Find a polynomial function f(x) of degree 3 with zeros, 2, -3 , 5 and f(3)=6

-63.63 m/s is the rate of change of the distance between the plane and the car when both are maximum speed and the plane is ahead by 70m?

Let's use the Pythagorean theorem to relate the distance between the car and the plane to their individual distances traveled. Let d be the distance traveled by the car, then the distance traveled by the plane is d + 70 (since the plane is ahead by 70m). Then, the distance between them is given by:

distance = [tex]\sqrt{d^{2}+500^{2} }[/tex] (using Pythagorean theorem)

Now, let's differentiate both sides with respect to time (t) to find the rate of change of the distance between the car and the plane:

d(distance)/dt = (1/2)[tex](d^{2} +500^{2} )^{(-1/2)}[/tex] * (2d/dd)(dd/dt)

where the first term on the right side is the derivative of the square root expression and the second term is the derivative of d with respect to time.

Now we need to find d in terms of t, given the maximum speeds of the car and the plane. Let's assume that they both start at time t = 0 and are racing for a time of T. Then, we can write:

d = 200T (distance traveled by the car)

d + 70 = 300T (distance traveled by the plane)

Solving for T, we get:

T = 70/100 = 0.7 hours = 42 minutes

Substituting T back into the expressions for d, we get:

d = 200(0.7) = 140 km

d + 70 = 300(0.7) = 210 km

Now we can substitute these values into the expression for the rate of change of the distance between the car and the plane:

d(distance)/dt = (1/2)[tex](d^{2} +500^{2} )^{(-1/2)}[/tex]  * (2d/dd)(dd/dt)

d(distance)/dt = (1/2)[tex](140^{2} +500^{2} )^{(-1/2)}[/tex] * (2*140/60)(300 - 200)

d(distance)/dt = -63.63 m/s

Therefore, the rate of change of the distance between the car and the plane when both are at maximum speed and the plane is ahead by 70m is approximately -63.63 m/s. Note that the negative sign indicates that the distance between them is decreasing, since the plane is ahead of the car.

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Answer:

Step-by-step explanation:

The length of the secant line JK is 32.

The secant-tangent power theorem states that if a tangent and a secant are drawn from a common external point to a circle, then the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment.

It is expressed as:

( tangent segment )² = External part of the secant segment × Secant segment.

From the diagram:

Tangent line JI = 24

External part of the secant segment LJ = 18

Secant segment JK = x + 18

Plug these values into the above formula and solve for b.

( tangent segment )² = External part of the secant segment × Secant segment.

24² = 18 × ( x + 18 )

576 = 18x + 324

18x = 576 - 324

18x = 252

x = 252/18

x = 14

Hence, secant line JK will be:

x + 18 = 14 + 18 = 32

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Answer: r=2sinθ.

Step-by-step explanation:To convert to polar coordinates, we use the relationships

xy=rcosθ=rsinθ.

Substituting these into the given equation, we find

x2+y2(rcosθ)2+(rsinθ)2r2cos2θ+r2sin2θ=2y=2(rsinθ)=2rsinθ

Factoring and applying the Pythagorean identity, we obtain

r2(cos2θ+sin2θ)r2(1)r2=2rsinθ=2rsinθ=2rsinθ

Dividing both sides by r yields

r2rr=2rsinθr=2sinθ

Thus, a polar equation representing the given function is r=2sinθ.

The measure of angle C is given as follows:

m < C = 44º.

To obtain the measures of the angles in this problem, we must consider that the sum of the measures of the internal angles of a triangle is of 180º.

Considering that the sum of the measures of the internal angles of a triangle is of 180º, and angles C, D and E, the value of x is obtained as follows:

4x - 16 + 6x - 1 + 4x - 13 = 180

14x - 30 = 180

14x = 210

x = 210/14

x = 15.

Hence the measure of angle C is obtained as follows:

m < C = 4 x 15 - 16 = 44º.

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Answer:

False. The product of two negative integers is a positive integer.

The value of y for this ordered pair is 7.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of line AC;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-2 + 8)/(-4 + 8)

Slope (m) = 6/4

Slope (m) = 3/2

At data point (-4, -2) and a slope of 3/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 2 = 3/2(x + 4)  

y = 3x/2 + 4

When x = 2, the y-value is given by;

y = 3(2)/2 + 4

y = 7.

