is the constant of integration.
To determine the value of C, we use the fact that the curve passes through the point (4,7):
7 = 4² - 4(4) + C
C = 7 + 4(4) - 16 = 3
Thus, the equation of the curve is y = x²- 4x + 3.
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Related Questions
a local restaurant sends a 20% off coupon to its email subscribers. based on past data, what is the typical amount that customers with certain incomes spend when they use the coupon?
Answers
The following is a supervised model.
Here we have to find that the following information given is of the supervised or unsupervised model.
Supervised model:
In the supervised model, we create a function (or model) by using labeled training data that consists of input data and a wanted output. The supervision comes in the form of the wanted output, which in turn lets you adjust the function based on the actual output it produces.
Here we are provided that a local restaurant sends a 20% off coupon to its email subscribers and it is asked to find the typical amount that customers with certain incomes sped when they use the coupon.
Therefore the input data and a wanted output is given so the following is a supervised model.
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The complete question:
Determine if the following is a supervised or unsupervised mode. A local restaurant sends a 20% off coupon to its email subscribers. based on past data, what is the typical amount that customers with certain incomes spend when they use the coupon?
what is the term for a procedure or set of rules to solve a problem as an alternative to mathematical optimization?
Answers
The term for a procedure or set of rules to solve a problem as an alternative to mathematical optimization is called a heuristic.
A heuristic is a procedure or set of rules to solve a problem as an alternative to mathematical optimization.
A heuristic is an approach to problem-solving that uses a practical and efficient method to make decisions, which often leads to a satisfactory result but does not guarantee the best solution.
In essence, a heuristic is an algorithm that provides a practical solution for a problem that is difficult to solve with precise mathematical optimization.
It's a method for finding a solution that works, even if it isn't the best possible one.
its a Heuristics are often used in situations where finding the exact optimal solution would require excessive computational resources or time. Instead, heuristics provide approximate solutions that are often "good enough" for practical purposes.
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What is the name of the green segment in the hyperbola below
Answers
The Length of the conjugate axis is equal to 2b. The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola.
In a hyperbola, the name of the green segment is called the transverse axis. The transverse axis is the longest distance between any two points on the hyperbola, and it passes through the center of the hyperbola. It divides the hyperbola into two separate parts called branches.
The transverse axis of a hyperbola lies along the major axis, which is perpendicular to the minor axis. Therefore, it is also sometimes called the major axis.
The other axis of a hyperbola is called the conjugate axis or minor axis. It is perpendicular to the transverse axis and passes through the center of the hyperbola. The length of the conjugate axis is usually shorter than the transverse axis.In the hyperbola above, the green segment is the transverse axis, and it is represented by the letters "2a". Therefore, the length of the transverse axis is equal to 2a.
The blue segment is the conjugate axis, and it is represented by the letters "2b".
Therefore, the length of the conjugate axis is equal to 2b.The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola. In particular, the distance between the two branches of the hyperbola is determined by the length of the transverse axis.
If the transverse axis is longer, then the branches of the hyperbola will be further apart, and the hyperbola will look more stretched out. Conversely, if the transverse axis is shorter, then the branches of the hyperbola will be closer together, and the hyperbola will look more compressed.
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Lillian wants to ride her bicycle 23.4 miles this week. She has already ridden 12 miles. If she rides for 3 more days, write and solve an equation which can be use x, the average number of miles she would have to ride each day to meet her go
Answers
9514 1404 393
Answer:
3.8 miles
Step-by-step explanation:
Lillian wants her mileage total to be ...
12 +3x = 23.4 . . . . an equation that can be used to find x
4 + x = 7.8 . . . divide by 3
x = 3.8 . . . . . . subtract 4
Lillian would have to ride an average of 3.8 miles each day to reach her goal.
Answer:
Hope it helps!
Step-by-step explanation:
Equation: 12+3x=23.4
Answer: x=3.8
a cone with volume 2880 m³ is dilated by a scale factor of 14. what is the volume of the resulting cone? enter your answer in the box.
Answers
For a cone with a volume 2880 m³, which is dilated by a scale factor of 14, the volume of the resulting cone is=2,744,832 m³.
The original volume of the cone is 2880 m³. It is given that the cone is dilated by a scale factor of 14.
