6. suppose in the damped equation had e2k1t and e2k2t, with k2 > k1. how would the graphs differ and why?

λ equals 15 when AC has a magnitude of 17.

λ is approximately -3.909 when ABC is a straight line.

λ equals 12 when ABC is a right angle.

We have,

A.

To find the value of λ in each case, we'll need to perform vector calculations based on the given information.

Find λ when AC = 17:

The position vector AC can be found by subtracting vector A from vector C:

AC = (6i + λj) - (-9i + 7j) = (6 + 9)i + (λ - 7)j = 15i + (λ - 7)j

To find the magnitude of vector AC, we can use the formula:

|AC| = √((15)² + (λ - 7)²) = 17

Squaring both sides and simplifying the equation, we get:

225 + (λ - 7)² = 289

Expanding and rearranging the equation, we have:

(λ - 7)² = 289 - 225

(λ - 7)² = 64

B.

Taking the square root of both sides (ignoring the negative root, as we are dealing with distance), we find:

λ - 7 = 8

λ = 8 + 7

λ = 15

Find λ when ABC is a straight line:

For ABC to be a straight line, the vectors AB and BC must be collinear, which means their direction ratios must be proportional.

The direction ratio of vector AB is:

(2 - (-9)) / (-1 - 7) = 11 / (-8) = -11/8

The direction ratio of vector BC is:

(6 - 2) / (λ - (-1)) = 4 / (λ + 1)

For AB and BC to be collinear, their direction ratios must be proportional. Therefore, we can set up the following equation:

-11/8 = 4 / (λ + 1)

Cross-multiplying and solving for λ, we have:

-11(λ + 1) = 32

Expanding and rearranging the equation, we get:

-11λ - 11 = 32

-11λ = 32 + 11

-11λ = 43

λ = 43 / (-11)

λ = -3.909

C.

Find λ when ABC is a right angle:

For ABC to be a right angle, the dot product of vectors AB and BC must be zero.

The dot product of AB and BC is:

(2i - j) · (6i + λj) = (2)(6) + (-1)(λ) = 12 - λ

Setting the dot product equal to zero, we have:

12 - λ = 0

λ = 12

Therefore,

λ equals 15 when AC has a magnitude of 17.

λ is approximately -3.909 when ABC is a straight line.

λ equals 12 when ABC is a right angle.

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Answer:

136 square millimeters

Step-by-step explanation:

Answer:

A vector graphic consists of a set of instructions for creating a picture is a true statement.

Step-by-step explanation:

A vector graphic is an image format that represents images as a set of mathematical instructions or geometric primitives such as lines, curves, and shapes. Instead of using a grid of pixels like raster graphics, vector graphics define images based on mathematical formulas and coordinates.

These instructions or mathematical representations describe the shapes, colors, and other visual attributes of the image. They allow the image to be scaled, resized, and manipulated without loss of quality since the instructions can be recalculated and redrawn at any resolution or size.

Vector graphics are often created and edited using specialized software such as Adobe Illustrator, CorelDRAW, or Inkscape. They are commonly used for logos, illustrations, diagrams, typography, and other graphical elements where scalability and flexibility are important.

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Answer:

yes this quote isabsolutely right as

life is very innocent , we can make our life whatever we like

Answer:

125

Step-by-step explanation:

i did it too

The value of the line integral ∫C y ds for the given curve C is 2.

