Question 1
Question 2
(1 point) Suppose that f(x) = (4x - 3)2(5x + 1)3. = Find f'(x), and then evaluate f' at x = 2 and x = -2. = f'(2) = f'(-2) = = Find dy dx 은 for the equation vx + y = x3 + y3 х X
Answers
f'(x) is found using the chain rule and evaluated at x=2 and x=-2 to be 26208 and -26208, respectively. dy/dx for vx+y=x^3+y^3 is (3x^2-v)/(1-3y^2), derived by implicit differentiation.
Using the chain rule, we can find the derivative of f(x) as
f'(x) = 2(4x - 3)(5x + 1)^3 + (4x - 3)^2 * 3(5x + 1)^2 * 5
Simplifying this expression, we get
f'(x) = 2(4x - 3)(5x + 1)^2[2(5x + 1) + 3(4x - 3)]
Evaluating f'(2) and f'(-2) is simply a matter of plugging in the values of x:
f'(2) = 2(4(2) - 3)(5(2) + 1)^2[2(5(2) + 1) + 3(4(2) - 3)] = 26208
f'(-2) = 2(4(-2) - 3)(5(-2) + 1)^2[2(5(-2) + 1) + 3(4(-2) - 3)] = -26208
Therefore, f'(2) = 26208 and f'(-2) = -26208.
To find dy/dx for the equation vx + y = x^3 + y^3, we can start by rearranging the equation to isolate y
y = x^3 + y^3 - vx
Taking the derivative of both sides with respect to x, we get
dy/dx = 3x^2 + 3y^2(dy/dx) - v
Simplifying this expression, we get
dy/dx - 3y^2(dy/dx) = 3x^2 - v
Factorizing out dy/dx, we get
dy/dx(1 - 3y^2) = 3x^2 - v
Dividing both sides by (1 - 3y^2), we get
dy/dx = (3x^2 - v)/(1 - 3y^2)
Therefore, the expression for dy/dx for the given equation is (3x^2 - v)/(1 - 3y^2).
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Related Questions
A line passes through the point (−7,−5,8), and is parallel to the vector 3i+6j+6k. Find the standard parametric equations for the line, written using the component of the given vector and the coordinates of the given point. Let z=8+6t. x=,y=,z=
Answers
So, the standard parametric equations for the line are: x = -7 + 3t; y = -5 + 6t; z = 8 + 6t.
To find the standard parametric equations for the line, we can use the point-slope form of the equation of a line.
The given point on the line is (-7, -5, 8), and the line is parallel to the vector 3i + 6j + 6k.
Using the point-slope form, the equations can be written as:
x = x₁ + at
y = y₁ + bt
z = z₁ + ct
where (x₁, y₁, z₁) is the given point and (a, b, c) are the components of the parallel vector.
Substituting the values:
x = -7 + 3t
y = -5 + 6t
z = 8 + 6t
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AB is tangent to the circle at B. M∠A=40 and mBC=130.
a. Find x
b. Find y
Answers
The values for x and y are respectively given as
x = 50y= 90This is further explained below.
What is the values for x and y ?Generally, the equation for secent is mathematically given as
\(secent = \frac{big arc - small arc}{2}\)
Therefore
\(40 = \frac{130-x}{2}\)
80 = 130-x
x = 50
b) To Solve for y Now we find a measure of arc CD
ArcCD = 360-130-50
ArcCD = 180
In conclusion,(1/2) of the arc measure is equal to the angle that is on and inside a circle.
y = 180/2
y= 90
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please answer this !!!
Answers
C=p+E what is the 95% confidence level of students who are planning to vote for Talia as president of the club
Answers
The the 95% confidence level of students who are planning to vote for Talia as president of the club is 33.7.
Total number of members in School Club = 80 members
Number of member randomly Selected,that is sample size used (P) = 50 members
Number of members who are planning to vote for Talia = 38 members
Z Score for 95% confidence interval =1.96
it is given that Margin of Error ,E,of the poll using a 95% confidence interval=12%
E = (Z + σ)/ √P
12/100 = (1.96 + σ)/√50
σ = 4.32890
Standard Deviation=4.3 (approx)
→95% confidence level for students who are planning to vote for Talia as president of the club lie between → 38 + 4.3 = 42.3 to 38 -4.3=33.7.
