Can someone please show me how to do this with steps?
Find an antiderivative of the given function x^-3 + 1/4√x
A. -1/2x^3 + 1/2x^1/2
B. -1/3x^2 + 1/2x^1/2
C. -1/2x^2 + 1/2x^1/2
D. -1/3x^3 + 1/2x^1/2

Answer:

It is the answer.

Step-by-step explanation:

-4-3=-7

Answer:

-4

Step-by-step explanation:

a -3 = -7

a = -7 + 3

a = -4

Entonces:

-4 -3 = -7

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Step-by-step explanation:

7/n=4)7

n=4/41

n=1.25

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Answer:

Step-by-step explanation:

Rational numbers include fractions ,  positive numbers, negative numbers ,zero that can be written as a ratio (fraction) of one number over another and so on.

The probability that the described situation could occur as required in the task content is; 1 / 100.

It follows from the task content that the you selection is done such that there's replacement.

Since the treasure chest contains 10 different toys, the probability of selecting a crazy straw two times consecutively is;

= 1/10 × 1/10

= 1 / 100.

Ultimately, the probability that the given situation occurs as described is; 1 / 100.

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Answer:

0.36

Step-by-step explanation:

0.6 squared is 0.36

it is essentially 6 times 6 but as a decimal

Answer:

ca=14

Step-by-step explanation:

1/3 - 2023√3 .This is the equation of the line with the desired slope and passing through the point of intersection A.The smaller angle between the two lines is π/6 radians or 30 degrees.

To find the smaller angle between the two lines defined by the linear functions Y₁₅ = √(3x) + 2022 and Y₂ = 1/√(3x) + 2022, we need to determine the slopes of the lines.

The slope of a line can be found by examining the coefficient of x in the linear function.

For Y₁₅ = √(3x) + 2022, the coefficient of x is √3.

For Y₂ = 1/√(3x) + 2022, the coefficient of x is 1/√3.

The slopes of the two lines are √3 and 1/√3, respectively.

To find the angle between these two lines, we can use the formula:

θ = atan(|m₂ - m₁| / (1 + m₁ * m₂))

Where m₁ and m₂ are the slopes of the lines.

θ = atan(|1/√3 - √3| / (1 + √3 * 1/√3))

  = atan(|1/√3 - √3| / (1 + 1))

  = atan(|1/√3 - √3| / 2)

To simplify this expression, we can rationalize the denominator:

θ = a tan(|1 - √3 * √3| / (2√3))

  = a tan(|1 - 3| / (2√3))

  = a tan(2 / (2√3))

  = a tan(1 / √3)

Since the angle is acute, we can further simplify by using the exact value of a tan(1/√3) = π/6.

Therefore, the smaller angle between the two lines is π/6 radians or 30 degrees.

To find the equation of the line with the slope corresponding to this angle and passing through the point of intersection A, we need to determine the coordinates of point A.

To find the intersection point, we equate the two linear functions:

√(3x) + 2022 = 1/√(3x) + 2022

To solve this equation, we can subtract 2022 from both sides:

√(3x) = 1/√(3x)

To eliminate the square root, we square both sides:

3x = 1 / 3x

Multiply both sides by 3x to get rid of the fractions:

9x^2 = 1

Taking the square root of both sides:

x = ± 1/3

Now we have the x-coordinate of the intersection point A.

Substituting x = 1/3 into Y₁₅, we get:

Y₁₅ = √(3(1/3)) + 2022

    = √1 + 2022

    = 1 + 2022

    = 2023

The y-coordinate of the intersection point A is 2023.

Therefore, the coordinates of point A are (1/3, 2023).

Now we can write the equation of the line with the slope corresponding to the angle π/6 and passing through point A using the point-slope form of a linear equation:

Y - 2023 = tan(π/6)(x - 1/3)

Simplifying:

Y - 2023 = √3(x - 1/3)

Multiplying through by √3:

√3Y - 2023√3 = x - 1/3

Rearranging the equation:

x - √3Y

= 1/3 - 2023√3

This is the equation of the line with the desired slope and passing through the point of intersection A.

