If a pistol bullet is fired vertically at an initial speed of 100 m/s, the height in metres after
t seconds is given by h = 100t – 10t2.
A)Find the maximum height attained by the bullet
B)When does the bullet return to the ground?

The integral ∫√(4x³+4x²+4) dx simplifies to 0.

To evaluate the integral ∫√(4x³+4x²+4) dx, we can start by factoring the integrand and then using partial fractions to simplify the expression.

First, let's factor the integrand:

√(4x³+4x²+4) = √(4(x³+x²+1))

Now, we can rewrite the integral as:

∫√(4(x³+x²+1)) dx

To simplify this further, we can rewrite it as:

2∫√(x³+x²+1) dx

Now, let's perform long division on the integrand:

Divide x³+x²+1 by x² to get x+1

So, x³+x²+1 = (x+1)(x²+1) + 0

Now, we can rewrite the integral as:

2∫√((x+1)(x²+1)) dx

Next, we can express the integrand as a sum of partial fractions:

2∫(A/(x+1) + Bx/(x²+1)) dx

To find the values of A and B, we can multiply the entire equation by the denominators (x+1) and (x²+1) and equate the coefficients of the corresponding powers of x.

(x+1)(x²+1)(A/(x+1) + Bx/(x²+1)) = (A(x²+1)) + (Bx(x+1))

Expanding and equating coefficients, we get:

A + Bx = xA + A + Bx² + Bx

Simplifying the equation, we have:

A + A = 0 (coefficient of x³)

0 + B = 0 (coefficient of x²)

0 = A + B (coefficient of x)

From the second equation, B = 0

Substituting B = 0 in the third equation, we get A = 0

Therefore, the partial fraction decomposition is:

2∫(0/(x+1) + 0x/(x²+1)) dx

Simplifying further, we have:

2∫0 dx = 0

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Answer:

No, they do not

Step-by-step explanation:

15/20 = 0.75

14/15 = 0.93

0.75 is not equal to 0.93

So the ratios do not form a proportions

the total number of squares that contain the black center square is\($1 + 4 + 9 + 16 + 1 = \boxed{31}$.\)

To solve this problem, we need to count the number of squares of each size that contain the black center square.

There is only one square of size\($5\times 5$\), which is the entire grid and obviously contains the black center square.

For squares of size\($4\times 4$\), there are \($4$\)possible squares that contain the black center square (one for each corner).

For squares of size\($3\times 3$,\) there are 9 possible squares that contain the black center square (one for each position that the center square could occupy, and then each of those squares could be oriented in three different ways).

For squares of size $2\times 2$, there are $16$ possible squares that contain the black center square (one for each pair of adjacent squares).

For squares of size \($1\times 1$\), there is only one possible square that contains the black center square (the center square itself).

Therefore, the total number of squares that contain the black center square is\($1 + 4 + 9 + 16 + 1 = \boxed{31}$.\)

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There are 11 squares containing the black center square in the 5x5 grid.

To find the number of squares that contain the black center square, we'll consider the sizes of the squares and their positions in the 5x5 grid.
The black center square is a 1x1 square itself, so that's 1 square.
For 2 x 2 squares containing the center square, there are 4 possible positions (the center square can be in any corner). So, that's 4 squares.
For 3x3 squares containing the center square, there is only 1 possible position (the center square is exactly in the middle). So, that's 1 square.
4. For 4x4 squares containing the center square, there are 4 possible positions (the center square can be in any corner). So, that's 4 squares.
5. For 5x5 squares containing the center square, there is only 1 possible position (the center square is exactly in the middle).

So, that's 1 square.
Now, we'll add up the number of squares we found in each step:
1 + 4 + 1 + 4 + 1 = 11.

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Based on the given data, the process is out of control.

To determine if the process is still in control, we need to compare the new sample measurements to the control limits established in the X-bar and R control charts.