→So, members which will vote for Talia as president of the club lies between minimum of 33 members and maximum of 42 members.
Therefore, the the 95% confidence level of students who are planning to vote for Talia as president of the club is 33.7.
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x + 2(y-6) = 0
3x + 4y = 30
2x = 4 + z
6x - 5z = 18
2w + 3x - 13 = 0
x + 5w - 13 = 0
I need this before 2:30.
Answers
6x - 5z = 18
3z - 2w = -18
If u want me to solve them it’s
1. X = -2y + 12
2. x = 10 - 4/3y | for y, y = 15/2 - 3/4x
3. x = 2+ 1/2z | for z , z = -4 + 2x
4. x = 3 + 5/6z | for z , z = - 18/5 + 6/5x
5. W = -3/2x + 13/2 | for x , x = -2/3w + 13/3
6. x = -5w + 13 | w = -1/5x + 13/5
Jane wants to measure the amount of precipitation in her backyard for the month of January. Which weather instrument should Jane use?
Answers
Answer:
rain gauges
Step-by-step explanation:
what happens when we replace the true standard deviation σ with the sample standard deviation s
Answers
It is important to note that the accuracy of our estimates based on the sample standard deviation will depend on the size and representativeness of the sample, as well as the underlying distribution of the population.
When we replace the true standard deviation σ with the sample standard deviation s, we are using an estimate of the population standard deviation based on the sample data.
This can lead to some degree of error or uncertainty in our calculations. Specifically, using the sample standard deviation in place of the true standard deviation can result in wider confidence intervals and larger margin of errors.
However, using the sample standard deviation is a common practice in statistical analysis, particularly when working with small sample sizes or when the true standard deviation is unknown.
It is important to note that the accuracy of our estimates based on the sample standard deviation will depend on the size and representativeness of the sample, as well as the underlying distribution of the population.
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8√12 / √15 = ?
I have the answer, I just don't know how to show my work. Can you please explain it?
Answers
Answer:
7.15541753
Step-by-step explanation:
8√12/ √15
8√2×2×3 / √3×5
8√2²×3/√3×5
8×2√3/√3×5
16√3/√3×5
7.15541753
What is the absolute value of -6
Answers
Answer:
6.
Step-by-step explanation:
The absolute value is defined as the distance from a number to 0 , and so it is always positive. So, the absolute value of −6 will be the distance from −6 to 0 on the number line, and it is 6.
source: https://socratic.org/questions/whats-the-absolute-value-of-6
i hope this helps!
Answer:
6
Step-by-step explanation:
Absolute value of -6 = 6
Absolute value refers to only the distance from the origin and not the direction. So, always it is positive
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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Mother Rabbit awoke one morning and looked to see if all her babies were safe. It was so cramped in her burrow, she could only count their ears and legs. She counted 10 more legs than ears. How many babies does she have?
Answers
She has 4 babies, which is the required solution to the given problem.
Mother Rabbit woke up one morning and looked for her babies to see if they were all safe. Since her burrow was so cramped, she could only count their ears and legs. There were ten more legs than ears.
Let's use algebra to solve this. Let's assume that she had x babies. Since each bunny has 4 legs and 2 ears, the equation is:
4x + 2x = 20
Simplify the equation.
6x = 20
Divide each side by 6.
x = 20/6
Round up to the nearest whole number, because she can't have a fraction of a bunny.
x = 4
Therefore, Mother Rabbit has four babies.
Therefore, she has 4 babies, which is the required solution to the given problem.
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please help!
25.25% off $11225
Answers
Answer:
$2,834.31
Step-by-step explanation:
11225 × 25.25/100
11225 x 0.2525
$2,834.31
Simplify this expression 6w+4+8w-1
Answers
Answer:
14w + 3
Step-by-step explanation:
6w + 4 + 8w -1 (Given)
14w + 3 (combine like terms)
"The Kid Laroi" - Rapper-Songwriter.
Answer:
14w+3
Step-by-step explanation:
6w+4+8w-1
(6w+8w)+(4-1)
14w+3
Suppose initially that the United States is consuming 18 boots and 2 shirts and Canada is consuming 4 boots and 12 shirts, as indicated in the figure. Then, suppose the United States and Canada specialize by each only producing the good for which they have a comparative advantage and then trade. In particular, suppose the United States trades Canada half of its production for half of what Canada produces.
The United States will have ___ additional shirt(s) after the trade (enter a numeric response using an integer) and __ additional boot(s). At the same time, Canada will be able to consume ___ additional shirt(s) as a result of the trade and ___ additional boot
Answers
The United States will have 16 additional shirt(s) after the trade (enter a numeric response using an integer) and 0 additional boot(s). At the same time, Canada will be able to consume 14 additional shirt(s) as a result of the trade and 0 additional boot
With Alaska in the northwest and Hawaii extending the country's reach into the Pacific Ocean, the United States is a confederation of 50 states that encloses a sizable portion of North America. Significant Atlantic Coast cities include Washington, DC, and New York, a centre of international culture and economics. Chicago, a major city in the Midwest, is renowned for its significant architecture, whereas Hollywood, near Los Angeles on the west coast, is renowned for its film production.
If the data are graphed symmetrically, the distribution demonstrates 0% skewness regardless of how long or fat the tails are. When the median of a data set is utilized, 50% of the data points in the collection have values lower than or equal to the median, and 50% of them have values greater than or equal to the median. The middle score in the set is known as the median. The first step in calculating the median is to order the data points from smallest to greatest. The median in an odd-numbered set will be the value that falls exactly in the middle of the list. You must determine the average of the two middle numbers in a set of even numbers. The average is determined by summing up each value individually and dividing that sum by the total number of observations.
The US will consume 16 shirts with trade. (4+12=16 and 16-2=14) The US will have 14 additional shirts.
With commerce, the US will consume 18 boots. 18-18=0
0 additional boots.
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1 8. An elevator at a warehouse can carry up to 180 kilograms of weight. An employee using the elevator is carrying two cases that have weights of 11.6 kilograms and 45.8 kilograms. The employee weighs 62.3 kilograms. The employee has room for one more case in the elevator. Which weight could represent the third case that the employee could carry without going over the maximum weight allowed in the elevator? F. 59.7 kilograms G. 119.7 kilograms H. 180 kilograms 60.7 kilograms
Answers
Given all the weights and the total capacity of the elevator, we have the following expression:
\(11.6+45.8+62.3+x\leq180\)where 'x' denotes the weight of the third case.
Solving for x, we get the following:
\(\begin{gathered} 11.6+45.8+62.3+x\leq180 \\ \Rightarrow119.7+x\leq180 \\ \Rightarrow x\leq180-119.7=60.3 \\ x\leq60.3 \end{gathered}\)therefore, the third case must weigh 60.3 kg or less.
Can u pls help me out with my math
Answers
The evaluation of the equations in the questions are as follows;
10. The equation 18·y - 10 = 2 + 18·y has no solutions
11. x = 0
12. x = 20
13. The consecutive integers are -46 and -45
What is an equation?An equation is a statement which indicates the equivalence between two expressions.
10. 18·y - 10 = 2 + 18·y
18·y - 18·y - 10 + 10 = 2 + 18·y - 18·y + 10
0 = 12
The equation 18·y - 10 = 2 + 18·y is a contradiction with no solution.
11. 2·(6·x - 4) - 16x = 4·(3·x - 2)
2·(6·x - 4) - 16x = 12·x - 8 - 16·x = -8 - 4·x
4·(3·x - 2) = 12·x - 8
2·(6·x - 4) - 16x = -8 - 4·x = 4·(3·x - 2) = 12·x - 8 therefore
-8 - 4·x = 12·x - 8
16·x = 0
x = 0 ÷ 16 = 0
x = 0
12. (3/4)·x + 2 = (3/5)·x + 5
(3/4)·x + 2 - (3/5)·x - 2 = (3/5)·x + 5 - (3/5)·x - 2
(3/4)·x - (3/5)·x = 5 - 2 = 3
(3/20)·x = 3
x = 3 × 20 ÷ 3 = 20
x = 20
13. The sum of the two integers = -91
Let a represent one of the integers, therefore, based on the details;
The other integer = a + 1
a + a + 1 = -91
2·a = -91 - 1 = -92
a = -92 ÷ 2 = -46
One of the integers, a = -46
The other integer, a + 1 = -46 + 1 = -45
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1) Fully factorise each expression 2x +8
Answers
2(x+4)
hope this helps!!!
Which exponential expression is equivalent to
Answers
Answer:
\(\bold{\big {2}^\frac27}\)
Step-by-step explanation:
\((\sqrt[7]2\,)^2=\left(\big2^\frac17\right)^2=\big2^{\frac17\cdot2}=\big2^{\frac27}\)
What are the approximate solutions to the equation? A. X=1.2 and x=3 B. X= 1.7 and x= 6 C. X= 2.6 and X = -3 D. X=1 and x=4.2
Answers
The solutions are where the red and blue lines cross each other.
Answer would be D. X ≅ 1 and x ≅ 4.2
Help please I need help
Answers
Answer:
x + 2/5 = 4
subtract 2/5 from both sides
That is
x + 2/5 - 2/5 = 4 - 2/5
x = 4 - 2/5
x = 18/5 or 3 3/5 as a mixed number
Hope this helps
put the 2/5 to the other side of the equation by cancelling it out
new—> x=4-2/5
then put a 1 under the 4 to make it a fraction
new—> x=4/1 - 2/5
next multiply 4/1 by five so the denominator us equal to 2/5
new—> x=20/5 - 2/5
now you subtract
answer is x= 18/5
This distance-time graph shows the journey of a robin.
Calculate the average speed of the robin between
4 and 14 seconds.
If your answer is a decimal, give it to 1 d.p.
Distance travelled (m)
40
35
30-
25
20-
15-
10-
5-
4
6 8 10 12 14 16
Time (s)
Answers
Step-by-step explanation:
speed/time
4/14
0.210divide by 100
210 m
The average speed of the robin between 4 and 14 seconds is 2.5 m/s.
Explanation:To calculate the average speed of the robin between 4 and 14 seconds, we need to find the total distance traveled within this time period. Looking at the graph, we can see that the distance traveled at 4 seconds is 35m and at 14 seconds is 10m. Therefore, the total distance is 35m - 10m = 25m.
We also need to find the total time taken. The difference between 4 seconds and 14 seconds is 14s - 4s = 10 seconds.
To calculate average speed, we use the equation:
average speed = total distance ÷ total time
Substituting the values:
average speed = 25m ÷ 10s = 2.5 m/s
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7. evaluate the definite integral (3x-4)^2dx
Answers
The value of the definite integral (3x-4)²dx is (3b³ - 12b² + 16b + C) - (3a³ - 12a² + 16a + C), since the limits are not mentioned.
To evaluate the definite integral of (3x-4)² dx, we first need to expand the expression and then find the antiderivative. Finally, we need to apply the limits of integration if they are provided.
Expanding the expression:
(3x-4)² = 9x² - 24x + 16
Finding the antiderivative:
∫(9x² - 24x + 16) dx = 3x³ - 12x² + 16x + C
Now, if we have limits of integration (a, b), we would evaluate the antiderivative at those points and subtract the results:
F(b) - F(a) =\((3b^3 - 12b^2\) \(+ 16b + C\)) - \((3a^3 - 12a^2 + 16a + C)\)
However, since no limits of integration were provided, we cannot evaluate the definite integral further.
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9. If one inch represents 14 feet,
what dimensions would you use
to make a scale drawing of a
building 84 feet by 126 feet?
Answers
Answer:
the answer would be 6in. by 9in.
Step-by-step explanation:
you have to divide 84 by 14 and 126 by 14
One angle of a triangle measures 90 the other two angles ratio is 5:13, what’s the measure for those 2 angles? No explanation just answer :)
Answers
Answer:
Angle 1 = 25 degrees
Angle 2 = 65 degrees
Given the system of equations.
{-4x+y = 3
{2x - y = 12
Which of the options represents the resulting equation after an equivalent expression for y ls substituted into the
second equation.
2x - (4 X+3) = 12
-4(4y+)+y=3
2 (4x+3) - y
-4x+4 x-3=3
Answers
Answer:
A. 2x - (4x + 3) = 12
Step-by-step explanation:
A. 2x - (4x + 3) = 12
B. -4(4y+)+y=3
C. 2 (4x+3) - y
D. -4x+4 x-3=3
Given equation:
-4x+y = 3. (1)
2x - y = 12. (2)
From (1)
y = 3 + 4x
Substitute y = 3 + 4x into (2)
2x - y = 12 (2)
2x - (3 + 4x) = 12
Or
2x - (4x + 3) = 12
2x - 4x - 3 = 12
- 2x = 12 + 3
- 2x = 15
x = 15/-2
x = -7.5
Substitute x = -7.5 into (1)
-4x+y = 3 (1)
-4(-7.5) + y = 3
30 + y = 3
y = 3 - 30
y = -27
what fraction of 1/2 square centimeter is 1/2 centimeter square
Answers
Answer:
1/2
Step-by-step explanation:
The ratio of interest is ...
(1/2 cm)²/(1/2 cm²) = (1/4)/(1/2) = 1/2
One-half centimeter squared is half of 1/2 square centimeter.
HELP ASAP!!! Solve for x if the figure is a rectangle. (Attachment) ignore my attempt
Answers
The value of x that makes the given image to be a rectangle is: x = 2.5
How to find the length of the diagonal of a rectangle?The length of the diagonals of a rectangle are equal and congruent to each other. It is also pertinent to note that the diagonals of a rectangle bisect each other at the center. Thus:
From the given parameters, we see that half of the diagonals have been labelled and as such we have:
8x - 3 = 4x + 7
Rearrange to have like terms on same side and so we have:
8x - 4x = 7 + 3
4x = 10
x = 10/4
x = 2.5
Thus, the value of x from the calculation above of the rectangle is 2.5
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What value of x makes the following equation true? ( 8th grade math )
Answers
Answer: 4
Step-by-step explanation:
2(x+7) = x + 18
2x + 14 = x + 18
x + 14 = 18
x = 4
Answer:
C. 4
Step-by-step explanation:
\(2(x + 7) = x + 18\)
\(2(x+7) = 2x + 2×7\)
\(=2x+14\)
\(2x + 14 = x + 18\)
\(2x + 14-x=18\)
\(2x - x = 18 - 14\)
\(x=18-14\)
\(x = 4\)
suppose you have 50 students and need to assign them to two independent groups. describe a randomization procedure that would achieve this.
Answers
To assign the 50 students to two independent groups, a randomization procedure can be used. The procedure involves first listing all the students in a random order. It minimizes bias and ensures an equal chance of assignment to either group.
To assign 50 students to two independent groups using randomization, follow these steps:
1. Start with a list of all 50 students.
2. Assign a unique number to each student, such as from 1 to 50.
3. Use a random number generator to generate 25 distinct random numbers from 1 to 50. These random numbers will represent the students for the first independent group.
4. The remaining 25 students, represented by the numbers not selected in step 3, will form the second independent group.
5. Assign the students to their respective groups based on the random numbers.
This procedure ensures that the students are assigned to two independent groups through randomization, reducing potential biases and ensuring a fair distribution of students across the groups.
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Which equation is the inverse of y=x^2 + 4?
Answers
Answer:
y = √(x - 4)
Step-by-step explanation:
To find the inverse, simply swap x and y in your equation, then solve for in terms of y. Keep in mind that this isn't the true inverse of y = x² + 4 because y = √(x - 4) has a restricted domain.
Answer:
B. y = √(x - 4)
Step-by-step explanation:
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