What is the slope and y-intercept of the
graph shown below?

Replace x for -3.

f(-3) = -3-2

f(-3) = -5

Answer:

correct answer = 2.367x107

wrong answer =  2.387x107

to find difference do big-small

or 2.387x107-2.367x107= (2.387-2.367)x107= 0.02x107=2.14

That w is in the range (0, 1), we can conclude that the peak time t_p = 0. Peak time t_p is equal to 0

(a) To write the transfer function relating the input u(t) and the output y(t), we can take the Laplace transform of the given differential equation. Using the Laplace transform property for derivatives, we have:

sY(s) + 2wnY(s) + wY(s) = wU(s)

Rearranging the equation, we get:

Y(s) (s + 2wn + w) = wU(s)

Dividing both sides by (s + 2wn + w), we obtain:

H(s) = Y(s)/U(s) = w / (s + 2wn + w)

Therefore, the transfer function relating the input u(t) and the output y(t) is H(s) = w / (s + 2wn + w).

(b) To find the unit step response of the system, we can substitute U(s) = 1/s into the transfer function H(s):

Y(s) = H(s)U(s) = (w / (s + 2wn + w)) * (1/s)

Taking the inverse Laplace transform of Y(s), we get:

y(t) = w(1 - e^(-2wn - w)t)

(c) To find the peak time t_p, we need to determine the time it takes for the unit step response y(t) to reach its first peak. The first peak occurs when dy(t)/dt = 0.

Differentiating y(t) with respect to t, we have:

dy(t)/dt = w(2wn + w)e^(-2wn - w)t

Setting dy(t)/dt = 0, we get:

w(2wn + w)e^(-2wn - w)t = 0

Since e^(-2wn - w)t is never equal to zero, we have:

2wn + w = 0

Simplifying the equation, we find:

wn = -w/2

Given that w is in the range (0, 1), we can conclude that the peak time t_p = 0.

Therefore, the peak time t_p is equal to 0

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The peak time t_p is 2ln(3) / w.

(a) The transfer function relating the input u and the output y is:

H(s) = Y(s) / U(s) = 1 / (s + 2ζwns + wn^2)

where s is the Laplace variable, ζ = 0.5, and wn is the natural frequency given by wn = w / sqrt(1 - ζ^2).

(b) The unit step response of the system is given by:

y(t) = (1 - e^(-ζwnt)) / (wnsqrt(1 - ζ^2)) - (e^(-ζwnt) / sqrt(1 - ζ^2))

(c) To find the peak time t_p, we need to find the time at which the first peak of the unit step response occurs. This peak occurs when the derivative of y(t) with respect to t is zero. Thus, we need to solve for t in the equation:

dy(t) / dt = ζwnsqrt(1 - ζ^2)e^(-ζwnt) - (1 - ζ^2)wnsqrt(1 - ζ^2)e^(-ζwnt) / (wnsqrt(1 - ζ^2))^2 = 0

Simplifying, we get:

e^(-ζwnt_p) = ζ / sqrt(1 - ζ^2)

Taking the natural logarithm of both sides and solving for t_p, we get:

t_p = -ln(ζ / sqrt(1 - ζ^2)) / (ζwn)

Substituting the given values of ζ and wn, we get:

t_p = -ln(1 / sqrt(3)) / (0.5w) = ln(3) / (0.5w) = 2ln(3) / w

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The value of the definite integral ∫[ (4x^3 - 6x^2 + 1) dx] from 1 to 2 can be evaluated using the definition of the definite integral as the limit of Riemann sums.

We start by partitioning the interval [1, 2] into n subintervals of equal width Δx = (2 - 1)/n = 1/n. Let xi be the sample point in each subinterval, where xi = 1 + (i-1)(Δx).

The Riemann sum for the given function over the interval [1, 2] is:

Σ[ (4xi^3 - 6xi^2 + 1) Δx] from i = 1 to n

Expanding the terms, we have:

Σ[ (4(1 + (i-1)(Δx))^3 - 6(1 + (i-1)(Δx))^2 + 1) Δx] from i = 1 to n

Simplifying and factoring Δx, we get:

Σ[ (4(1 + (i-1)/n)^3 - 6(1 + (i-1)/n)^2 + 1) ] Δx from i = 1 to n

Taking the limit as n approaches infinity, this Riemann sum becomes the definite integral:

∫[ (4x^3 - 6x^2 + 1) dx] from 1 to 2

To compute the integral, we can find the antiderivative of the integrand, which is (x^4 - 2x^3 + x) evaluated at the limits of integration:

∫[ (4x^3 - 6x^2 + 1) dx] from 1 to 2 = [(2^4 - 2(2)^3 + 2) - (1^4 - 2(1)^3 + 1)]

Simplifying further, we obtain the numerical value of the definite integral.