To evaluate the line integral ∫C y ds, where C is the upper half unit circle x^2 + y^2 = 1 from (1, 0) to (-1, 0), follow these steps:
Parametrize the curve C.
Since C is the upper half unit circle, we can parametrize it using the following parametric equations:
x(t) = cos(t)
y(t) = sin(t)
Here, the parameter t ranges from 0 to π, as we only consider the upper half of the circle.
Compute the derivatives of x(t) and y(t) with respect to t.
dx/dt = -sin(t)
dy/dt = cos(t)
Calculate the magnitude of the tangent vector.
The tangent vector to the curve is given by  = <-sin(t), cos(t)>.
The magnitude of the tangent vector is ||<-sin(t), cos(t)>|| = √((-sin(t))^2 + (cos(t))^2) = √(sin^2(t) + cos^2(t)) = 1.
Substitute the parametrization into the integrand.
The integrand is given by y, which is sin(t) in our parametrization.
Compute the line integral.
∫C y ds = ∫[0, π] (sin(t) * 1) dt = ∫[0, π] sin(t) dt
Evaluate the integral.
To evaluate the integral, we find the antiderivative of sin(t) with respect to t:
∫ sin(t) dt = -cos(t) + C
Now, we evaluate the antiderivative at the limits of integration:
[-cos(π) + cos(0)] = [(-(-1) - 1)] = 2
The value of the line integral ∫C y ds for the given curve C is 2.

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Answer:

2/h

Explanation:

Given that a tank can be filled in h hours, to determine what part of the tank can be filled in 2 hours, all we need to is divide 2 by h.

Therefore, 2/h part of the tank will be filled in 2 hours.

Answer:

Step-by-step explanation:

Salma has 4/5 kg of the flour . She wants to bake some cake. She uses 1/8kg of flour for each cake. What is the most number of cakes she can bake?

Answer:

Hello! Your answer is BELOW

Step-by-step explanation:

D Both pairs of opposite sides are congruent.

B Both pairs of opposite of angles are congruent.

A One pair of parallel sides.

Hope I helped! Hope you make an 100%

-Amelia♥

Answer:

maybe A? B, D, E

Give brainlest if u agree :)

Step-by-step explanation:

A - Parrallelgrams do indeed have 1 pair of parrlell sides, but are not limited to 1. They in fact have 2 sides. If ur instructor is super literal i would put A, if not then technically a parallelogram has 2 pairs of parrallel sides.

B - True. opposite  pairs have the same measure of radians

C - Not true because of B

D - True, sides are same length

E - True, consecutive angles add to 180

Source: https://www.mathplanet.com/education/geometry/quadrilaterals/properties-of-parallelograms

Step-by-step explanations

explanation is in the image above hope this helps please mark me brainiest

Answer:

18.5

Step-by-step explanation:

28^2 - 21^2 = y^2

y = 18.5

A soccer ball kicked from the ground with an initial velocity of 72 ft/s will be in the air for 4.5 seconds.

The time that a soccer ball will be in the air is determined by the equation:

t = (2 × v₀) / g

where:

t is the time in seconds

v₀ is the initial velocity in feet per second

g is the acceleration due to gravity, which is 32 feet per second squared

In this case, the initial velocity is 72 ft/s, so the time in the air is:

t = (2 × 72) / 32 = 4.5 seconds

Therefore, a soccer ball kicked from the ground with an initial velocity of 72 ft/s will be in the air for 4.5 seconds.

The time in the air will be longer if the initial velocity is higher, and shorter if the initial velocity is lower. The time in the air will also be shorter if the acceleration due to gravity is lower.

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Answer:

0

Step-by-step explanation:

Y-intercept is when the slope touches the y-axis and it touches it at 0.

Answer:

y = 4

its also y = 4 x

Step-by-step explanation:

UPDATE:

the answer was 0 according to some ppl.

Answer:

1 and 1/8

Step-by-step explanation:

Answer:

your answer is C. 45-j= 27

Step-by-step explanation:

any problem with a equal sign is a equation.

Answer:

3

Step-by-step explanation:

72/9 = 8 ( The quotient of 72 and 9)

8-5 = 3 (Decrease by 5)

Let x be the number of cans of food, since we need more than or equal to 2000 cans, we can write

where 668 is the number of cans that they have been collected.

Now, we must find x. If we move 668 to the right hand side as -668, we get

which gives

this means that they must collect more than or equalt to 1332 cans of food.