The formula to find the volume of a cone is
V = (1/3)πr²h.
We know that the volume of a cone depends on the radius and height. When a cone is dilated by a scale factor, both the radius and height are multiplied by that scale factor.
So, the new volume can be calculated using the following formula:
New Volume = (scale factor)³ x (original volume)
Substituting the given values, we get:
New Volume = 14³ × 2880
New Volume = 2,744,832 m³
Therefore, the volume of the resulting cone is 2,744,832 m³.
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-7(w+4) +2w - 15 simplify
Answers
Answer:
w=-8.6 is your answer
-5w-43. is the simple version
Step-by-step explanation:
First distrubute the -7 and set equal to 0 so that we can move the w to the other side.
-7w-28+2w-15=0
-5w-43=0
add 43 to both sides so you can slove for w
-5w=43
divide both sides by -5 to isolate the w
w=-8.6
Find two other pairs of polar coordinates of the given polar coordinate, one with
r > 0
and one with
r < 0.
Then plot the point.
(a)
(3, π/4)
(b)
(2, −2π/3)
(c)
(−2, π/6)
Answers
Step-by-step explanation:(a) To find two other pairs of polar coordinates of (3, π/4):
One with r > 0: (3, 9π/4)
One with r < 0: (-3, 5π/4)
To plot the point (3, π/4), we start at the origin and move 3 units along the line that makes an angle of π/4 radians with the positive x-axis.
(b) To find two other pairs of polar coordinates of (2, -2π/3):
One with r > 0: (2, 4π/3)
One with r < 0: (-2, π/3)
To plot the point (2, -2π/3), we start at the origin and move 2 units along the line that makes an angle of -2π/3 radians (which is the same as 4π/3 radians) with the positive x-axis.
(c) To find two other pairs of polar coordinates of (-2, π/6):
One with r > 0: (2, 7π/6)
One with r < 0: (-2, 19π/6)
To plot the point (-2, π/6), we start at the origin and move 2 units in the direction that makes an angle of π/6 radians with the positive x-axis, but since r is negative, we move in the opposite direction. So we end up at a point on the line that makes an angle of 7π/6 radians with the positive x-axis.
A recent study reported that 60% of the children in a particular community were overwoight or obese. Suppose a random sample of 200 public school children is taken from this community. Assume the sample was taken in such a way that the conditions for using the Central Limit Theorem are met. We are interested in finding the probability that the proportion of overveightfobese children in the sample will be greater than 0.57. Complete parts (a) and (b) below. a. Before doing any calculations, determine whether this probability is greater than 50% or less than 50%. Why? A. The answer should be less than 50%. because 0.57 is less than the population proportion of 0.60 and because the sampling distribution is approximately Normal. B. The answer should be greater than 50%, because the resulting z-score will be positive and the sampling distribution is approximately Normal. C. The answer should be greater than 50%, because 0.57 is less than the population proportion of 0.60 and because the sampling distribution is approximately Normal. 0. The answer should be less than 50%, because the resulting z-score will be negative and the sampling distribution is approximately Normal.
Answers
The probability that the proportion of overweight or obese children in the sample will be greater than 0.57 is less than 50%.
The first paragraph summarizes the answer, stating that the probability is less than 50% because 0.57 is less than the population proportion of 0.60, and the sampling distribution is approximately normal.
In the second paragraph, we can explain the reasoning behind this conclusion. The Central Limit Theorem states that for a large sample size, the sampling distribution of the sample proportion will be approximately normal, regardless of the shape of the population distribution. In this case, the sample was taken in a way that meets the conditions for using the Central Limit Theorem.
Since the population proportion of overweight or obese children is 0.60, any sample proportion below this value is more likely to occur. Therefore, the probability of obtaining a sample proportion greater than 0.57 would be less than 50%. This is because the resulting z-score, which measures how many standard deviations the sample proportion is away from the population proportion, would be negative.
To summarize, the probability of the proportion of overweight or obese children in the sample being greater than 0.57 is less than 50% because 0.57 is less than the population proportion of 0.60, and the sampling distribution is approximately normal.
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When Mr. Morgan preheated his oven, the oven's temperature rose 3 degrees in of a
minute. At that rate, how much will the oven heat up in 1 minute?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
degrees
Answers
Answer:
it would be 18 in 1 minute
Suppose bob's exam score was at the 80th percentile on an exam whose mean was 90. what was bob's exam score?
