show all work on a piece of paper and explanation calc 3c
(D13, D14) = The acceleration of a particle on a path r(t) is given by a(t) = (3t, -4e--, 12t2). Find the velocity function, given that the initial velocity U(0) = (0, 1, -3) and initial position r(0)

Answer:

23

Step-by-step explanation:

Answer: 23

Step-by-step explanation:

When your finding the absolute value your just seeing how far away the number is from 0 on a number line...so if the number is negative it turns into a positive.

Answer:

x=25

Step-by-step explanation:

x+5+6x=180

7x+5=180

7x=175

x=25

P.S. sorry it's out of order >< i added arrows to show what corresponds to which of the two questions

Answer:

Invasive species are primarily spread by human activities, often unintentionally. People, and the goods we use, travel around the world very quickly, and they often carry uninvited species with them. Ships can carry aquatic organisms in their ballast water, while smaller boats may carry them on their propellers.

Step-by-step explanation: hope i helped mark brainlist plz

Answer:

12x^2 -21x -6

Step-by-step explanation:

(3x-6)(4x+1)

FOIL

first 3x*4x= 12x^2

outer 3x*1 = 3x

inner -6*4x = -24x

last  -6*1 = -6

Add them together

12x^2 +3x -24x -6

Combine like terms

12x^2 -21x -6

By induction, we have shown that if the formula holds for k, then it also holds for k+1. Since it holds for the base case T(1) = c, we can conclude that the formula T(n) = c * (a log₇ n) is the solution to the given recurrence relation T(n) = aT(n/7) with base condition T(1) = c.

Paragraph 1: The solution to the recurrence relation T(n) = aT(n/7) with base condition T(1) = c is given by T(n) = c * (a log₇ n), where c and a are constants. This formula represents the closed-form solution for the recurrence relation and is derived using mathematical induction.

Paragraph 2: We begin the proof by showing that the formula holds for the base case T(1) = c. Substituting n = 1 into the formula, we get T(1) = c * (a log₇ 1) = c * 0 = c, which matches the given base condition.

Next, we assume that the formula holds for some positive integer k, i.e., T(k) = c * (a log₇ k). Now, we need to prove that it also holds for the next value, k+1. Substituting n = k+1 into the recurrence relation, we have T(k+1) = aT((k+1)/7). Using the assumption, we can rewrite this as T(k+1) = a * (c * (a log₇ (k+1)/7)). Simplifying further, we get T(k+1) = c * (a log₇ (k+1)).

By induction, we have shown that if the formula holds for k, then it also holds for k+1. Since it holds for the base case T(1) = c, we can conclude that the formula T(n) = c * (a log₇ n) is the solution to the given recurrence relation T(n) = aT(n/7) with base condition T(1) = c.

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Answer:

7

Step-by-step explanation:

Answer:

x=−1,y=13

Step-by-step explanation:

Answer:

x = -1 and y = 13 Please Mark Brainliest

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is B

The reason for this is all you have to do is multiply 29.4 x 4 and you get 118.4 and round it to get 115 fl oz

✨Hope it helps✨

Brainliest?...

Answer:

7√5

Step-by-step explanation:

3√5 + 4√5

= 7√5

1) This is a problem of rational equations, so let's set them so that we can solve it:

Note that on the left we have the mixture, 35% = 0.35 of a solution +0.85 times the number of liters we want to produce minus x. This is going to be equal to 60% (0.6) times 90.

2) Now, we can solve it:

Once the hardest part is done, we had to deal with the good old Algebra.

Answer:

2,000

4,000

7,000

put points on (2, 2,000) - (4, 4,000) - and (7, 7,000)

Step-by-step explanation:

Probability distribution is an assignment of probabilities to each distinct value of a discrete random variable or to each interval of values of a continuous random variable.

What is Probability ?

What is the probability of each value of a discrete random variable?

The probability P(x) that a discrete random variable X will take the value x in one trial of the experiment is connected to each possible value x of the variable.

Which is a discrete random variable?

What is the other name of mean of discrete random variable?

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Answer:

x = 11/3

Step-by-step explanation:

x2 + x = 11

Combine like terms

3x = 11

Divide both sides by 3

x = 11/3

To find the slope of the line tangent to the polar curve r = 9 + 7 cos(theta) at the point (16, 0), we can use the formula:

dy/dx = (dy/dtheta) / (dx/dtheta) = (r' sin(theta) + r cos(theta)) / (r' cos(theta) - r sin(theta))

where r' = dr/dtheta.

