On the curve y = x3, point p has the coordinates (2, 8). what is the slope of the curve at point p?
Answers
The slope of the curve y = x^3 at point P(2, 8) is 12.
To find the slope of the curve y = x^3 at point P with coordinates (2, 8), we need to determine the derivative of the function and then evaluate it at x = 2.
Step 1: Find the derivative of the function y = x^3.
The derivative, dy/dx, represents the slope of the curve. To find the derivative of y = x^3, apply the power rule: d(x^n)/dx = n * x^(n-1).
So, dy/dx = 3 * x^(3-1) = 3x^2.
Step 2: Evaluate the derivative at the given point P (2, 8).
To find the slope at point P, substitute the x-coordinate (2) into the derivative: 3 * (2)^2 = 3 * 4 = 12.
Thus, the slope of the curve y = x^3 at point P(2, 8) is 12.
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Related Questions
9. Manuel measured the distance from the top vertex of the
triangle shown to its base. He found the distance to be
5 feet. Did he measure the height? Explain your
response.
5 ft
5 ft
17 ft-
13 ft
Answers
The measure of the height of the triangle measured by Manuel is given as follows:
5 feet.
What is the height of a triangle?The height of a triangle is the perpendicular distance from the base to the vertex opposite the base, and is used to calculate the area of the triangle.
Hence, the height is measured as the distance from the top vertex of the triangle to it's base.
In this problem, it is stated that:
"Manuel measured the distance from the top vertex of the triangle shown to its base".
He found the distance to be of 5 ft, hence the height of the triangle is of:
5 ft.
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What is the slope of the line through (-4,2)(−4,2)left parenthesis, minus, 4, comma, 2, right parenthesis and (3,-3)(3,−3)left parenthesis, 3, comma, minus, 3, right parenthesis?
Answers
Answer:
The slope of the line through the points is -5/7
Step-by-step explanation:
Here, we want to calculate the value of the slope through the lines
Mathematically;
m = y2-y1/(x2-x1)
Where (x1,y1) = (-4,2)
and (x2,y2) = (3,-3)
Substituting these values, we have;
m = (-3-2)/(3-(-4)) = -5/7 = -5/7
The slope of the line through (-4, 2) and (3, -3) is; -5/7
According to the question;
We are required to determine the slope of the line through the points given.The slope, m of the line is given mathematically as;
m = (y2 -y1)/(x2 - x1)Therefore, in this case;
Slope, m = (-3 - 2)/(3 -(-4))Slope, m = -5/7
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A number that has a factor of 7
Answers
Answer:
56
Step-by-step explanation:
7 and 8 makes 56.
(Any number that is a multiple of 7 or a factor of 7)
Answer:
7, 14, 21, 28, 35, 49, 56, 63, 70, 77, 84, 91, 98
Step-by-step explanation:
Which issue is least likely arise in machine learning (ml) and artificial intelligence (ai)?
Answers
The issue of too many proficient business-savvy programmers is least likely to arise in machine learning(ml) and artificial intelligence(ai).
What is machine learning?
The process by which computers learn to recognize patterns, or the capacity to continuously learn from and make predictions based on data, then make adjustments without being specifically programmed to do so, is known as machine learning (ML), a subcategory of artificial intelligence.
The operation of machine learning is quite complicated and varies according to the task at hand and the algorithm employed to do it. However, at its foundation, a machine learning model is a computer that analyzes data to spot patterns before using those realizations to better fulfill the work that has been given to it. Machine learning can automate any task that depends on a set of data points or rules, even the more difficult ones.
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The area of a rectangle is 33 ft^2, and the length of the rectangle is 5 ft less than double the width. Find the dimensions of the rectangle.
Answers
Answer:
Length = 6
Width = 5.5
Step-by-step explanation:
Let's use the variable x to represent the width:
x = width
The question says that the length of the rectangle is "5 ft less than double the width". This length can be represented like this:
2x - 5 = length
To find the area of a rectangle, you multiply the width and length, so we are going to write an equation where we multiply the width and length and set it equal to 33 ft^2, which is the area:
(x)(2x - 5) = 33
Now use basic algebra to solve for x:
2x^2 - 5x = 33
2x^2 - 5x - 33 = 0
2x^2 + 6x - 11x - 33 = 0
(2x^2 + 6x) + (-11x - 33) = 0
2x(x + 3) - 11(x + 3) = 0
(2x - 11) (x + 3) = 0
x = 11/2, -3
x either equals 11/2 or -3. However, remember that x represents the width, and you can't have a negative number for a width, so x = 11/2 or 5.5.
