If I was birn in 2004, I’m 17 years old and I graduate in 2022. What year would it have been in my 9th year?

Answer: 12k+2

Step-by-step explanation:

The equation of the parabola is given as follows:

y = -28/19600(x - 140)² + 28.

The distances from the center for a height of 13 meters are given as follows:

37.53 m and 242.47 m.

The equation of a parabola of vertex (h,k) is given by the equation presented as follows:

y = a(x - h)² + k.

In which a is the leading coefficient.

It has a span of 280 meters, hence the x-coordinate of the vertex is given as follows:

x = 280/2

x = 140 -> h = 140.

The maximum height is of 28 meters, hence the y-coordinate of the vertex is given as follows:

y = 28 -> k = 28.

Hence the equation is:

y = a(x - 140)² + 28.

When x = 0, y = 0, hence the leading coefficient a is obtained as follows:

19600a = -28

a = -28/19600

Hence:

y = -28/19600(x - 140)² + 28.

The distance from the center at which the height is 13 meters is obtained as follows:

13 = -28/19600(x - 140)² + 28.

28/19600(x - 140)² = 15

(x - 140)² = 15 x 19600/28

(x - 140)² = 10500.

Hence the distances are obtained as follows:

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The measure of the arc BC using the congruency of central angle and intercepted arc is 85°.

Given a circle.

Also given that,

Measure of arc AE = 70°

Also, m ∠BDC = 85°

Now, ∠BDC is the central angle corresponding to the intercepted arc BC.

central angle and intercepted arc are congruent.

So, m arc BC = 85°

Hence the required measure is 85°.

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Answer:

\(6x = - 4 \\ x = \frac{ - 2}{3} \)

The solution of the inequality is, x ∈ (- ∞, 5) ∪ (10, ∞)

Where, x represent the number of totts.

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

My friend Raw has either no more than 5 toots and more than 10 toots.

Now, Let number of toots = x

Hence, We get;

⇒ x < 5

And, x > 10

Thus, The solution of the inequality is,

⇒ x ∈ (- ∞, 5) ∪ (10, ∞)

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Answer:

1. RQ

2. R, Y and V

3. T

4. No

Step-by-step explanation:

If we imagine a plane as a rectangle, we can easily see that planes RSTQ and RVUQ intersect in line RQ. Basically, if two planes intersect each other, that intersection is always a line.

Collinear points lie on the same line. Every two points make a line, so the third one also needs to lie along that line. On the diagram, R, Y and V are the only three points on the same line.

From the diagram, we can infer that QT and TX intersect in point T. Additionally, every two lines intersect in a point (of course, unless they're parallel).

Coplanar points lie in the same plane. Three points are enough to define a plane. Whichever three points (R, Q, W and U) we choose we'll have a plane, but the fourth point won't lie in it. This means they are not coplanar.

(a) To find the flux of the vector field F→(x, y, z) = ⟨x, y, 5z⟩ through the closed boundary S of the solid W bounded by the paraboloid z = x² + y² and the plane z = 16, we can apply the divergence theorem.

AS

The divergence theorem states that the flux of F→ through S is equal to the triple integral of the divergence of F→ over the volume V enclosed by S.

First, we need to calculate the divergence of F→. Taking the divergence, we have div(F→) = ∂/∂x(x) + ∂/∂y(y) + ∂/∂z(5z) = 1 + 1 + 5 = 7.

Next, we evaluate the triple integral of the divergence over the volume V. The limits of integration for V are determined by the region bounded by the paraboloid and the plane, which can be expressed as 0 ≤ z ≤ x² + y² and 0 ≤ z ≤ 16. The integral becomes ∭V div(F→) dV = ∭V 7 dV.

To evaluate this triple integral, we need to express it in appropriate coordinates, such as cylindrical or spherical coordinates, depending on the symmetry of the problem. Then we can determine the limits of integration and perform the integration to compute the flux value.

(b) To find the flux of F→ out of the bottom of S (the truncated paraboloid) and the top of S (the disk), we need to consider the orientation of the surface and apply the divergence theorem separately for each surface.