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The measure of angle EBF where he angle measures are given as m∠ABF = (8w − 6)° and m∠ABE = [2(w + 11)] is m∠EBF = 4w - 28

The angle measures are given as

If m ∠ A B F = ( 8 w − 6 ) ° m ∠ A B E = [ 2 ( w + 11 ) ] ° m ∠ E B F

Rewrite the angle measures properly.

This is done, as follows

m∠ABF = (8w − 6)°

m∠ABE = [2(w + 11)]

The measure of angle m∠EBF is calculated as:

m∠ABF = m∠ABE + m∠EBF

Substitute the known values in the above equation

8w - 6 = 2(2w + 11) + m∠EBF

Open the brackets

8w - 6 = 4w + 22 + m∠EBF

Evaluate the like terms

m∠EBF = 4w - 28

Hence, the measure of angle EBF where he angle measures are given as m∠ABF = (8w − 6)° and m∠ABE = [2(w + 11)] is m∠EBF = 4w - 28

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The sales tax of his purchase if he lives in Florida where the sales tax rate is 6 percent is $67.92

The word "percent" comes from the Latin per centum, which means "hundred" or "by the hundredth." The symbol for "percent" emerged gradually from the Italian expression per cento, which means "for a hundred." The "per" was frequently shortened as "p." and eventually vanished. The "cento" symbol was simplified to two circles divided by a horizontal line, from which the contemporary "%" symbol was formed.

The abbreviation "pct.", "pct," and sometimes "pc" are also used. A % is a dimensionless (pure) number with no unit of measurement.

Given,

Total purchase=$878

For two tables,

2×127=254

Total=878+254

=1132

6% of 1132 is,

(6/100)×1132

=$67.92

The sales tax of his purchase if he lives in Florida where the sales tax rate is 6 percent is $67.92

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The speed of the water wave is 2.0 meters per second.

The speed of a wave is calculated by dividing the distance traveled by the time it takes to travel that distance. In this case, the distance traveled by the water wave is 10.0 meters, and the time taken is 5.0 seconds.

To determine the speed, we use the formula:

Speed = Distance / Time

Substituting the given values, we have:

Speed = 10.0 meters / 5.0 seconds = 2.0 meters per second

Therefore, from the given information, we can determine that the speed of the water wave is 2.0 meters per second.

This information about the speed of the water wave is useful for various purposes. It allows us to understand how quickly the wave is propagating through the medium. It also helps in analyzing wave behavior, such as interference, reflection, or refraction, and studying the characteristics of the medium through which the wave is traveling. Additionally, the speed of the wave can be used in calculations involving wave frequencies, wavelengths, and periods.

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125

1) Examining the sequence 1, 8, 27, 64 we can find a pattern like this:

2) As we can see, when we raise to 3rd power we can get the numbers of that sequence.

3) So the next number in that sequence is 125

Answer:

The solution to the equation 2(x+4) = 5 is x = -3/2.

Step-by-step explanation:

To solve the equation 2(x+4) = 5, we can use the following steps:

Distribute the 2 on the left side of the equation:

2x + 8 = 5

Subtract 8 from both sides of the equation:

2x = -3

Divide both sides of the equation by 2:

x = -3/2

Therefore, the solution to the equation 2(x+4) = 5 is x = -3/2.

Answer: 2,504?

Step-by-step explanation: baccically times the 2 only by 100, or at least that’s what I am seeing. LOL

Any number which has digit 2 at its thousandth place will have  the digit 2 one hundred times larger than it is in the number 524

Place value is the value of each digit in a number.

For example, the 5 in 350 represents 5 tens, or 50; however, the 5 in 5,006 represents 5 thousands, or 5,000.

It is important that while a digit can be the same, its value depends on where it is in the number.