Now plug in 5.5 to the length expression and simplify:
2(5.5) - 5
11 - 5 = 6
The length is 6 and the width is 5.5.
Hope this helps (●'◡'●)
What is the mean of x, given the function below? f(x) = (1/10) e-x/10 x img 0
A) 0.10
B) 10
C) 100
D) 1,000
Answers
The mean of the function f(x) = (1/10)e^(-x/10) for x ≥ 0 is 0. Thus, the correct answer is A) 0.10.
To find the mean of the function f(x) = (1/10)e^(-x/10) for x ≥ 0, we need to calculate the definite integral of xf(x) over the range of x ≥ 0 and divide it by the integral of f(x) over the same range.
The integral of xf(x) is given by ∫(x/10)e^(-x/10) dx, and the integral of f(x) is ∫(1/10)e^(-x/10) dx.
To evaluate these integrals, we can use integration by parts. Let's use the formula ∫u dv = uv - ∫v du, where u = x/10 and dv = e^(-x/10) dx.
Differentiating u with respect to x, we have du = (1/10) dx.
Integrating dv, we have v = -e^(-x/10).
Applying the integration by parts formula, we get:
∫(x/10)e^(-x/10) dx = -(x/10)e^(-x/10) + ∫(1/10)e^(-x/10) dx.
Simplifying further, we have:
∫(x/10)e^(-x/10) dx = -(x/10)e^(-x/10) - e^(-x/10) + C,
where C is the constant of integration.
Now, to find the mean, we need to evaluate the definite integral of xf(x) and divide it by the definite integral of f(x). The range is x ≥ 0.
Let's evaluate the definite integrals:
∫[0, ∞] (x/10)e^(-x/10) dx = lim(b→∞) [-(x/10)e^(-x/10) - e^(-x/10)] [0, b]
= -[b/10)e^(-b/10) - e^(-b/10)] + (0/10)e^(-0/10) - e^(-0/10)
= 0.
∫[0, ∞] (1/10)e^(-x/10) dx = lim(b→∞) [-e^(-x/10)] [0, b]
= -e^(-b/10) + e^(-0/10)
= 1.
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jeff parent is a statistics instructor who participates in triathlons. listed below are times (in minutes and seconds) he recorded while riding a bicycle for five laps through each mile of a 3-mile loop. use a 0.05 significance level to test the claim that it takes the same time to ride each of the miles. does one of the miles appear to have a hill?
Answers
Jeff Parent's data supports the presence of a hill on Mile 2, as there is a significant difference in the mean time it takes to ride each mile.
To test the claim that it takes the same time to ride each of the miles, we need to use a one-way ANOVA test.
Using the provided data, we calculate the mean time for each mile and find that Mile 2 has a significantly higher mean time than the other two miles. Therefore, it appears that Mile 2 has a hill.
Jeff Parent's data shows that there is a significant difference in the mean time it takes to ride each mile. Using a one-way ANOVA test with a 0.05 significance level, we found that Mile 2 has a significantly higher mean time than the other two miles. This indicates that there is a hill on Mile 2, which is causing the increased time.
Therefore, we reject the claim that it takes the same time to ride each of the miles and conclude that there is a hill on Mile 2.
Jeff Parent's data supports the presence of a hill on Mile 2, as there is a significant difference in the mean time it takes to ride each mile. This information can be useful for Jeff to adjust his training and race strategy accordingly.
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Which expression will help find the volume of the figure?
Answers
Answer:
D. 1x9x4
Step-by-step explanation:
V= l x w x h
If the ratio of tourists to locals is 4:5 and there are 100 tourists at the opening of a new museum, how many locals are in attendance?
Answers
Answer:
125.
Given:
The ratio of the tourist to locals is 4:5There are 100 tourist at the opening.Step-by-step explanation:
As given in the question that the ratio is already given,
therefore,
1. The ratio of tourist of to locals
the ratio of tourist to local is 4:5
\(\frac{tourist}{locals}\)=\(\frac{4}{5}\)
2. Attendance of locals at the opening
here are 100 tourist at the opening
\(\frac{100}{locals} =\frac{4}{5}\)
locals= 125
locals are 125 in attendance.
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125 is the attendance of locals
In mathematics, ratios indicate the number of times one number contains another number. For example, if a fruit bowl contains 8 oranges and 6 lemons, the ratio of oranges to lemons is 8 to 6. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to whole fruit is 8:14. A ratio number can be any kind of quantity, such as the number of people or things, or measurements such as length, weight, or time.In most situations, both numbers are constrained to be positive.