For the bottom surface (truncated paraboloid), the outward orientation is in the negative z-direction. The flux through this surface is given by the negative of the integral ∭V div(F→) dV over the volume V enclosed by the bottom surface.

For the top surface (disk), the outward orientation is in the positive z-direction. The flux through this surface is equal to the integral ∭V div(F→) dV over the volume V enclosed by the top surface.

In both cases, we can use the same divergence value calculated earlier, div(F→) = 7, and integrate over the appropriate limits of integration based on the geometry of the surfaces.

In summary, to find the flux of F→ through the closed boundary S, we apply the divergence theorem by calculating the divergence of F→ and evaluating the triple integral over the volume enclosed by S. To find the flux out of the bottom and top surfaces separately, we consider the orientations and integrate over the appropriate volumes.

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Answer:

x = 3

Step-by-step explanation:

Subtract 8x from both sides.

3x+4−8x=8x−11−8x

−5x+4=−11

Subtract 4 from both sides.

−5x+4−4=−11−4

−5x=−15

Divide both sides by -5.

−5x

−5

=

−15

−5

x=3

Answer:

2/16

Step-by-step explanation:

your adding 2 and 16 so 2/16

Answer:

16 + 9 = 25

Step-by-step explanation:

For each term in the sequence, we can see that the second number being added increases by 2 each time (3, 5, 7)

And that the first number of each term increases by the value of the second term

(1 increases by 3; 4 increases by 5)

we can follow out these two observations to find T4

the first term (9) will increase by the value of the second term (7)

{the sum of the previous term is the first number}

so the first number of T4 will be 16.

Because we left off on +7, we are now on +9

so, T4 is

16 + 9 {and then do the math accordingly}

16 + 9 = 25

So, T4 is

16 + 9 = 25

hope this helps!! have a lovely day!! :)

The basic subtraction of rational expression simplified is (7)/(12d).

To subtract these rational expressions, we need to find a common denominator. The least common denominator (LCD) of 4d and 6d is 12d. We can then rewrite the expressions with the LCD as the denominator:

(3)/(4d) = (3 * 3)/(4d * 3) = (9)/(12d)
(1)/(6d) = (1 * 2)/(6d * 2) = (2)/(12d)

Now we can subtract the numerators and keep the same denominator:

(9)/(12d) - (2)/(12d) = (9 - 2)/(12d) = (7)/(12d)

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF), which is 1:

(7)/(12d) = (7/1)/(12d/1) = (7)/(12d)

So the final answer is (7)/(12d).

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Answer:

5) x = 77

7) b = 210

Step-by-step explanation:

5) 11 = X/7

multiply both sides by 7. doing this gets rid of the 7 on the right side of the equation.

(7)(11) = x

77 = x

7) 14 = b/15

same thing as above! multiply both sides by 15.

(15)(14) = b

210 = b

Hope this helps you!

Answer: we can try 0.5x4 OR we can try 0.5+0.5+0.5+0.5=2

Step-by-step explanation:

basic math.

A graph which represents the linear function y = -2x is: graph B.

In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.

Generally speaking, the graph of any proportional relationship is characterized by a straight line with the data points passing through the origin (0, 0) because as the values on the x-axis (x-coordinate) either increases or decreases, the values on the y-axis (y-coordinate) increases or decreases simultaneously.

In this context, we can reasonably infer and logically deduce that the relationship between x-values and y-values in the graph of y = -2x is proportional as it passes through the origin (0, 0).

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Given statement solution is :- a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

Set A: {apple, banana}, Set B: {cat, dog}

Power set of A: {{}, {apple}, {banana}, {apple, banana}}

Power set of B: {{}, {cat}, {dog}, {cat, dog}}

Set A: {red, blue}, Set B: {circle, square}

Power set of A: {{}, {red}, {blue}, {red, blue}}

Power set of B: {{}, {circle}, {square}, {circle, square}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}

Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}

Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}

Set A: {red, blue, green}, Set B: {circle, square, triangle}

Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}

Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

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If the numbers denoting the perimeter and area of the square are equal, the length of the diagonal will be 4√2 units.

What are Area and Perimeter?

An object's shape defines a region as its area. The area of a figure or any other two-dimensional geometric shape is how much space it takes up in a plane.