Answers
The mean score of 90, and percentile of Bob's score of 80, gives Bob's exam score as approximately 92.5%
What is the formula that gives the exam score from the percentile?The Z-Score of the 80th percentile is 0.8416
The formula for Z-Score is presented as follows;
\(z = \frac{x - \mu}{ \sigma} \)
Where;
\( \sigma = The \: standard \: deviation\)
\( \mu = The \: mean = 90\%\)
x = The given score
Taking the mean as a proportion, we have;
\( \sigma = \sqrt{\frac{\mu \cdot (1-\mu)}{n}}\)
Which gives;
\( \sigma = \sqrt{\frac{0.9 \times (1-0.9)}{100}}= 0.03\)
Therefore, when z = 0.8416, gives;
\(0.8416 = \frac{x - 0.9}{ 0.03} \)
x = 0.8416 × 0.03 + 0.9 ≈ 0.925
Therefore;
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Mr. collins counts 54 Cartons and 5 boxes of paper clips Each carton contains 8 boxes a box of paper clips cost $2How many How many boxes are clips does he have?
Answers
The number of boxes of clips that Mr. Collins has is 437 boxes.
In order to determine the number of boxes of clips that Mr. Collins has, we have to determine the number of boxes of clips in the 54 cartons.
The boxes of clips in the carton can be determined by multiplying 54 by 8
The boxes of clips in the carton = 54 x 8 = 432
The second step is to add 432 to 5.
432 + 5 = 437 boxes
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Determine the number of x-intercepts of the graph of f(x)-ax²+bx+c (a 0), based on the discriminant of the related equation f(x)-0. (Hint: Recall that the discriminant is b²-4ac.) f(x)-3x²-3x+6
Answers
The graph of f(x) = 3x² - 3x + 6 does not intersect the x-axis. It does not have any x-intercepts.
The number of x-intercepts of the graph of f(x) = ax² + bx + c can be determined based on the discriminant of the related equation f(x) = 0.
The discriminant (Δ) is given by the formula: Δ = b² - 4ac.
In the given equation, f(x) = 3x² - 3x + 6, we can compare it with the standard form of the quadratic equation f(x) = ax² + bx + c. Here, a = 3, b = -3, and c = 6.
Calculating the discriminant:
Δ = (-3)² - 4 * 3 * 6
Δ = 9 - 72
Δ = -63
The discriminant (Δ) is negative (-63) in this case. When the discriminant is negative, the quadratic equation does not have any real roots or x-intercepts. Instead, it has complex roots.
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What is the length of BC in the right triangle below?
12
16
OA. 4
OB. 28
OC. 20
OD. 400
OE. 96
OF. √96
Answers
Answer:
C. 20
Step-by-step explanation:
Use the Pythagorean theorem which is \(a^{2} +b^{2} =c^{2}\).
\(a^{2}\) and \(b^{2}\) are the sides of the triangle squared, AB and AC. \(c^{2}\) is the hypotenuse (the slanted side of the triangle) or BC.
So, \(12^{2} + 16^{2} =400^{2}\). Then you square root 400 to get your answer.
\(\sqrt{400}\) = 20.
20 is your answer.
Where is the graph of f(x)=4[x-3]+2 discontinuos
Answers
Answer:
Below
Step-by-step explanation:
4 [x-3] + 2 = y is not discontinuous anywhere
However 4 / [x-3] + 2 DOES have a discontinuity at x = 3 because this would cause the denominator to be zero <===NOT allowed !!
Solve for the variable
10 + 25a = 75
Please help
Answers
Answer:
a = 2.6
Step-by-step explanation:
10 + 25a = 75
- 10. - 10
25a = 65
÷25. ÷25
a = 2.6
HOPE THIS HELPS
PLZZ MARK BRAINLIEST
Answer:13/5 or 2.6
Step-by-step explanation:
If a 750 ml bottle of juice costs £1.90 and a 1 litre bottle of the same juice costs £2.50 then the 750 ml bottle is better value.