For the X-bar chart:

The UCL (Upper Control Limit) is calculated as the grand average (X-Double Bar) plus A2 times R-Bar:

UCL = 25 + (0.483 * 5) = 27.415

The LCL (Lower Control Limit) is calculated as the grand average (X-Double Bar) minus A2 times R-Bar:

LCL = 25 - (0.483 * 5) = 22.585

For the R chart:

The UCL (Upper Control Limit) for the R chart is calculated as D4 times R-Bar:

UCL = 2.004 * 5 = 10.020

The LCL (Lower Control Limit) for the R chart is 0.

Given the new sample measurements: 33, 37, 25, 35, 34, and 32, we can determine if any of the measurements fall outside the control limits. If any data point falls outside the control limits, it indicates that the process is out of control.

Upon comparing the new sample measurements to the control limits, we find that the measurement 37 exceeds the UCL of the X-bar chart. Therefore, the process is considered out of control.

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Answer: Nany watched 62.5% of the movies

Step-by-step explanation:

5/8 as a percentage is 62.5%

For testing, if x is a significant predictor of y in simple linear regression, we need to determine if the slope is significantly different from zero.

Given,

Simple linear regression .

A statistical technique known as linear regression is used to represent the connection between a scalar answer and one or more explanatory factors. When there is just one explanatory variable, simple linear regression is employed; when there are numerous explanatory variables, multiple linear regression is utilized.

Based on the value of another variable, linear regression analysis makes predictions about the value of the first variable. The dependent variable is the one you're trying to forecast. The independent variable is the one you are utilizing to make a prediction about the value of the other variable.

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Answer:

The correct answer is:

It is a continuous random variable (C)

Step-by-step explanation:

Continuous Random Variables are variables that do not take on a distinct value. They take on values that are a range of different possibilities to infinity. In continuous random variables, the values cannot be counted. In this example, the time it takes for a light bulb to burn out can be any rational number which is greater than 0, up to infinity; for instance, it can be 24 hours, 24.5 hours, 30.8 hours, 51.2 hours etc. There is an infinite possibility of the time it takes for the bulb to burn out.

Discrete Random Variables are ones in which the variables take on distinct values and nothing in between. Here, the outcomes can be counted. For example if a coin is tossed, there are only two possibilities which can be the outcome and that is either head, or tail. The number of possible outcome is 2, and there is nothing inbetween head or tail.

Answer:

It’s C

(Gibberish words to so i can to 29 words)

hciejdgrifgirgrittrufifgeydifufgfidhfuvifgdudugcudydgdidhdhf

Hope this helped,if not, don’t hate.

The largest value that f(4) can possibly be is 29.

The mean value theorem states that for a function f(x) that is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), there exists a number c in the open interval (a, b) such that:

f(b) - f(a) = f'(c)(b - a)

In this case, we are given that f(0) = -3 and that f'(x) ≤ 8 for all values of x. To determine how large f(4) can possibly be, we can use the mean value theorem with a = 0 and b = 4:

f(4) - f(0) = f'(c)(4 - 0)

Substituting the given values:

f(4) - (-3) = f'(c)(4)

f(4) + 3 = 4f'(c)

Since f'(x) ≤ 8 for all values of x, we can say that f'(c) ≤ 8. Therefore:

f(4) + 3 ≤ 4f'(c) ≤ 4(8) = 32

Therefore, we have:

f(4) ≤ 32 - 3 = 29

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The time it takes for the cannonball to strike the ground if a certain cannon is fired from a height of 8.1 meters above the​ ground, at a certain​ angle, the height of the cannonball above the​ ground, h, in​ meters, at​ the time, t, in​ seconds, is found by the function h(t) =-4.9 t² + 27.5t + 8.1 is 5.612 seconds.

A vector measure of movement's speed and direction is called velocity. Simply described, velocity is the rate of movement in a specific direction.