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The surface area of the larger pyramid in discuss would be 25 times the surface area of the smaller pyramid.

It follows from the task content that the surface area of the larger pyramid and the smaller pyramid are to be compared.

By observation; the differing dimensions are such that the ratio of the larger pyramid to the smaller pyramid is; 10 / 2 = 5.

On this note, the ratio of the area of the pyramids are such that the larger pyramid is 5² = 25 times larger than that of the smaller pyramid.

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Answer:

  3/23 or 0.1304 or 13%

Step-by-step explanation:

Given 3 students have a brother and sister, and 20 students have only a brother, you want the probability that a student who has a brother also has a sister.

The conditional probability formula is ...

  P(A | B) = P(A&B)/P(B)

Here, this means ...

  P(has a sister | has a brother) = P(has both)/P(has a brother)

  = 3/(3 +20)

  = 3/23 ≈ 0.1304 ≈ 13% . . . . . probability of a sister if has a brother

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Answer:

Concave up on the intervals (-π/2, π/2), and concave down on the intervals (-π,-π/2) and (π/2,π).

Step-by-step explanation:

To find the intervals where the function y = -cot(x) is concave up and concave down, we need to find the second derivative of the function and then determine its sign for different intervals.

First, we find the first derivative of y = -cot(x):

dy/dx = csc^2(x)

Then, we find the second derivative by differentiating the first derivative:

d^2y/dx^2 = -2csc^2(x) * cot(x)

We know that the function is concave up when the second derivative is positive, and concave down when the second derivative is negative.

Now, we need to determine the intervals where the second derivative is positive and negative.

d^2y/dx^2 > 0 when:

-2csc^2(x) * cot(x) > 0

csc^2(x) < 0 and cot(x) < 0 or csc^2(x) > 0 and cot(x) > 0

Since csc^2(x) is always positive, we can ignore the first inequality. Therefore, the second derivative is positive when cot(x) > 0.

d^2y/dx^2 < 0 when:

-2csc^2(x) * cot(x) < 0

csc^2(x) > 0 and cot(x) < 0 or csc^2(x) < 0 and cot(x) > 0

Since csc^2(x) is always positive, we can ignore the first inequality. Therefore, the second derivative is negative when cot(x) < 0.

Recall that cot(x) = cos(x)/sin(x), which changes signs at x = kπ, where k is an integer.

So, we can now use this information to determine the intervals of concavity:

   For x in (-π/2,0) and (0,π/2), cot(x) is positive and therefore, the function is concave up.

   For x in (-π,-π/2) and (π/2,π), cot(x) is negative and therefore, the function is concave down.

Therefore, the function y = -cot(x) is concave up on the intervals (-π/2, π/2), and concave down on the intervals (-π,-π/2) and (π/2,π).

The solution to the equation is x = 10 or x = -2.

An equation refers to a mathematical expression showing that two expressions are equal.

It must have variables (e.g. a, c, x, y), constants (like 1, 13, 50, etc), and mathematical operations (like +, -, *, /).

To solve for x, we shall start with the given equation:

x + 6 = √(2x + 29) + 9

Subtract 9 from both sides:

x - 3 = √(2x + 29)

Square both sides:

[tex](x - 3)^2[/tex] = 2x + 29

Expand the left side:

[tex]x^2[/tex] - 6x + 9 = 2x + 29

We then subtract 2x and 9 from both sides:

[tex]x^2[/tex] - 8x - 20 = 0

Next, actor the quadratic equation:

(x - 10)(x + 2) = 0

Therefore, the equation x = 10 or x = -2

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Answer:

Fred doesn't run

Step-by-step explanation:

Fred doesn't run, Fred likes to walk, you obviously don't know Fred enough to answer this question, so tell your teacher how you can get in touch with Fred for a better relationship

let's firstly convert the mixed fractions to improper fractions, then sum them up.