Answers
Answer:
The 1 liter bottle is better value
Step-by-step explanation:
Cost of 750 ml = £1.90
Cost of 1 liter = £2.50
1000 ml = 1 liter
Cost per 250 ml
750 ml / 3 = £1.90 / 3
250 ml = £0.6333333333333
Approximately,
£ 0.633
Cost per 250 ml
1 liter / 4 = £2.50 / 4
250 ml = £0.625
The 750 ml bottle is not a better value
The 1 liter bottle is better value
Look at the figure below: A triangle ABC is drawn. D is a point on BC such that BD is equal to DC. A straight line joins points A and D. This line extend Based on the figure, which pair of triangles is congruent by the Side Angle Side Postulate? a Triangle ABD and triangle ECD b Triangle ABC and triangle ECD c Triangle ABD and triangle ADC d Triangle ADC and triangle ABC
Answers
Answer:
Triangle ABD and triangle ECD (A)
Step-by-step explanation:
For two triangles to have a Side Angle Side Postulate, their corresponding sides and angle in the postulate must be equal.
To determine the pair of triangles that is congruent to the Side Angle Side Postulate let's check the options.
a) Triangle ABD and triangle ECD:
Looking at this two triangles, AB = EC
BD =CD
∠B = ∠D
Since the sides are and angle are equal, they are congruent
For the other options (b-d), you find that the corresponding sides of the two triangles and angle between them are not equal
b) Triangle ABC and triangle ECD
c) Triangle ABD and triangle ADC
d) Triangle ADC and triangle ABC
Answer:
Triangle ABD and triangle ECD (A)
Step-by-step explanation:
Got the answer.
If in δ abc angle a is 50° and angle c is 75°, which triangle is similar to δ abc?.
Answers
The triangle similar to triangle ABC will be the triangle with the corresponding angles as same as 50°, 75°, 55°.
What is triangle?
A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
The sum of two sides of a triangle is greater then the third side. Mathematically -
a + b > c
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given is a triangle ABC in which angle [A] is 50° and angle [C] is 75°
The third angle of the triangle would be -
A + B + C = 180
50 + 75 + C = 180
C = 180 - 125
C = 55°
The triangle similar to triangle ABC will be the triangle with the corresponding angles as same as 50°, 75°, 55°.
Therefore, the triangle similar to triangle ABC will be the triangle with the corresponding angles as same as 50°, 75°, 55°.
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i need the perimeter of this two asap!!
u will get the brainlezt for the best answer
Answers
Answer:
a. 44 cm b. 126 cm
Step-by-step explanation:
a. it is semi circle
perimeter is πd
22/7*14
44 cm
b. it is equilateral triangle
so perimeter is side* 3
42 *3 = 126cm
Answer:
(a) 44 cm (b) 214 cmStep-by-step explanation:
(a)
The figure perimeter it is half of a circle with a diameter d₁=14 cm and two halfs of circle with a diameter d₂=14 cm÷2=7 cm.
The length of a circle is L₀ = πd, where d is the diameter.
Therefore:
\(\bold{L=\frac12d_1+2\cdot\frac12d_2 = \frac12\cdot14\pi+\frac12\cdot2\cdot7\pi=14\pi\,cm\approx44\,cm}\)
(b)
A full circle it is 360°, so the circle sector of 60° is \(\frac{60^o}{360^o}=\frac16\) of the circle. So the arc of 60° is ¹/₆ of the full circle length.
The figure is an equilateral triangle and two 60°-sectors of circles with radiuses of length of the triangle's side (r=42 cm).
Its perimetr it's two radiuses, two arcs of 60° and one side of the triangle.
The length of a circle is L₀ = 2πr, where r is a radius.
Therefore:
\(\bold{L=2r+2\cdot\frac16\cdot 2\pi r+r=3r+\frac23\pi r}\\\\\bold{L=3\cdot42+\frac23\pi\cdot42=(126+28\pi)\,cm\approx214\,cm}\)
2.9(x) = 4x + 8 What is g(8)?
Answers
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\(g(x) = 4x + 8\)
\(g(8) = 4(8) + 8\)
\(g(8) = 32 + 8\)
\(g(8) = 40\)
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Find the length of the segment indicated below
Answers
The length of line segment AB in the triangle using the midsegment theorem is 64.
What is the length of line segment AB?
The Midsegment Theorem states that "the segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side."