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Answer:

8 square feet

Step-by-step explanation:

The formula of a volume of a prism:

We have

Substitute:

            divide both sides by 9

Answer:

Step-by-step explanation:

The first one is 8

The second one is 4

Answer:

2/5 mile

Step-by-step explanation:

Let's give the total distance the variable x.

1/4x = 1/10

x = 4/10

x = 2/5

Answer:

14 mph

Step-by-step explanation:

Speed of boat in calm water = x

Speed of current = y

Speed of boat with the current = 72 mi / 4 hr = 18 mph

Speed of boat against current = 40 mi / 4 hr = 10 mph

x + y = 18

x - y = 10

2x = 28

x = 14

Answer: 14 mph

Answer:

14 m/hr

Step-by-step explanation:

72 m / 4 hr = 18 m/hr

40 m / 4 hr = 10 m/hr

still water speed =  (18+ 10 )/2 = 14 m/hr

 current speed   (14 -x) 4 = 40

                       x = current speed = 4 m/hr

We can conclude that only some of the ratios in Table A are greater than the ratios in Table B. (option-c)

To compare the ratios of squares to circles in the tables, we must divide the value in the Squares column by the value in the Circles column for each row in the table.

For Table A, the ratios of squares to circles are:

5/3 = 1.67

10/6 = 1.67

For Table B, the ratios of squares to circles are:

10/3 = 3.33

20/9 = 2.22

Comparing the ratios in Table A to the ratios in Table B, we see that the first two ratios are equal (1.67) and the last two ratios are different (3.33 in Table B is greater than 1.67 in Table A, and 2.22 in Table B is less than 1.67 in Table A).

Specifically, the ratio in the second row of Table B is greater than both ratios in Table A, but the ratios in the first row of each table are equal.(option-c)

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The length of y in the triangle is 14√3 units.

A right angle triangle is a triangle with one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the value of the indicated variable can be found as follows:

using trigonometric ratios,

sin 60° = opposite / hypotenuse

Where

opposite side = y

hypotenuse side = 28

sin 60° = y / 28

cross multiply

y = 28 sin 60°

y = 28 × √3 / 2

y = 14√3

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Answer:

120

Step-by-step explanation:

just do 10*12 which is 120.

Answer:

It is 120 brochures distributed "I hope this helps"

Step-by-step explanation:

12x10=120

Answer:

Step-by-step explanation:

I don't see a graph from which to choose.  Are the brackets in "[x+1]" supposed to be parentheses, or are they absolute value signs?

The graph of functions

(F(x) = (x+1), and

(F(x) = |x+1| are both attached.

Answer:

C. 2

Step-by-step explanation:

2 can go into 36 and 60.

36/2 = 18

60/2 = 30

The other answers cannot go into 36 or 60.

Answer:

120 km

distance = speed * time

90 minutes can be converted to 1.5 hours

speed given 80 km/h and time given 1.5 hours

so distance =  80 * 1.5 = 120 km

Answer:

The panther will run 120 km in 90 mins

Step-by-step explanation:

An hour is 60 mins and you know in 1 hour the panther can run 80km

all you need to do is figure out how many miles an xtra 30 mins will be

60 minutes divided by 2 = 30 minutes and 80 km divided by 2 = 40km

Therefore 30 minutes = 40km

just add this to the original statement and you're good

60 mins + 30 mins = 90 mins

80km + 40km = 120km

The panther will run 120km in 90 mins

Answer : Option (c) 2xy² is the right answer

Answer:

Ann's bakery

Step-by-step explanation:

450/3=150

560/4=140

Answer:

Native Americans relied heavily on bison for their survival and well-being, using every part of the bison for food, clothing, shelter, tools, jewelry and in ceremonies

The  Trigonometric Identity sin² x + cos²x = 1 is: A. Pythagorean Identity.