Given:

The height of the cannon = 8.1 m

The height equation, h  = -4.9 t² + 27.5t + 8.1

Calculate the time by putting the value of  height in the equation as shown below,

h = (-4.9 t² + 27.5t + 8.1)

8.1 = (-4.9 t² + 27.5t + 8.1)

-4.9 t² + 27.5t = 0

Solve the quadratic equation,

t = 5.61224 sec

Therefore, the time it takes for the cannonball to strike the ground if a certain cannon is fired from a height of 8.1 meters above the​ ground, at a certain​ angle, the height of the cannonball above the​ ground, h, in​ meters, at​ the time, t, in​ seconds, is found by the function h(t) =-4.9 t² + 27.5t + 8.1 is 5.612 seconds.

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Answer: X= 16

Step-by-step explanation:

SOLUTION.

The area of the entire region will be to find the area of the isosceles triangle and the semi-circle.

Then

The area of the isosceles triangle is 30.354 square units

We need to obtain the diameter of the semi-circle using the cosine rule

We need to obtain the value of x,

Take square root of both sides, we have

Hence, the diameter is 9.74

Then the radius will be

The area of the semi-circle is

The area of the semi circle is 37.42 square units

Therefore the area of the region will be

Thus

The area of the region is 67.96 units²

Answer:

ROC=10/1

Step-by-step explanation:

ROC=change in y-change in x

We can first write out a few more points.

(7,70), (14,140), (21,210)

210-140=70

140-70=70

21-14=7

14-7=7

So the ROC is 70/7 or 10/1

Based on the analysis, only Table 2 represents a linear function.

To determine if a table represents a linear function, we need to check if there is a constant rate of change between the values of x and y. If the ratio of the change in y to the change in x remains constant, then the table represents a linear function. Let's analyze each table:

Table 1:

x   |   y

1   |  -3

1   |  -2

1   |  -1

1   |   0

1   |   1

In this table, the value of y does not change as x changes. Therefore, it does not represent a linear function.

Table 2:

x   |   y

-4  |   4

-2  |   2

0    |   0

2    |   2

4    |   4

In this table, as x increases by 2, y also increases by 2. The ratio of the change in y to the change in x is 2/2 = 1. Therefore, this table represents a linear function.

Table 3:

x   |   y

-5  |   -1/2

-3  |   1

-1  |   2

1    |   7/2

3    |   5

In this table, the ratio of the change in y to the change in x is not constant. Therefore, it does not represent a linear function.

Table 4:

x   |   y

-6  |   5

-4  |   13/3

-2  |   11/3

0    |   3

2    |   7/3

In this table, the ratio of the change in y to the change in x is not constant. Therefore, it does not represent a linear function.

Based on the analysis, only Table 2 represents a linear function, where the values of y change at a constant rate as x increases.

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

\(\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\)

                  Find the circumference of the circle and show work. [refer to  

                  attachment]

\(\large\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}\)

          Formula for Circumference of a Circle:-

        \(\dashrightarrow\star\bigstar\boxed{\boxed{C=2\pi r}}}\)

Where

Substitute the value of r and solve:-

         C=2π(8)

        On simplification,

C=16π

On further simplification,

C=50.3

Therefore, we conclude that the circumference of this circle is

\(\dashrightarrow\star\bigstar\boxed{\boxed{\underline{\bold{C=50.3\:yd}}}}\bigstar\star\dashleftarrow\)

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

Perimeter would be approximately 23.57 ft

Consider triangle ABC is an isosceles triangle,

In which AB = AC,

And, m∠A = 150°,

∵ AB = AC ⇒ m∠B = m∠C,

Now sum of all interior angles of a triangle is 180°,

i.e. m∠A + m∠B + m∠C = 180°,

150°+ m∠B + m∠B= 180°,

2m∠B + 150° = 180°

2m∠B = 30°

⇒ m∠B = 15°

Let D ∈ BC such that AD ⊥ BC,

∵ Altitude of an isosceles triangle is its median,

i.e, BD = DC or BD = (1/2) BC

In triangle ADB,

⇒ Tan 15 = AD/BD

⇒ Tan 15 = 2AD/BC

⇒ AD = (BC tan15)/2     ......(i)