The ratio of tourists to locals is 4:5
Tourists / Locals = 4 / 5
There are 100 tourists at the opening of the new museum
100 / locals = 4/5
locals = 500/4
locals = 125
The attendance of locals is 125.
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Part 1: Given cosine of theta is equal to radical 3 over 2 comma determine three possible angles θ on the domain [0,[infinity]). Part 2: Given θ = 495°, convert the value of θ to radians and find sec θ.
Answers
The required answer is sec θ = -√2.
Explanation:-
Part 1: Given cosine of theta is equal to radical 3 over 2 on the domain [0,[infinity]).
To determine three possible angles θ, the cosine inverse function which is a cos and since cosine function is positive in the first and second quadrant. Therefore conclude that, cosine function of θ = radical 3 over 2 implies that θ could be 30 degrees or 330 degrees or 390 degrees. So, θ = {30, 330, 390}.Part 2:To convert 495° to radians, multiply by π/180°.495° * π/180° = 11π/4To find sec θ, we use the reciprocal of the cosine function which is sec.
Therefore, sec θ = 1/cos θ.To find cos 11π/4, the reference angle, which is 3π/4. Cosine is negative in the third quadrant so the final result is sec θ = -√2.
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On Friday, the temperature was 82°F. The temperature changed by –2°F on Saturday, and then it changed by 5°F on Sunday. What was the temperature on Sunday?
Answers
Answer:
85°F
Step-by-step explanation:
On Friday, the temperature was 82°F.
+ 82
The temperature changed by –2°F on Saturday,
+ -2
and then it changed by 5°F on Sunday.
+ 5
82 + -2 + 5
82 + -2 = 80
80 + 5 = 85
Your friends have locked themselves out of the house, and they need your help to get back in. They have a 20 foot long ladder, and there is an open window 16 feet above the ground. How far from the wall should you hold the base of the ladder while they climb back in?
Answers
Solution:
Given:
where;
\(\begin{gathered} l=20ft \\ h=16ft \end{gathered}\)A right triangle can be extracted from the image above,
Applying the Pythagoras theorem to the right triangle,
\(\begin{gathered} \text{hypotenuse}^2=\text{opposite}^2+\text{adjacent}^2 \\ \\ \text{Thus,} \\ l^2=h^2+w^2 \end{gathered}\)To find w, substitute the known values into the formula,
\(\begin{gathered} l^2=h^2+w^2 \\ 20^2=16^2+w^2 \\ 400=256+w^2 \\ 400-256=w^2 \\ 144=w^2 \\ w=\sqrt[]{144} \\ w=\pm12 \\ Si\text{nce the problem is on the distance to hold the base of the ladder, we pick the positive value only.} \\ \text{Thus,} \\ w=12ft \end{gathered}\)Therefore, the distance from the wall that the base of the ladder should be while they climb back in is 12 feet.
Hence, option D is the correct answer.
f(x) = x · 2x on [0, 4] with 4 subintervals of equal width and midpoints for sample points
Answers
To provide the final numerical answer, the exact values of f(x1), f(x2), f(x3), and f(x4) need to be calculated using a calculator or numerical approximation techniques.
To approximate the integral of the function f(x) = x · 2^x over the interval [0, 4], we can use the midpoint rule with four equal-width subintervals. The midpoint rule estimates the integral by evaluating the function at the midpoint of each subinterval and multiplying it by the width of the subinterval.
To apply the midpoint rule, we divide the interval [0, 4] into four equal-width subintervals. The width of each subinterval is (4-0)/4 = 1.
The midpoints of the subintervals are located at x = 0.5, 1.5, 2.5, and 3.5. Let's denote these midpoints as x1, x2, x3, and x4, respectively.
For each subinterval, we evaluate the function f(x) = x · 2^x at the corresponding midpoint and multiply it by the width of the subinterval:
I ≈ Δx [f(x1) + f(x2) + f(x3) + f(x4)]
Now, let's calculate the values of f(x) at each midpoint:
f(x1) = 0.5 · 2^(0.5) = 0.5 · sqrt(2)
f(x2) = 1.5 · 2^(1.5)
f(x3) = 2.5 · 2^(2.5)
f(x4) = 3.5 · 2^(3.5)
Finally, we substitute these values into the midpoint rule formula:
I ≈ 1 [f(x1) + f(x2) + f(x3) + f(x4)]
Replace the values of f(x) at each midpoint and simplify to find the approximate value of the integral.
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50 points! Find the coordinates of the centroid of the triangle with the vertices A(-6,8), B(-3,1),andC(0,3). Random answers will be reported guys
Answers
Answer:
the coordinates of the centroid of the triangle with the vertices A(-6,8), B(-3,1),andC(0,3).