The Pythagorean Identity which  tend to asserts that for every angle x, the sum of the squares of the sine and cosine of x is equal to one  is known as or called a  trigonometric identity.

The  Pythagorean identity can be expressed as:

sin² x + cos² x = 1

This identity is crucial to understanding trigonometry and tend to have several uses in numerous branches of science and engineering.

Therefore the correct option is A.

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Answer:

The function of g(x) = 5x + 2

Step-by-step explanation:

Let us use the composite function to solve the question

∵ f(x) = 2x - 1

∵ f(g(x)) = 10x + 3

→ f(g(x)) means substitute x in f(x) by g(x)

∴ f(g(x)) = 2[g(x)] - 1

→ Equate the two right sides of f(g(x))

∴ 2[g(x)] - 1 = 10x + 3

→ Add 1 to both sides

∴ 2[g(x)] - 1 + 1 = 10x + 3 + 1

∴ 2[g(x)] = 10x + 4

→ Divide each term into both sides by 2

∵ \(\frac{2[g(x)]}{2}\) = \(\frac{10x}{2}\) + \(\frac{4}{2}\)

∴ g(x) = 5x + 2

∴ The function of g(x) = 5x + 2

Since g is twice-differentiable and the limit of g as x approaches infinity is 4, we know that g'(x) approaches 0 as x approaches infinity (otherwise, the limit of g would not exist).

Using L'Hopital's rule, we can take the derivative of both the numerator and denominator of the expression 1/infinity, which gives us:
lim as x->infinity g'(x) / 1 = lim as x->infinity g''(x) / 0
Since g''(x) is the derivative of g'(x), we can apply the same logic and use L'Hopital's rule again:
lim as x->infinity g''(x) / 0 = lim as x->infinity g'''(x) / 0
We can continue applying L'Hopital's rule until we reach a finite limit. Since g is twice-differentiable, we know that g'''(x) exists, but we don't know what its limit is as x approaches infinity. However, we do know that g'(x) approaches 0 as x approaches infinity, so we can conclude that: lim as x->infinity g'(x) / 1 = 0
Therefore, 1/infinity multiplied by 0 is equal to 0.
In summary: 1/infinity times the limit of g'(x) as x approaches infinity is equal to 0.

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Answer:

y < 9

Step-by-step explanation:

Hello!

We can solve the inequality for y by dividing both sides by 7.

Remember, when dividing or multiplying both sides of an inequality with a negative number, make sure to flip the sign. Since 7 is positive, we don't have to flip the sign.

So the inequality is true for all y values less than 9.

Hey there!

63 > 7y

7y < 63

DIVIDE 7 to BOTH SIDES

7y/7 < 63/7

SIMPLIFY IT

y < 63/7

y < 9

You have an open circle starting at 9 and going down to left side of the number line.

Therefore, your answer should beD

y < 9

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

1,000,000 times larger

Step-by-step explanation:

2 x \(10^{8}\) = 200,000,000

2 x \(10^{2}\) = 200

200,000,000 divided by 200 is 1,000,000

It can also be solved by subtracting the exponents from 10. Then dividing the two number being put the scientific notation.

\(10^{8} - 10^{2}\) = \(10^{6\)

2 ÷ 2 = 1

Now solve:

1 x \(10^{6\) = 1,000,000

Answer:

1) 2 + 5k ≤ -18

5k ≤ -20

K ≤ -4

2) -7 > 3 + r/5

-10 > r/5

-50 > r

3) -6 + a/2 < -6

a/2 < 0

a < 0

4) -10 ≤ 5 - 3y

-15 ≤ -3y

5 ≤ y

5) 5 - 6z < 29

-6z < 24

z < -4

6) 5c + 2 ≥ -28

5c ≥ -30

c  ≥ -6

7) -4 + x/2 ≥ -10

x/2 ≥ -6

x ≥ -12

8) 4d + 5 ≤ -27

4d ≤ -32

d ≤ -8

9) -9 > -5 + y/6

-4 > y/6

-24 > y

10) -45 > 3 + 6g

-48 > 6g

-8 > g

For all of the graphs:

Start the point on the number that I got from the inequality.