Now, area of triangle ABC = (1/2)xBCxAD

If area = 9 square ft,

From equation (1),

(1/2)x(BC tan15)/2 x  BD =  9

⇒ BC² = 36/tan15 = 134.35

⇒ BC = 11.59 ft

From equation (1),

AD = 1.55

Using Pythagoras theorem,

⇒ AB = √(AD² + BD²)

⇒ AB = 5.99 ft

Hence, perimeter of the triangle ABC= AB + BC + CA

= 5.99 + 11.59 + 5.99

= 23.57 ft

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Answer:

Let ac=ab=5

With this, bc= 5√2

Step-by-step explanation:

So to find ad, Let ad be x

5√2=(2)(x)

(5√2/2)= x

This proves that bc=2ad

Not a robot! I don't think.

Y in the beginning goes up to 3.

Y in the end goes down to -2 before shooting back up in an infinite sense.

Increasing: The beginning and the end the line on the graph. (Also the jump in the middle, the round part.)

Decreasing: The middle of the graph. (The jump, downward slope.)

Constant, Y at the near end going in a straight line from 9-12 at a -2.

End behavior: Decide for yourself. Is the line going up without fault at the end an appearing continuous or a discontinuous line?

Answer:

End Behavior:

x⇒-8,y⇒-∞

x⇒∞,y⇒∞

(-∞,1},{3,5},{12,∞)

{1,3},{5,9}

(9,12)

hope it helps...

have a great day

Answer:

the y intercept is 5

Step-by-step explanation:

If your required return is 6% per year, compounded monthly, and you are offered an investment that will pay you $800 a month for 40 years, the approximate amount you would be willing to pay for this investment is $16.80.

To determine the present value of the investment, we need to calculate the discounted value of the future cash flows. In this case, the cash flow is $800 per month, and the time period is 40 years, or 480 months.

Using the formula for present value, which is \(PV = CF / (1 + r)^n\), where PV is the present value, CF is the cash flow, r is the required return per period, and n is the number of periods, we can substitute the given values:

PV = $800 / (1 + 0.06/12)\(^(480)\)

Simplifying the expression, we find that the present value is approximately $16.80. This means that if you want to achieve a required return of 6% per year, compounded monthly, you would be willing to pay approximately $16.80 for this investment.

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Answer:

2 + 2x = 262x = 24x=12 3.

Step-by-step explanation:

i think its right

Answer: A equals -2

Step-by-step explanation:

First, start off by replacing x with -4.

Then add 4 to -4 and -8.

Afterwards, you should be left with 2A = -4. Then divide 2A and -4 by 2

Your answer should be “A = -2”

Hope this helps :)

Answer:

Equation of the line in point-slope form: y - 5 = -⅚(x - 2)

Equation of the line in slope-intercept form: y = -⅚x + 20/3

Step-by-step explanation:

Equation of a line can be expressed in the point-slope form as y - b = m(x - a), where,

m = slope = -⅚

a = 2

b = 5

Substitute the values into y - b = m(x - a):

y - 5 = -⅚(x - 2) => point-slope form.

We can rewrite this in the slope-intercept form, such as:

Multiply both sides by 6

6(y - 5) = -5(x - 2)

6y - 30 = -5x + 10

6y - 30 + 30 = -5x + 10 + 30

6y = -5x + 40

Divide both sides by 6

y = -5x/6 + 40/6

y = -⅚x + 20/3

Answer:

If you distribute 4(x+2) using the distributive property, which states that multiplying each number individually by a same # is the same as multiplying the #s' sum by that #.