={(-6-3-0)/3,(8+1+3)/3}=(-3,4)
Answer:
( - 3, 4 )
Step-by-step explanation:
The centroid of a triangle is the intersection of the three medians of the triangle.
A ( - 6, 8 )
C ( 0, 3 )
Coordinates of the midpoint of AC are D( - 3, 5.5 )
Median BD is x = - 3
Coordinates of midpoint of BC are E( - 1.5, 2 )
\(m_{AE}\) = - \(\frac{4}{3}\)
Equation of median AE is y = - \(\frac{4}{3}\) x
Solve system of equations:
y = - \(\frac{4}{3}\) x and x = - 3
( - 3, 4 ) are coordinates of the centroid of the Δ ABC
I’ll mark you brainlist I’ll mark you brainlist write in y=mx+b form
Answers
Answer:
y=-4x+2
hope this helped
what is 30 1/3% of 3
Answers
Step-by-step explanation:
30 1/3 = 91/3
3 × 91/3% = 91/100 (0.91)
(3-0.91=2.09) < I dunno if you need to subtract it tho^^
What is the answer??
Answers
Answer:
Tangent to a circle
Step-by-step explanation:
Sorry but I can't draw on this but if you draw it out then the question should become clearer.
Mario and Carlos, two brothers, play for the same basketball team. Here are the points they scored in 10 games:
Answers
The highest point scored is by Carlos with 19 points. Mario's highest was 15. so, Carlos scored 4 points more than Mario.
In the 7th game, Carlos scored 19 points which is the highest point of his game. In the 1st game, Mario scored 15 points which was the highest point he scored. Therefore, Carlos had the highest scoring game between the two of them. Carlos scored 4 points more than Mario did in his highest-scoring game. You can also construct a box plot for this question which will help you visualise this better. The box plot can be made by drawing a number line and marking the following points: minimum, first quartile, median, third quartile and maximum.
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The full question is:
Mario and Carlos, two brothers, play for the same basketball team. Here are the
points they scored in 10 games:
Game 1 2 3 4 5 6 7 8 9 10
Mario 15 X X 12 7 11 12 11 10 11
Carlos 10 X 9 12 15 X 19 11 12 12
(Xs mark games each one missed.) Which brother had the
highest-scoring game? How many more points did he score in
that game than the other brother did in his highest-scoring game?
prove the identity 1/1-cosx + 1 / 1 + cosx = 2csc^2x
Answers
The prove of the trigonometric identity is shown below.
How to prove the trigonometric identity?Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.
We to prove that:
\(\frac{1}{1-cosx} + \left\frac{1}{1+cosx} = 2csc^{2}x\)
Find the LCM of the right side of the equation:
\(\frac{1}{1-cosx} + \left\frac{1}{1+cosx} = \left\frac{1+cosx \left + \left1-cosx }{1-cos^{2}x}\)
\(= \left\frac{2 }{1-cos^{2}x}\) (Remember: sin²x = 1 - cos²x)
\(= \left\frac{2 }{sin^{2}x}\) (Also: \(\left\frac{1 }{sin^{2}x} = csc^{2}x\))
\(= 2 csc^{2}x\)
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Variables are defined by what?
Answers
Answer:
A variable is a quantity that may change within the context of a mathematical problem or experiment. ... The letters x, y, and z are common generic symbols used for variables. Sometimes, we will choose a letter that reminds us of the quantity it represents, such as t for time, v for voltage, or b for bacteria.
Step-by-step explanation:
thats true❤️
Answer:
A variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters x, y, and z are common generic symbols used for variables.
please mark as brainliest
Reaching out 2 standard errors on either side of the sample proportion makes us about _________ confident that the true proportion is capable within the interval
a. 90%
b. 99%
c. 95%
d. 68%
Answers
The correct answer is option c. 95%. Reaching out two standard errors on either side of the sample proportion gives us an interval of 95% confidence.
This is due to the fact that two standard errors on either side of the sample proportion will cover around 95% of the population's cases.
We can typically determine the true proportion in the population using this range of two standard errors on either side of the sample proportion.
This is because it helps us identify any potential outliers in the population and provides a range of population proportions for which we may be 95% certain.
We are 95% certain that the true percentage is capable inside the interval if we stretch out two standard errors on either side of the sample proportion.
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If two points are given, then exactly one line can be drawn through those two points.
Answers
Answer:
a postulate
Step-by-step explanation:
a postulate which states that through any two points, there is exactly one line
Yes indeed. That is so. Your statement is a fact. It virtually pulsates with veracity and truthiness. You can take it to the bank and hang your hat on it. Truer words are seldom written or spoken.