The whole length encircling a shape is referred to as its perimeter. Simply put, if a shape is stretched into a linear form, its perimeter is its length. In a two-dimensional plane, a shape's perimeter is the sum of its total dimensions.

Let the side of the square to be 'a'.

If Area and Perimeter of a square are equal then,

So,  Area = Perimeter

      a^2 = 4a

we get, a = 4 units.

Now, we can find the diagonal by using Pythagoras theorem,

We know that, Hypotenuse^2 = Base^2 + Perpendicular^2

Here, the hypotenuse will be the diagonal of the square.

So, We have,

            Diagonal^2 = 4^2 + 4^2

                                = 16 + 16

                                = 32

∴ Diagonal = √32 = 4√2 units.

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  v/24 = 23

   x 24 | x 24       23 x 24 = 552

    24v | 552

     24  |  24

        v = 23

Answer:

66

Step-by-step explanation:

180-119=61

53+61-180

=66

In the basis step of the mathematical induction proof for P(n), we show that the equation is true for n = 1. The equation of the inductive hypothesis (IH) is P(k), where k is an arbitrary natural number. In the inductive step, we need to show that if P(k) is true, then P(k+1) is also true.

In the basis step, we substitute n = 1 into the equation 11⋅2+12⋅3+⋅⋅⋅+1n⋅(n+1)=nn+1. This gives us the equation 1⋅2 = 1+1, which is true.

The inductive hypothesis (IH) is denoted as P(k), where k is an arbitrary natural number. We assume that P(k) is true, meaning that 11⋅2+12⋅3+⋅⋅⋅+1k⋅(k+1)=kk+1 holds.

In the inductive step, we need to show that if P(k) is true, then P(k+1) is also true. This involves substituting n = k+1 into the equation 11⋅2+12⋅3+⋅⋅⋅+1n⋅(n+1)=nn+1 and demonstrating that the equation holds for this value. The specific equation we need to show in the inductive step is 11⋅2+12⋅3+⋅⋅⋅+1(k+1)⋅((k+1)+1)=(k+1)(k+1+1).

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In the basis step, we need to show that the equation P(1) is true. The equation of the inductive hypothesis (IH) is P(k), where k is any natural number greater than or equal to 1. In the inductive step, we need to show that if P(k) is true, then P(k+1) is also true.

To prove the equation P(n): 11⋅2 + 12⋅3 + ... + 1n⋅(n+1) = n(n+1) using mathematical induction, we follow the two-step process.

1. Basis Step:

We start by showing that the equation is true for the base case, which is n = 1:

P(1): 11⋅2 = 1(1+1)

Simplifying, we get: 2 = 2, which is true.

2. Inductive Step:

Assuming that the equation is true for some arbitrary value k, the inductive hypothesis (IH) is:

P(k): 11⋅2 + 12⋅3 + ... + 1k⋅(k+1) = k(k+1)

In the inductive step, we need to show that if P(k) is true, then P(k+1) is also true:

P(k+1): 11⋅2 + 12⋅3 + ... + 1k⋅(k+1) + 1(k+1)⋅((k+1)+1) = (k+1)((k+1)+1)

By adding the (k+1)th term to the sum on the left side and simplifying the right side, we can demonstrate that P(k+1) is true.

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In my opinion the answer it either A or C because they make the most sense if you calculate.

Answer:

Step-by-step explanation:

A: The denominator doubles every step.

B: 1/16 1/32 1/64

Using algebraic expressions, the product of 9 and the difference between the number (x) and 5 is expressed as: 9(x - 5).

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.

Let variable x represent the number

Product of 9 and the difference between (x - 5) is expressed as an algebraic expression as: 9(x - 5).

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Answer:

The answer is -68

Step-by-step explanation:

Hope this is helpful ⇔

Answer:

-68

Sorry I forget how I solved it but I had to do this question in school yesterday and I remembered the answer.

Here c1 and c2 are constants determined by the initial conditions. To determine whether the given functions form a fundamental solution set to the equation x’(t) = ax, we need to check if they are linearly independent and if they satisfy the equation. Let the given functions be f1(t) and f2(t).

First, we need to check if they satisfy the equation x’(t) = ax. We have:
f1’(t) = a f1(t) and f2’(t) = a f2(t)
This shows that both f1(t) and f2(t) satisfy the equation.
Next, we need to check if they are linearly independent. To do this, we can form a matrix with the two functions as its columns and take its determinant.
| f1(t)  f2(t) |
| f1’(t) f2’(t) |
Expanding the determinant, we get:
f1(t) f2’(t) - f2(t) f1’(t) = W(t)
where W(t) is the Wronskian of f1(t) and f2(t). If W(t) is not identically zero, then f1(t) and f2(t) are linearly independent and form a fundamental solution set.
Therefore, if W(t) is not identically zero, we can find a fundamental matrix for the system as follows:
| f1(t)  f2(t) |
| f1’(t) f2’(t) |
And the general solution can be written as:
x(t) = c1 f1(t) + c2 f2(t)
where c1 and c2 are constants determined by the initial conditions.

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A simple random sample of 60 items resulted in a sample mean of 80. The population standard deviation is unknown based on the given information.

The sample mean of 80 is provided, which represents the average value of the 60 items in the sample. However, the population standard deviation, which measures the variability of the values in the entire population, is not specified. In order to determine the population standard deviation, either the population standard deviation itself or additional information about the sample or population would be needed.

Without the population standard deviation, we cannot make direct inferences about the variability of the population based solely on the sample mean of 80. To estimate the population standard deviation, additional data or assumptions would be necessary, such as the use of inferential statistical methods or the availability of the population standard deviation from previous studies or sources.

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Answers: The solutions are m = 7/2 and m = -3/2

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

Explanation:

\(\text{If } |x| = k, \text{ then } x = k \text{ or } x = -k, \text{ where } k > 0\)

Use that rule to break up the absolute value into two equations. Then solve each equation for m.

\(|2m-2| = 5\\\\2m-2 = 5 \ \text{ or } \ 2m-2 = -5\\\\2m = 5+2 \ \text{ or } \ 2m = -5+2\\\\2m = 7 \ \text{ or } \ 2m = -3\\\\m = 7/2 \ \text{ or } \ m = -3/2\\\\\)

Notes:

The patient needs to take 4 tablets daily to receive the prescribed dose of 3 grams of the drug.

To determine how many tablets the patient needs to take daily, we need to divide the total amount of the drug prescribed by the dose of each tablet.

Since the patient is prescribed 3 grams of the drug daily, we first need to convert this to milligrams (mg), as the tablets are available in milligram form.

1 gram = 1000 milligrams, so 3 grams = 3,000 milligrams

The pharmacist has 750 mg tablets available, so we can calculate the number of tablets the patient needs to take daily by dividing the prescribed dose by the dose of each tablet:

Number of tablets = Prescribed dose ÷ Dose per tablet

Number of tablets = 3,000 mg ÷ 750 mg

Number of tablets = 4

Therefore, the patient needs to take 4 tablets daily to receive the prescribed dose of 3 grams of the drug.

Therefore, the patient will take 4 tablets daily.

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The equation of the degree 6 polynomial with a root at 3, a double root at 2, and a triple root at -1, and y-intercept at y = 5 is given as follows:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

The zeros of the function, along with their multiplicities, are given as follows:

Then the linear factors of the function are given as follows:

The function is then defined as:

y = a(x - 3)(x - 2)²(x + 1)³.

In which a is the leading coefficient.

When x = 0, y = 5, due to the y-intercept, hence the leading coefficient a is obtained as follows:

5 = -12a

a = -5/12

Hence the polynomial is:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

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We know at centroid medians bisect each other in the ratio 2:1.

\(\\ \sf\longmapsto TY=2x\)

\(\\ \sf\longmapsto 2x=30\)

\(\\ \sf\longmapsto x=\dfrac{30}{2}\)

\(\\ \sf\longmapsto x=15\)

Answer:

A

Step-by-step explanation:

On the median TW the distance from the vertex to the centroid is twice the distance from the centroid to the midpoint , then

YW = \(\frac{1}{2}\) × TY = \(\frac{1}{2}\) × 30 = 15