Thus, 4*(x+2) is the same as 4*x+4*2 which simplifies to 4x+8, Option 2

To start the ABCD process on the server as a regular user, the "sudo" command would be used to execute the process with root privileges. The "sudo" command allows a regular user to perform administrative tasks on a Unix or Linux system, provided they have the necessary permissions.

The "sudo" command allows a regular user to perform administrative tasks on a Unix or Linux system, provided they have the necessary permissions. In this case, since the ABCD process can only be run by root, using "sudo" allows the regular user to temporarily acquire root privileges and execute the process.

The command to start the ABCD process with root privileges would be: "sudo <command>". Replace "<command>" with the actual command needed to start the ABCD process. When executing this command, the system will prompt the user to enter their password to verify their identity. Once the password is authenticated, the command will be executed with root privileges, allowing the ABCD process to start.

It's important to note that the use of "sudo" should be done with caution and only when necessary. It grants elevated privileges, and users should be mindful of the commands they run with root access to avoid any unintended consequences or potential security risks.

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The probability of getting a green wrinkled pea from a yyrr x yyrr cross is 1/4.

A cross was made between a pure round yellow seeded pea plant (RRYY) with wrinkled green seeded pea plant (rryy). The yellow colour is dominant over green and round seed shape is dominant over wrinkled seed shape.

The possibility of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given occurrence will occur.

All of the children were yellow because yellow has a dominant gene over green. The green phenotype was no longer present. To see how the second generation would appear, let the yellow pea plants self-fertilize.

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Answer:

its SUMMER wth

Step-by-step explanation:

Its time too TURN UPPP!

Answer:

450/31=14.51km/litre

Answer:

the coordinate

Step-by-step explanation:

Answer:

It is simply called a coordinate!

Step-by-step explanation:

When you think of coordinates, you would often think of a coordinate plane. Coordinate planes technically contain two number lines, thus numbers that correspond to a point on a number line are coordinates.

The set Z(2) consists of the remainders of integers when divided by 2, and 2/6 is congruent to 2 modulo 2, which is not an element of Z(2), we can conclude that Z(2) does not contain 2/6.

To determine if the set Z(2) contains the fraction 2/6, we need to understand what Z(2) represents.

The notation Z(2) typically refers to the set of integers modulo 2, also known as the integers modulo 2 ring. In this set, the elements are the remainders of integers when divided by 2, which are 0 and 1.

To check if 2/6 is in Z(2), we need to reduce 2/6 modulo 2. When we divide 2 by 6, the remainder is 2, which means 2/6 is congruent to 2 modulo 2.

In Z(2), the only possible values are 0 and 1, so 2 is not an element of Z(2). Therefore, 2/6 is not in Z(2).

In summary, since the set Z(2) consists of the remainders of integers when divided by 2, and 2/6 is congruent to 2 modulo 2, which is not an element of Z(2), we can conclude that Z(2) does not contain 2/6.

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Given:

\(ST=4y,TU=2y+6\)

To find:

The value of  y, ST and TU.

Solution:

In triangle STV and UTV,

\(m\angle TSV\cong n\angle TUV\)            (Given right angles)

\(m\angle SVT\cong n\angle UVT\)            (Given)

\(TV\cong TV\)            (Common side)

The corresponding two angles and a non included sides in both triangles are congruent. So, the triangles are congruent by using AAS congruence postulate.

\(\Delta STV\cong \Delta UTV\)           (AAS congruence postulate)

Corresponding parts of congruent triangles are congruent. So,

\(ST\cong UT\)              (CPCTC)

\(4y=2y+6\)

\(4y-2y=6\)

\(2y=6\)

\(y=3\)

Now,

\(ST=4y\)

\(ST=4(3)\)

\(ST=12\)

And,

\(TU=2y+6\)

\(TU=2(3)+6\)

\(TU=6+6\)

\(TU=12\)

Therefore, \(y=3,\ ST=12\ units,\ TU=12\ units\).