First, we need to find r' by taking the derivative of r with respect to theta:

r' = dr/dtheta = -7 sin(theta)

Then, we can plug in the given values to find the slope at (16, 0):

dy/dx = [(r' sin(theta) + r cos(theta)] / [r' cos(theta) - r sin(theta)]

= [(-7 sin(0) sin(0) + (9 + 7 cos(0)) cos(0))] / [(-7 sin(0) cos(0)) - (9 + 7 cos(0)) sin(0))]

= (9 + 7) / (-9) = -2

Therefore, the slope of the line tangent to the polar curve r = 9 + 7 cos(theta) at the point (16, 0) is -2.

To find the slope of the line tangent to the polar curve r = 9 + 7 cos(theta) at the point (2, pi), we can use the same formula as above:

dy/dx = (r' sin(theta) + r cos(theta)) / (r' cos(theta) - r sin(theta))

First, we need to find r' by taking the derivative of r with respect to theta:

r' = dr/dtheta = -7 sin(theta)

Then, we can plug in the given values to find the slope at (2, pi):

dy/dx = [(r' sin(theta) + r cos(theta)] / [r' cos(theta) - r sin(theta)]

= [(-7 sin(pi) sin(2) + (9 + 7 cos(pi)) cos(2))] / [(-7 sin(pi) cos(2)) - (9 + 7 cos(pi)) sin(2))]

= (-2) / (7)

Therefore, the slope of the line tangent to the polar curve r = 9 + 7 cos(theta) at the point (2, pi) is -2/7.

The polar curve r = 9 + 7 cos(theta) intersects the origin when r = 0, which occurs when cos(theta) = -9/7, which is not possible since the range of cosine function is [-1, 1]. Therefore, the curve does not intersect the origin.

Since the curve does not intersect the origin, the answer is "The curve does not intersect the origin" for the equation of the tangent line in polar coordinates.

Answer:

Step-by-step explanation:

to solve this question, we need to use the graph on the left to find the proportions of students who prefer each pasta dish, and then multiply those proportions by 400 to get the estimated number of students in the whole school who prefer each pasta dish. Then we need to plot those numbers on a bar graph with the pasta dishes on the horizontal axis and the number of students on the vertical axis. The graph below shows one possible way to create the bar graph:

We can see that the vertical axis is numbered from 0 to 120 in increments of 20. The bars show the estimated number of students who prefer each pasta dish, based on the sample of 16 students. For example, since 4 out of 16 students prefer spaghetti, we can estimate that 4/16 x 400 = 100 students in the whole school prefer spaghetti. Similarly, since 3 out of 16 students prefer lasagna, we can estimate that 3/16 x 400 = 75 students in the whole school prefer lasagna. We can repeat this process for the other pasta dishes and plot them on the graph.

✧☆*: .｡. Hope this helps, happy learning! (*✧×✧*) .｡.:*☆

Answer:

e (2,-1)

f (4,-1)

g (5,-4)

h (1,-4)

The left side of the equation is equal to the right side, which confirms that a = 11/10 is the correct solution.

To solve the equation, we need to isolate the variable "a". The equation is given as a - 1/2 = 3/5.
To eliminate the fraction, we can multiply both sides of the equation by the least common denominator (LCD), which is 10. This will clear the fractions and make the equation easier to solve.
Multiplying the left side of the equation by 10, we get:
10(a - 1/2) = 10(3/5)
10a - 5 = 6
Next, we can simplify the equation by adding 5 to both sides:
10a - 5 + 5 = 6 + 5
10a = 11
Finally, we can solve for "a" by dividing both sides of the equation by 10:
(10a)/10 = 11/10
a = 11/10
Therefore, the solution to the equation is a = 11/10 or a = 1 1/10.
To check the solution, substitute a = 11/10 back into the original equation:
11/10 - 1/2 = 3/5
(11/10) - (5/10) = 3/5
6/10 = 3/5
In summary, the solution to the equation a - 1/2 = 3/5 is a = 11/10 or a = 1 1/10. This solution has been checked and is correct.

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Looking at the description of the shape, The Reflect shape A in the line y = x, will then be (y, -x).

The Reflecting of a  shape implies that one should  turn it over  a mirror line.

Note that in doing this, each part of the shape is said to be moved to the other side of the mirror line and as such it still have to be the same with the same distance away from the line. The image attached shows the best form of the reflected shape in line y = x.