[tex]\stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}}~\hfill \stackrel{mixed}{1\frac{3}{8}} \implies \cfrac{1\cdot 8+3}{8} \implies \stackrel{improper}{\cfrac{11}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{4}+\cfrac{11}{8}\implies \cfrac{(2)5~~ + ~~(1)11}{\underset{\textit{using this LCD}}{8}}\implies \cfrac{10+11}{8}\implies \cfrac{21}{8}\implies 2\frac{5}{8}~miles[/tex]

Answer:

Step-by-step explanation:

January, June, and July

are 3 months out of 12, which equals 1/4 (12 : 3 = 4),

1/4 equals 25% (100 : 4 = 25%)

The probability that a random point on the AK line will be on the BE line is 0.5 or 50%, since the length of the BE line is 10 units and the length of the AK line is 20 units.

To find the probability that a random point on the AK line will be on the BE line, we need to determine the length of the BE line and the length of the AK line.

The BE line extends from point -5 to point 5, a distance of 5 - (-5) = 10 units.

The AK line extends from point -10 to point 10, a distance of 10 - (-10) = 20 units.

Therefore, the probability that a random point on the AK line will be on the BE line is

Length of BE line / Length of AK line = 10 / 20 = 0.5

So, the probability that a random point on the AK line will be on the BE line is 0.5 or 50%.

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Answer:

p≥35

Step-by-step explanation:

because you have done 15 so you subtract 15 from 50 giving you 35 and then you would say p is greater than or equal to 35 cause 50 pages is your minimum

Answer: 3.1

Step-by-step explanation: they are giving you the diameter so you halve it then you multiply it my 3.14 (pi) then you round it to the nearest tenth which is the 1 so you look to the left and it's not bigger than 5 so you round down so it stays as a 1

The lateral surface area of the cylinder is approximately 175.84 square meters.

We have,

The lateral surface area of a cylinder.

= 2πrh

where r is the radius of the base, h is the height of the cylinder, and π is approximately 3.14.

Now,

r = 2 m, h = 14 m

Substituting these values in the formula, we get:

Lateral surface area = 2πrh

= 2 x 3.14 x 2 x 14

= 175.84 m² (rounded to the nearest tenth)

Therefore,

The lateral surface area of the cylinder is approximately 175.84 square meters.

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To determine what percentage of working adults in your neighborhood regularly ride the bus to work, the best sampling method and survey question are D. Enter the names of all adults in your neighborhood into a computer program to randomly select a sample and ask, "Do you ever ride the bus to work?"

The best sampling method involves random sampling of the population.

A random sample gives each member of the population an equal chance of being selected as a participant in the survey.

It is also described as a probability sampling method.

Thus, in this instance, the correct option is D.

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According to the information, It's important to acknowledge both of their perspectives and try to find a way to resolve the situation and move forward positively.

The situation is: two friends are having an argument because one of them forgot to invite the other to a party.

I can imagine that it must be really difficult for both of your friends right now. One of them might be feeling hurt and left out because they didn't get an invitation to the party, while the other might be feeling guilty and regretful for forgetting to invite them. It's important to acknowledge both of their perspectives and try to find a way to resolve the situation and move forward positively.

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Answer:

Me: 60

Zayn and Attia: 6

Step-by-step explanation:

12 = 2 × 2 × 3

20 = 2 × 2 × 5

LCM of 12 and 20 = 2 × 2 × 3 × 5 = 60

My number is 60.

Zayn's and Attia's numbers are 6.

Answer:

16

Step-by-step explanation:

2×2×2×2=16

So, the answer is 16.

The next number in the series would be 31 so the complete series is 101, 001, 66, 31.

The first thing we observe is that 101 equals 100 plus one. The second term, 001, equals 0 plus 1. Now consider the distinctions between consecutive terms:

101 - 001 = 100

001 - 66 = -65

When we look at the disparities (100, -65), we can see a pattern. The difference between 100 and 65 is a factor of 35. We can now apply this distinction to the final term in the series:

66 - 35 = 31

So the next number in the series is 31, completing the sequence: 101, 001, 66, 31.

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Step-by-step explanation:

a) 11*5=55

15*5=75

8*5+5=45

b) No, because (55+75+45=175°) and the perimeter of a triangle is 180°

Answer:

The union of sets A and B is:

A U B = {1, 2, 3, 4, 6, 8}