Given that, we need to determine that which number is the digit 2 one hundred times larger than it is in the number 524,

So, if we consider a number having 2 at its thousandths place,

For example : 32000, the place value of 2 is 2000,

In the number 524, the place value of 2 is 20,

Now, 2000/20 = 100

So, here we see that, the digit 2 in 32000 is 100 times larger than the digit 2 in 524

Hence, any number which has digit 2 at its thousandth place will have  the digit 2 one hundred times larger than it is in the number 524

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Answer:

the first answer is no

the second one is square

sorry if it is wrong

Answer:

6x²-x-15

degree: second

leading coefficient : 6 , -1

constant : -15

Step-by-step explanation:

(2x + 3) (3x – 5)=

6x²+9x-10x-15=

6x²-x-15

degree: second

leading coefficient : 6 , -1

constant : -15

Answer:

divide by - 4

Step-by-step explanation:

Given

- 4M = 48 ( isolate M by dividing both sides by - 4 )

M = - 12

Answer:

1. 0.45

2. 0.06

3. 0.39

4. 7.77

Step-by-step explanation:

causeeeeeeee

0.688 will be the probability of getting a nickel from the jar.

Given,

Probability;-

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Here,

The number of fortunate situations divided by the total number of coins would be the product between the probability of each occurrence and the likelihood of each event.

Therefore,

P(nickel) = 19/69

P(penny) = 17/68

That is,

P = 19/69 × 17/68

P = 323/4692

P = 0.0688

That is,

The probability of getting nickel from the jar is 0.06888

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Step-by-step explanation:

Color     number

Blue       7

Red        4

Purple    5

Yellow    4

TOTAL=20 responses

if 40 more students are surveyed assuming the ratios remain the same

we can calculate the number of students that will choose a color by multiplying the results from the previous survey which had 20 participants by 2 to find the correct answer  

20*2=40

so

Color     number  new results

Blue       7*2    = 14

Red        4*2    =8

Purple    5*2    = 10

Yellow    4*2    =8

so the correct answer will be

D. There will be 8 students who choose yellow

Answer:

3/35

11/84

Step-by-step explanation:

1/7*3/5=3/35

1*3=3

7*5=35

1/3*11/7*1/4=11/84

1*11*1=11

3*7*4=84

Answer:

20 weeks

Step-by-step explanation:

1315$-415$=900$

900/45=20

Hence 20 weeks

Answer: 45b  

Step-by-step explanation: Divide 1315 with 45xb.

The missing side is 37.8, option B is correct in the triangle.

In the given triangle we have to find the value of x

We know than tan function is a ratio of opposite side and adjacent side

tan 71 = x/13

2.90 = x/13

Multiply both sides by 13

13×2.9=x

37.8=x

Hence, the missing side is 37.8, option B is correct in the triangle.

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Answer:

x-y+16

Step-by-step explanation:

add the like terms, 6 and 10 which is 16. since the variables are not like terms, thats your final answer. hope it helped :)

The inverse of the given matrix does not exist. To determine if the inverse of a matrix exists, we need to check if the matrix is invertible, which is equivalent to checking if the matrix has a nonzero determinant.

The given matrix is a 2x2 matrix with elements 4, 5, 7, and 9. To calculate the determinant, we multiply the diagonal elements and subtract the product of the off-diagonal elements. In this case, the determinant is (4 * 9) - (5 * 7) = 36 - 35 = 1. Since the determinant is nonzero, we conclude that the matrix is invertible. However, to find the inverse of the matrix, we need to calculate the matrix of cofactors, transpose it, and divide by the determinant.

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Answer:

work is pictured and shown

Answer:

SL = KR

Step-by-step explanation:

We're given two different lengths, both of which are on other sides of KL. Now, since these two givens are congruent, and we're overlapping it over a new line, the lines SL and KR are going to be congruent.

Answer:

FH = 24

Step-by-step explanation:

HG = 13

FH = 37 - 13

= 24

Answer:

The value of FH is 24.

Step-by-step explanation:

The equation will be,

→ FHG = FH + HG

Then the value of FH will be,

→ 37 = FH + 13

→ FH = 37 - 13

→ [ FH = 24 ]

Hence, the value of FH is 24.

Answer:

Put it in math-way and please write the expression so I can solve it

Step-by-step explanation:

Answer:

900 people

Step-by-step explanation:

540 / 60 = 9

10% = 9

9 x 100 = 900 people

Hope that helps!

Step-by-step explanation:

how should we express the speed ? in meters per second ? kilometers per hour ?

or anything else ?

he moves 250 meters in 500 seconds.

that is 250/500 m/s = 0.5 m/s (meters per second)

for kilometers per hour we need to convert this to an expression that bases on an hour instead of one second.

we know there are 3600 seconds (60 seconds × 60 minutes) in an hour.

and to keep the ratio unchanged, we need to do the same thing to the top and the bottom of it.

so, we multiply 0.5 m/s by 3600/3600.

0.5/1 × 3600/3600 = 1800/3600 m/s = 1800/1 m/h =

= 1.8 km/h

in other words - he is really slow. a normal person walks much faster.