Answer:

the median is 80.5

Step-by-step explanation:

first we put them in order

75,76,77,79,80,81,85,86,90,91

the median is the middle number...however, in cases where there are an even number of numbers, ur gonna have 2 middle numbers....so u take the average of those 2 numbers...basically, u add them and divide by 2.

So we have 2 numbers in the middle.....we add them and divide by 2 to get the median.

(80 + 81) / 2 = 161/2 = 80.5 <== the median

Answer:

80.5

Step-by-step explanation:

a. To find df/dx at x = 2, we need to take the derivative of the function f(x) = 4x + 6 with respect to x. The derivative of a linear function is the coefficient of x, so in this case, f'(x) = 4. Therefore, f'(2) = 4.

b. To find the inverse function f^(-1)(y), we need to solve the equation y = 4x + 6 for x. Rearranging the equation, we get x = (y - 6)/4. So the formula for f^(-1)(y) is f^(-1)(y) = (y - 6)/4.

c. To find dy/dx, we need to take the derivative of the inverse function f^(-1)(y) with respect to y. The derivative of (y - 6)/4 with respect to y is 1/4. Therefore, (f^(-1))'(f(2)) = 1/4.

Note: In Question 2, the given expression "7 sin-¹(" is incomplete, so it is not possible to provide a complete answer without the rest of the expression.

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Answer:

Following are responses to the given question:

Step-by-step explanation:

For Girls:

\(Range:66 \\\\Lower\ Quartile: 22 \\\\Upper\ Quartile: 56 \\\\IQ\ Range: 34 \\\\Mean\ Absolute \ Deviation: 19.4\\\\\)

For Boys:

\(Range: 75 \\\\Lower \ Quartile: 12\\\\Upper \ Quartile: 45\\\\IQ \ Range: 33 \\\\Mean\ Absolute\ Deviation: 20.8\\\\\)  

Answer:

There is an 62.5% chance that he makes his next free throw.

Step-by-step explanation:

20:32

20 ÷ 32 = 0.625 = 62.5%

Answer:

..........................

Yes, the test in an "if" function must evaluate to either a True or a False value.

An "if" function, also known as a conditional statement, is used to perform specific actions based on whether a certain condition is met or not. The test or condition within the "if" function needs to be evaluated as either True or False in order for the program to decide which action to execute. If the test evaluates to True, the program will perform the action within the "if" block, and if it evaluates to False, it will either execute the action in the "else" block (if present) or simply skip the "if" block.

When using an "if" function in programming, it is essential for the test or condition within the statement to result in a boolean value, which is either True or False. This is because the program needs to determine whether the condition is met or not, so it can decide which set of actions to execute. If the condition evaluates to True, the code within the "if" block will be executed, while if it evaluates to False, the code within the "else" block (if present) will be executed, or the "if" block will be skipped altogether.

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The written description of the relationship between the variables as discussed in the task content is; Choice C; You leave home, drive for 2 hours at a constant speed, and then stop for 1 hour. Finally you continue at a slower (but constant) speed than before.

According to the task content, the time (hours) is plotted on the x-axis while the distance (miles) is plotted on the y-axis.

Since the graph is described by a line, it follows that it's slope is constant and consequently, its distance covered increases to 2 hours. This signifies driving.

Also, since the distance covered is constant through 3 hours, it follows that no distance is covered in that time and hence, speed is zero which signifies a stop.

Ultimately, when the distance increases through 6 hours, it follows that although the speed is constant, it is slower than the first 2 hour distance.

Therefore, Choice C correctly represents the interpretation of the relationship between the variables.

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Answer:

1695.6m

Step-by-step explanation:

The equation for how they find the volume of a cylinder is V=πr^2h

so the radius is 6x6=36

then 36x3.14=113.04

then you multiply that by 15

113.04x15=1695.6

The unit are M

Answer:106

Step-by-step explanation:

106