A filled circle means:

Greater than or equal to or less than or equal depending on where the line goes.

A hallow circle means:

Greater than or less than also depending on where the line is pointed towards too.

In order to graph an inequality you have to find and simply first then graph it.

For example on number 1, K ≤ -4.

Let's graph!

As you can see I filled in the circle and started at the point, -4.

Once I did it I made it bold from -4 and there on to the left. Making -4 be greater than or equal to K.

I showed that -4 is greater than or equal to K by making the line bold behind -4, also by filling in the circle.

Answer:almost everywhere.

Step-by-step explanation:

Answer:

this is binomial

3 is the degree of this equation.

Part (d)

Answer: 180 degrees

----------------------

Explanation:

QS is a diameter, which makes angle SPQ to be 180 degrees (ie a straight angle). Arc QTS is also going to be 180 degrees, because all semicircles are half of the full circle of 360 degrees. So (1/2)*360 = 180.

==================================================

Part (e)

Answer: 50 degrees

----------------------

Explanation:

Angle QPR is a central angle that subtends (cuts off) the minor arc RQ, which is shown to be 50 degrees. The central angle is equal to this arc measure, so angle QPR is also 50 degrees

Answer:  the value of f′′′(4) is 3/256.

Step-by-step explanation:

Given the third-degree Taylor polynomial:

f(x) = (x−4)³/512 − (x−4)²/64 + (x−4)⁴/2

To find the value of f′′′(4), we need to differentiate the polynomial three times and evaluate it at x = 4.

First derivative:

f'(x) = 3(x−4)²/512 − 2(x−4)/64 + 4(x−4)³/2

Second derivative:

f''(x) = 6(x−4)/512 − 2/64 + 12(x−4)²/2

Third derivative:

f'''(x) = 6/512 + 24(x−4)/2

Now, substitute x = 4 into f'''(x):

f'''(4) = 6/512 + 24(4−4)/2

= 6/512 + 0

= 6/512

= 3/256

Therefore, the value of f′′′(4) is 3/256.

A patent is a form of intellectual property that gives an individual or organization the exclusive right to manufacture, use, and/or sell an invention for a set period of time.

The length of a patent varies by country, but generally lasts for 20 years from the date the patent is filed with the government. This period can be extended in certain cases if the patent office grants a patent term extension.

The formula for calculating the length of a patent is: Length of Patent = Initial 20 Year Period + Extension. The initial 20 year period starts from the filing date of the patent application and is the same for all countries. However, the length of the extension varies depending on the country and the circumstances of the patent. For example, some countries may offer a 5-year extension, while others may offer a 10-year extension.

The length of a patent must be carefully calculated so that the patent owner can maximize the benefits of the patent. By calculating the patent length and extension, the patent owner can ensure that they are able to take advantage of their exclusive right to the invention for the maximum amount of time possible.

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If 7 out of every 9 people had Internet access, then 2 out of every 9 people did not have Internet access. The fraction of the world population that did not have Internet access in that year would be 2/9.

A fraction represents a portion of a whole or, more broadly, any number of equal pieces; a fraction describes the number of parts of a specific size, for example, one-half.

A fraction is a portion of a larger total. The number is stated in arithmetic as a quotient, which is the numerator divided by the denominator. Both are integers in a simple fraction. A complicated fraction contains a fraction in either the numerator or the denominator. A suitable fraction has a numerator that is smaller than the denominator.

There are three primary forms of fractions in mathematics. Proper fractions, improper fractions, and mixed fractions are the three types. Fractions are phrases that have a numerator and a denominator. We describe its kinds based on these two concepts.

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