Note that if one reflect over the line y = -x, the x-coordinate and y-coordinate tends to alter places and are then negated the line y = x is the change to (y, x).

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Based on the given information, the scale factor of the cuboid is 2.5.

What is the scale factor?

A scale factor is a number that represents the amount of magnification or reduction applied to an object, image, or geometrical shape. It is a ratio that describes how much larger or smaller an object is compared to its original size.

To find the scale factor of a cuboid, we need to compare the corresponding dimensions (length, width, and height) of the pre-image (original) and the image (after transformation).

Given that the length of the pre-image is 2 cm and the length of the image is 5 cm, we can find the scale factor as follows:

scale factor = length of image/length of pre-image

scale factor = 5 cm / 2 cm

scale factor = 2.5

Therefore, the scale factor of the cuboid is 2.5.

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The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.

The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.

Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.

The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.

In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

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Answer:

y = 1/4x - 2

Step-by-step explanation:

y = 1/4x + b

-1 = 1/4(4) + b

-1 = 1 + b

-2 = b

A scatter plot or scattergram chart will show the relationship between two different variables or reveals distribution trends.

Now, According to the question:

A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.

Use a scatter plot to determine whether or not two variables have a relationship or correlation. Are you trying to see if your two variables might mean something when put together? Plotting a scattergram with your data points can help you to determine whether there's a potential relationship between them.

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Hi, you would predict getting the blue more, because the probablility of picking that has a higher chance than the others, because it is 5/12 while the others are less. Hope this helps.

Answer:

Slope: -1/6

Midpoint of AB: (1, 8.5)

Distance of AB: √37

Step-by-step explanation:

Slope formula: \(m = \frac{y2-y1}{x2-x1}\)

Midpoint formula: \((\frac{x1+x2}{2} ,\frac{y1+y2}{2} )\)

Distance formula: \(d = \sqrt{(x2-x1)^{2}+(y2-y1)^{2}}\)

System sequence diagram is the best model to use to document the inputs and the outputs to a system.

In the realm of software engineering, a sequence diagram, also known as a system sequence diagram (SSD), depicts process interactions grouped in chronological order. It illustrates the processes involved and the order in which messages must be exchanged for the processes to provide the functionality. In the 4+1 architectural perspective model of the system under development, sequence diagrams are often connected to use case realizations. Event diagrams and event scenarios are other names for sequence diagrams.

The diagrams display the events that external actors produce, their order, and any potential inter-system events for a given scenario of a use case. [1] The diagram emphasizes events that cross the system boundary from actors to systems and treats all systems as black boxes. The main success scenario of the use case, as well as frequent or complex alternate situations, should be represented using a system sequence diagram.

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The general solution for the given differential equation using Laplace transforms, where F(s) is the Laplace transform of f(t) is y(t) = L⁻¹{(F(s) + α) / (s + 3)}.

We Laplace transforms to solve the following differential equation: y'(t) + 3y(t) = f(t), with the initial condition y(0) = α, where α is a constant.
Take the Laplace transform of both sides of the equation.
L{y'(t) + 3y(t)} = L{f(t)}

Apply the Laplace transform to each term.
L{y'(t)} + 3L{y(t)} = L{f(t)}

Use the properties of Laplace transforms.
sY(s) - y(0) + 3Y(s) = F(s)

Substitute the initial condition y(0) = α.
sY(s) - α + 3Y(s) = F(s)

Solve for Y(s).
Y(s)(s + 3) = F(s) + α

Y(s) = (F(s) + α) / (s + 3)

Take the inverse Laplace transform of Y(s) to find the solution y(t).
y(t) = L⁻¹{(F(s) + α) / (s + 3)}
This is the general solution for the given differential equation using Laplace transforms, where F(s) is the Laplace transform of f(t).

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The equation of the parabola is ( x² = 85.2y ).

We are given that;

Focus of parabola= (0,21.3)

Now,

If a quadratic equation is written in the form

y=a(x-h)² + k

then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)

The equation of a parabola with vertex at the origin and focus at ( (0,21.3) ) is given by ( x²= 4ay ),

where ( a ) is the distance from the vertex to the focus.

Since the focus is at ( (0,21.3) ),

we have ( a = 21.3 ).

Therefore, by equation the answer will be ( x² = 85.2y ).

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The complete question is

Find the equation for the parabola that has its vertex at the origin and has a focus at (0,21.3)