From the diagram:
Midsegment = 3x + 5
Third side = 7x + 1
First, we solve for x, using the midsegment theorem:
( 3x + 5 ) = 1/2 × ( 7x + 1 )
Multiply both sides by 2:
2( 3x + 5 ) = ( 7x + 1 )
6x + 10 = 7x + 1
Collect and add like terms:
7x - 6x = 10 - 1
x = 10 - 1
x = 9
Now, we solve for line AB:
Line AB = 7x + 1
Plug in x = 9
Line AB = 7(9) + 1
Line AB = 63 + 1
Line AB = 64
Therefore, the line segment AB is 64.
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Which equations define y as a nonlinear function of x? Select ALL that apply.
Answers
Answer:
c and f
Step-by-step explanation:
4(x+15) = 2(2x+25) has how many solutions?
Answers
Answer: There are no solutions.
Step-by-step explanation: Hope this help :D
____a is a numerical measure that describes a population, whereas a is a numerical measure that describes a sample.
Answers
Central tendency a is a numerical measure that describes a population, whereas a is a numerical measure that describes a sample.
A population refers to the entire group of people or objects that we're interested in studying, while a sample is a smaller group of individuals that we use to represent the larger population.
Now, let's talk about the two numerical measures you mentioned that it is a numerical measure that describes a population.
It's a measure of the central tendency of the data, which means it tells us where the "center" of the data is located.
There are different ways to calculate depending on the type of data we're working with, but one common method is to find the arithmetic mean, which is the sum of all the values divided by the number of values.
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next question get a similar question a car is driving at 85 kilometers per hour. how far, in meters, does it travel in 3 seconds?
Answers
The car travels 70.83 meters in 3 seconds.
To find the distance the car travels in 3 seconds, we first need to convert its speed from kilometres per hour to meters per second.
1 hour = 3600 seconds
1 kilometer = 1000 meters
So, 85 km/hr = 85 x 1000/3600 m/s = 23.61 m/s
Now we can use this speed to find the distance the car travels in 3 seconds:
distance = speed x time
distance = 23.61 m/s x 3 s = 70.83 m
So the car travels 70.83 meters in 3 seconds.
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--The given question is incorrect; the correct question is
"A car is driving at 85 kilometres per hour. How far, in meters, does it travel in 3 seconds?"--
I am confuse on the area for kites help please!!!
Answers
Answer:
20 in
Step-by-step explanation:
Width is half the height, so if the height is 31+9, or 40, then 20 is the width
6) g(n) = n² + 2; Find g(3)
Answers
Answer:
g(3) = 11
Step-by-step explanation:
g(n) = n^2 +2
g(3) = 3^2 +2
g(3) = 9 + 2
g(3) = 11
Solve the equation for x.
x2 = 9
Answers
= 2x = 9
= x = 9 ÷ 2 ( transposing ×2 from LHS to RHS changes ×2 to ÷2 )
= x = 4.5
Therefore , x = 4.5 .
-2 -2
———
x=7
To answer this problem make sure you subtract 2 from each side and 7 is your answer.
PROOF PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
Answers
Answer:
16
Step-by-step explanation:
The formula used to find the area of a triangle is
\( \frac{1}{2} b \times h\)
so the area of the triangle is
\( \frac{1}{2} \times 8 \times 4\)
because 8 is the base and 4 is the height of the triangle
Therefore the area of the triangle is 16
WILL MARK BRAINLIEST!!!! 40 POINTS ACTUAL ANSWERS PLZ!!! LAST QUESTION!!!!
Answers
Answer:
Step-by-step explanation:
the x-intercepts represent that the profit is $0
maximum value represents the highest profit which is $270
increasing intervals: (0, 4)
decreasing intervals: (4, 8)
in order to find the average rate of change, find the x and y coordinates for when x = 1 and x =4. The coordinates are (1, 120) and (4, 270). The average rate of change is basically the slope, which is (270-120)/(4-1) = 160/3= approximately 53.3333. The rate represents the change in profit in $ over the increase of cost of erasers.
As you can see, this a parabola, which consists of going up and down. The constraints of the domain represent that 4 is the best price for eraser because it yields the highest profit. The domain (x values) that are above and below 4 do not yield the best profit.