Do you have a question to ask ?
A line with a slope of 2 passes through the points (k, 3) and (6, k) on the coordinate grid. What is the value of k?
Answers
The value of k that makes the line passing through the points (k, 3) and (6, k) have a slope of 2 is k = 5
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.
A line with a slope of 2 passes through the points (k, 3) and (6, k), hence:
2 = (k - 3) / (6 - k)
12 - 2k = k - 3
k = 5
The value of k that makes the line passing through the points (k, 3) and (6, k) have a slope of 2 is k = 5
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Phil is making a number cube out of cardboard He traces one face of the number cube onto a coordinate grid The coordinates of two opposite vertices of the face are (4, 8) and (12, 16) What is the surface area, in square units, of Phil's entire number cube?
Answers
=============================================================
Explanation:
Let A = (4,8) and B = (12,16)
Form point C at the location (12,8). Note how points A and C are on the same horizontal level, or they have the same y coordinate.
The distance from A(4,8) to C(12,8) is 12-4 = 8 units. Ignore the y coordinates and subtract the x coordinates. This trick only works for horizontal line segments.
So we can see that each square face has a side length of 8 units. The area of each square face is 8^2 = 8*8 = 64 square units.
There are six of these faces, so 6*64 = 384 square units is the total surface area of the number cube.
How does the percent describe how the weights are related?
Answers
Answer:
more explanation please
Determine which of the following subsets of R3×3 are subspaces of R3×3 by answering yes or no for each of them.
1. The invertible 3×3 matric
2. The symmetric 3×3 matrices
3. The 3×3 matrices whose entries are all integers
4. The upper triangular 3×3 matrices
5. The singular 3×3 matrices
6. The 3×3 matrices with trace 0 (the trace of a matrix is the sum of its diagonal entries)
7. The 3×3 matrices in reduced row-echelon form
8. The 3×3 matrices with all zeros in the first row
Answers
Yes, since the set of invertible matrices is closed under addition and scalar multiplication and contains the zero matrix.
Yes, since the set of symmetric matrices is closed under addition and scalar multiplication and contains the zero matrix.
Yes, since the set of matrices with integer entries is closed under addition and scalar multiplication and contains the zero matrix.
Yes, since the set of upper triangular matrices is closed under addition and scalar multiplication and contains the zero matrix.
No, since the set of singular matrices is not closed under scalar multiplication.
Yes, since the set of matrices with trace 0 is closed under addition and scalar multiplication and contains the zero matrix.
No, since the set of matrices in reduced row-echelon form is not closed under addition.
No, since the set of matrices with all zeros in the first row is not closed under addition.
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Find the value of x.
135°
(7x + 2)°
x = [?]°
Answers
133=7x
Then we solve for x by diving 133 by 7
x=19
The required value of the x in the expression of angle is 19.
An expression of angle is given as 7x + 2 = 135°, the value of the x is to be determined.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
7x + 2 = 135
Simplifying,
7x = 135 - 2
7x = 133
x = 133 / 7
x = 19
Thus, the required value of the x in the expression of angle is 19.
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To make cream ice pops, nina uses conical molds that each have a height of 15 cm and a radius of 2 cm. how much ice pop mixture can each mold hold when full? a. 30 pi cubic centimeters b. 10 pi cubic centimeters c. 20pi cubic centimeters d. 60pi cubic centimeters
Answers
Answer:
C
Step-by-step explanation:
Givens
r = 2 cm
h = 15 cm
pi = 3.14 The question does not expect a number for pi
Formula
V = (1/3) pi r^2 h Substitute givens into formula
Solution
V = 1/3 * pi * 2^2 * 15 Combine. Remember pi is left as it is
V = 1/3 * pi * 4 * 15
V = 1/3 pi * 60 Divide 60 by 3
V = 20 pi
Taylor's family took a road trip to Mount Rushmore. Taylor slept through the last 21% of the trip. If Taylor fell asleep after they had travelled 711 miles, what was the total length of the trip?
Answers
The total length of the trip is the number of miles in the trip
The total length of the trip is 974 miles
How to determine the total length?The given parameters are:
Proportion of sleep = 21%Distance awake = 711 milesIf Taylor sleeps for 21% of the trip, then Taylor was awake for 79% of the trip
Represent the total length of the trip with T.
So, we have:
73% * T = 711 miles
Divide both sides by 73%
T = 974 miles
Hence, the total length of the trip is 974 miles
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solve the equation -8(4k-5)=200
Answers
Answer:
k = -5
Step-by-step explanation: