If y= -3x7+2x3+ x, the derivative of y with respect to x is

Answers

Answer 1

Answer:

\(\frac{dy}{dx}\) = - 21\(x^{6}\) + 6x² + 1

Step-by-step explanation:

Differentiate each term using the power rule

\(\frac{d}{dx}\) (a\(x^{n}\) ) = na\(x^{n-1}\)

Given

y = - 3\(x^{7}\) + 2x³ + x , then

\(\frac{dy}{dx}\) = (7 × - 3 )\(x^{6}\) + (3 × 2)x² + (1 × 1 )\(x^{0}\)

    = - 21\(x^{6}\) + 6x² + 1


Related Questions

If a ball is thrown upward at 112 feet per second from the top of a building that is 120 feet high, the
height of the ball can be modeled by s = 120 + 112t - 16t^2where t is the number of seconds after the ball
is thrown. How long after it is thrown is the height 120 feet?

Answers

Answer: 7 seconds

Step-by-step explanation:

Obtain the time after the ball is thrown at the height of 120 feet.

Substitute s = 120 in s = -16t^2 + 112t + 120 and solve for t as follows:

\(\begin{aligned}&120=-16 t^{2}+112t+120 \\&-16 t^{2}+112 t+120-120=0 \\&-16 t^{2}+112t=0 \\&16 t^{2}-112t=0 \\&16 t(t-7)=0 \\&12 t=0, t-7=0 \\&\Rightarrow t=0, t=7\end{aligned}\)

Note that, time cannot be negative or 0. So, ignore t = 0

Therefore, after 7 seconds the ball will reach at a height of 120 feet.

The length of a rectangle is three times its width.
If the perimeter of the rectangle is 48 cm, find its area.

Answers

The area of the rectangle is 108cm²

What is area of a rectangle?

The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units.

So, the area of a rectangle is the number of unit squares within the boundary of the rectangle or the space occupied within the perimeter of this shape is called the area of the rectangle.

The area of a rectangle is Length ×width

perimeter of a rectangle = 2(l+w)

l= 3w

therefore P= 2(3w+w)

P= 2(4w)

p= 8w

p=48cm

48= 8w

divide both sides by 8

w= 6cm

from l= 3w

l= 3×6= 18cm

therefore the area of the rectangle is 18×6= 108cm²

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A candy company produces packets of candy every day. Each packet they produce has a slightly unique weight. The mean of the weights is 72g, and the variance of the weights is 16g.

What is the minimum weight of a packet of candy with a z-score of -0.6? (round to the nearest tenth as needed)

Answers

To determine the minimum weight of a packet of candy with a z-score of -0.6, we need to use the formula:

z = (x - μ) / σ

where:

z = -0.6 (given)

μ = 72g (given)

σ = sqrt(16g) = 4g (since variance = standard deviation squared)

Substituting the values in the formula, we get:

-0.6 = (x - 72) / 4

Multiplying both sides by 4, we get:

-2.4 = x - 72

Adding 72 to both sides, we get:

x = 69.6g

Therefore, the minimum weight of a packet of candy with a z-score of -0.6 is approximately 69.6g (rounded to the nearest tenth).

An item is priced at $14.29. If the sales tax is 5%, what does the item cost including sales tax?

Answers

Answer:3-5=787879. youu

Step-by-step explanation:

Use the two given functions to write y as a function of x.
y = -3a + 3, a = -5x + 1

Answers

Answer:

Step-by-step explanation:

To write y as a function of x using the given functions, we can substitute the value of "a" in the first equation with the expression "-5x + 1" from the second equation.

Given:

y = -3a + 3

a = -5x + 1

Substituting the value of "a" in the first equation:

y = -3(-5x + 1) + 3

Now, let's simplify this expression:

y = 15x - 3 + 3

y = 15x

Therefore, y can be expressed as a function of x as:

y = 15x

Which of these is not a possible r-value?

ОА. 1.2

Ов. 0.5

Ос. -0.75

OD. -0.1

Answers

Answer:

Step-by-step explanation:

A

find the area of the triangle

find the area of the triangle

Answers

9514 1404 393

Answer:

  108 cm²

Step-by-step explanation:

The area of a triangle is given by the formula ...

  A = 1/2bh

where b represents the base length, and h represents the height--the perpendicular distance from the base to the opposite vertex. The area of this triangle is ...

  A = 1/2(12 cm)(18 cm) = 108 cm²

A bucket contains six white balls and five red balls. A sample of four balls is selected
at random from the bucket, without replacement. What is the probability that the
sample contains...
Exactly two white balls and two red balls?
At least two white balls?

Answers

To solve this problem, we can use the formula for probability:

P(event) = number of favorable outcomes / total number of outcomes

First, let's find the total number of outcomes. We are selecting 4 balls from 11 without replacement, so the total number of outcomes is:

11C4 = (11!)/(4!(11-4)!) = 330

where nCr is the number of combinations of n things taken r at a time.

Now let's find the number of favorable outcomes for each part of the problem.

Part 1: Exactly two white balls and two red balls

To find the number of favorable outcomes for this part, we need to select 2 white balls out of 6 and 2 red balls out of 5. The number of ways to do this is:

6C2 * 5C2 = (6!)/(2!(6-2)!) * (5!)/(2!(5-2)!) = 15 * 10 = 150

So the probability of selecting exactly two white balls and two red balls is:

P(2W2R) = 150/330 = 0.45 (rounded to two decimal places)

Part 2: At least two white balls

To find the number of favorable outcomes for this part, we need to consider two cases: selecting 2 white balls and 2 red balls, or selecting 3 white balls and 1 red ball.

The number of ways to select 2 white balls and 2 red balls is the same as the number of favorable outcomes for Part 1, which is 150.

To find the number of ways to select 3 white balls and 1 red ball, we need to select 3 white balls out of 6 and 1 red ball out of 5. The number of ways to do this is:

6C3 * 5C1 = (6!)/(3!(6-3)!) * (5!)/(1!(5-1)!) = 20 * 5 = 100

So the total number of favorable outcomes for selecting at least two white balls is:

150 + 100 = 250

And the probability of selecting at least two white balls is:

P(at least 2W) = 250/330 = 0.76 (rounded to two decimal places)

2x-y≤-3

graph the inequality

Answers

Therefore , the solution of the given problem of inequality graph comes out to be  the graph of the inequality 2x - y ≤ -3 is a line that cuts through the x-y plane

What do you mean by inequality graph?

An inequality graph is a graph that represents the solution set of an inequality, showing the values of the independent variable (usually represented on the x-axis) for which the inequality is true.

Here,

An inequality can be represented graphically by shading the region on a coordinate plane that satisfies the inequality. The direction of shading (above or below the line) depends on the inequality symbol.

The graph of the inequality 2x - y ≤ -3 in the x-y plane can be plotted by finding the boundary line for the inequality and shading the region that satisfies the inequality. To do this, we can start by setting the equation 2x - y = -3 and finding the x- and y-coordinates of the points on the line. Then we can plot these points and draw the line that connects them.

Next, we will determine which side of the line represents the solution set. To do this, we can pick a point that is not on the line and substitute its x- and y-coordinates into the inequality. If the inequality is true for the point, we shade the region that contains the point. If the inequality is false, we shade the region that does not contain the point.

So the graph of the inequality 2x - y ≤ -3 is a line that cuts through the x-y plane and is shaded on one side. The shaded region represents all the x- and y-coordinates that satisfy the inequality.

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witch of the following best described perpendicular lines?

Answers

Answer: I have to make one up In geometry, a branch of mathematics, perpendicular lines are defined as two lines that meet or intersect each other at right angles (90°).

Step-by-step explanation:

Find the exact length of each line segment.
Then estimate the length of each line segment to the
nearest tenth of a unit.
Use the sketch tool if it helps you with your thinking.

Find the exact length of each line segment.Then estimate the length of each line segment to thenearest

Answers

The actual and estimated distances are

AB = √17 = 4.1

GH = √32 = 5.7

Calculating the distance of the points

From the question, we have the following parameters that can be used in our computation:

A = (0, 4) and B = (1, 0)

The distance is then calculated as

AB = √[(4 - 0)² + (1 - 0)²]

Evaluate

AB = √17

When estimated, we have

AB = 4.1

Also, we have

G = (0, 0) and H = (4, -4)

So, we have

GH = √[(4 - 0)² + (4 - 0)²]

Evaluate

GH = √32

When estimated, we have

GH = 5.7

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A cylinder has a volume of 659.4 cubic centimeters. The diameter of the cylinder is 10 cm. What is the height of the cylinder?
(Assume = 3.14)

A.
42 cm
B.
2.1 cm
C.
8.4 cm
D.
21 cm

Answers

The height is 8.4.

Calculated with H = V / πr^2, with H for height, V for volume, and r for radius (the diameter divided by 2).

The average snail can move 1.81 X 10³ mi in 5 hours. What is its rate of speed in miles per hour?

Answers

Answer:

Step-by-step explanation:

How Far Can A Snail Travel In One Hour

If a snail can travel over half an inch per minute, that means in one hour a snail can travel up to 40 inches. If you want to think about how far this is in feet, it means that snails move up to 3.5 feet per hour.

Consider the fact that the average human being can walk about a mile, or 5280 feet, in one hour.

This means that snails can take up to 1,500 days, or over 4 years, to travel just one mile.

A baker makes 60 muffins. He sells 24 of the muffins.
He put the rest of the muffins in boxes. Each box can hold 4 muffins.
Which equation can be used to find b, the number of boxes the baker will need?
OA.
B.
OC.
OD. (60
60+ 24 ÷ 4 = b
60 24 ÷ 4 = b
-
(60+24) ÷ 4 = b
24) = 4 = b
-

A baker makes 60 muffins. He sells 24 of the muffins.He put the rest of the muffins in boxes. Each box

Answers

Answer:c

Step-by-step explanation:

c

Answer:b

Step-by-step explanation:

What is the distance between Point A and Point C?

A: 27−−√ units

B: 41−−√ units

C: 34−−√ units

D: 130−−−√ units

What is the distance between Point A and Point C?A: 27 unitsB: 41 unitsC: 34 unitsD: 130 units

Answers

The answer is c I took a test of that

Maria, Ahmad, and Bob sent a total of 52 text messages during the weekend. Maria sent fewer messages than Bob. Ahmad sent times as many messages as Bob. How many messages did they each send?

Answers

Answer:

Maria sent 7 messages

Bob sent 5 messages

Ahmad sent 45 messages

Step-by-step explanation:

Given that Maria, Ahmad, and Bob sent a total of 52 text messages during the weekend.

If Maria sent fewer messages than Bob, and Ahmad sent times as many messages as Bob

Since the exact figures were not given, then let make an assumption that Ahmad sent 9 times as many messages as Bob.

If Bob sent 5 messages, then, Ahmad will send 5 × 9 = 45 messages

Also, it is given that Maria sent fewer messages than Bob. Take 45 away from 52. That is,

52 - 45 = 7

Therefore,

Maria sent 7 messages

Bob sent 5 messages

Ahmad sent 45 messages

true or false HELP me

true or false HELP me

Answers

Answer:

True

Step-by-step explanation:

Write an expression for 3 more than twice the number n.

Please answer my question

Answers

Answer:

2n+3

Step-by-step explanation:

please help!! find the reciprocal of these numbers.
6.2
-2.3
0.9
-22.7

Answers

Answer:

They have its own reciprocal

6.2 will be 0.16 -2.3 will be -0.43 0.9 will be 1.11 and -22.7 will be 0.04. You need to change the decimals into fractions. Flip the fraction and then turn that fraction back into a decimal. I hope this is right!

Estimate 32.79 dived by 8.1

Answers

the answer to this problem is 4.

What is the slope of the line that goes through the points -4–2 and 8–5

Answers

Answer:

-7/12

Step-by-step explanation:

-5-2 = -7    y

and

8- (-4)=12    x

Answer:

slope = -1/4

Step-by-step explanation:

m = (y2-y1)/(x2-x1)

m = (-5-(-2))/(8-(-4)

m = -3/12

m = -1/4

Hope this helps!    :3

plz mark as brainliest!

What is the equation in point-slope form of the line that passes through the point (−1,−4) and has a slope of –3? Drag and drop the appropriate number, symbol, or variable to each box.

Answers

Answer:

y+4=-3(x+1)

Step-by-step explanation:

Hope this helps may all your sweet dreams come true!

Answer:

y+4=-3(x+1)

Step-by-step explanation:

this is right im in the test

27 points! please help me if you can <3 and yes I have been working on this for almost 4 hours

27 points! please help me if you can &lt;3 and yes I have been working on this for almost 4 hours

Answers

Answer:

330 milkshakes

Step-by-step explanation:

240 divided by 8 = 90

90 = number of large milkshakes

240 + 90 = 330

Write a story that could represent this math problem. (2 points)

Write a story that could represent this math problem. (2 points)

Answers

If John has 3 of 4 slices of pie, and Tom has 2 of 6 slices of pie, how many do they have all together?

I believe that is what type of story you needed, if wrong let me know.

Answer: Suppose Rita is trying to find the area of the carpet of 3/4 and 2/6 for a room of 4/4 sq to 6/6 sq with balcony of 1/4 and 4/6

Explanation: In the given rectangle fig. length is given 3/4 and breadth is given 2/6 for the whole rectangle is 4/4 to 6/6.

for each block length is given 1/4 and breadth is given 1/6. The darker shaded area represents the carpet of the above story.

The answer after multiplying it is 6/24 or 1/4.  

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Simplify 6x^2y^3(2x^2y)^3

Answers

Answer: 6x2y3(2x2y)3

=48x^8 y^6

write an equation in slope - intercept form for the line that passes through the given point and has the given slope.

Answers

The equation of slope is y = mx + (y1 - mx1)

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept.

To write an equation in slope-intercept form for the line that passes through a given point and has a given slope, we can use the point-slope form of a linear equation, which is:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the given slope.

We can then simplify the equation to get it into slope-intercept form:

y - y1 = m(x - x1)

y = mx - mx1 + y1

By rearranging the terms, we can see that the y-intercept is y1 - mx1. Thus, the final equation in slope-intercept form is:

y = mx + (y1 - mx1)

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Note: The full question is

write an equation in slope - intercept form for the line that passes through the given point and has the given slope m.

Which is the simplified form of the expression three 7/5 X +4-232 -5/4 X

Answers

The simplified form of the expression is 123/20 x - 228

How to determine the simplified form of the expression?

From the question, we have the following parameters that can be used in our computation:

three 7/5 X +4-232 -5/4 X

Rewrite the above expression properly

So, we have the following representation

37/5 x + 4 - 232 - 5/4 x

Collect the like terms in the above expression

So, we have the following representation

37/5 x - 5/4 x + 4 - 232

Evaluate the like terms in the above expression

So, we have the following representation

123/20 x + 4 - 232

Solving further, we have

123/20 x - 228

Hence, the solution is  123/20 x - 228

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At the start of track camp, Mary-Margaret could do 30 squats. Mary-Margaret performed 36 more squats every week while participating in the
track camp. The total number of squats is modeled by 36w + 30, where w is the number of weeks participating in the camp.
Which of the following expressions is equivalent to 36w +30 ?
A
6w+5
B
66
6 (6w +5
D
66w

Answers

Answer:

C) 6 (6w +5)

Step-by-step explanation:

6w+5 ≠ 36w +30

66 ≠ 36w +30

6 (6w +5) -> 36w + 30 = 36w +30

66w ≠ 36w +30

This leaves us with the option of 6 (6w +5)

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

0=x^2-10x+30 by completing the square

Answers

Answer:

15 and -5

Step-by-step explanation:

D=(-10)^2-4*30*1=100-120=-20

x1=(10+20):2=15

x2=(10-20):2=-5

Section 1

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Calculator

Iten

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A box of blocks contains 35 red, 40 blue, and 50 green blocks. If the box only contains red, blue, and green blocks, and a child randomly

selects a block, what is the probability the block is red?

Answers

Answer:

\(P(Red) = \frac{7}{25}\)

Step-by-step explanation:

Given

\(Red = 35\)

\(Blue = 40\)

\(Green = 50\)

Required

Determine the probability of red

\(P(Red) = \frac{n(Red)}{Total}\)

Substitute value for n(Red) and calculate Total

\(P(Red) = \frac{35}{35 + 40 + 50}\)

\(P(Red) = \frac{35}{125}\)

Divide numerator and denominator by 5

\(P(Red) = \frac{7}{25}\)

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