1.formulate and write mathematically the four maxwell’s equations in integral form

Answer:

y-8=-7/5(x-5)

Step-by-step explanation:

find the slope by rewriting the line's equation.

5y=3-7x

5y=-7x+3

y=-7/5x +3/5

since its parallel, the slope will be the same (-7/5)

use the formula y-y1=m(x-x1) for the point (5,8)

y-8=-7/5(x-5)

rearrange in the form y=mx+b if you wish.

Answer:

The point where f(x), g(x), and h(x) have the same value is (8, 11)

Step-by-step explanation:

The points where g(x) and h(x) have the same value is given as follows;

2x - 5 = 8/x + 10

2x² - 15x - 8 = 0

Using an online tool, we have;

(x - 8)(2x + 1) = 0

x = 8 or x = -1/2

∴ g(x) and h(x) = 11 or y = -6

For x = 8, we have;

f(x) = 2^(x - 5) + 3 = 2^(8 - 5) + 3 = 2^3 + 3 = 11

For x = -1/2, we have;

f(x) = 2^(-1/2 - 5) + 3 = 3.022

Therefore, the point where f(x), g(x), and h(x) have the same value is (8, 11), therefore, for x = 8, f(x) = g(x) = h(x) = 11.

Proved that \(a_n\) = a(n-1) + \(3^n\) - 2n - 1 for all non-negative integers n.

We will use mathematical induction.

Base Case:

For n = 0, we have:

a0 = 1 - 0 = 1

And

a(-1) = 0 //Since a sequence is not defined for negative indices.

Therefore, the statement is true for the base case.

Inductive Hypothesis:

Assume that the statement is true for some non-negative integer k:

\(a_k = ak-1 + 3^k - 2k - 1\)

Inductive Step:

We will prove that the statement is also true for k+1:

\(ak+1 = ak + 3^{k+1} - 2(k+1) - 1\)

= (ak-1 + 3^k - 2k - 1) + 3^(k+1) - 2(k+1) - 1 //Using inductive hypothesis.

= ak-1 + 3^(k+1) - 2(k+1) + 3^k - 2k - 2

Now, we will show that ak+1 can be written in the form ak+1 = ak + 3^(k+1) - 2(k+1) - 1:

\(a_{k+1} = (ak-1 + 3^k - 2k - 1) + 3^{k+1} - 2(k+1) - 1\)

\(= (a_k-1 + 3^{k+1} - 3.3^k - 2k - 2) + 3^{k+1} - 2(k+1) - 1\)

\(= (a_k-1 + 3^{k+1} - 2.3^k - 2(k+1)) + 3^{k+1} - 2(k+1) - 1\)

\(= a_k-1 + 2.3^{k+1} - 2(k+2) - 1\)

\(= a_k + 3^{k+1} - 2(k+1) - 1\)

Therefore, the statement is also true for k+1, completing the inductive step.

By the principle of mathematical induction, the statement is true for all non-negative integers n. Hence, we have proved that \(a_n = a_{n-1} + 3^n - 2n - 1\) for all non-negative integers n.

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Answer:

d

Step-by-step explanation:

d does not have any repeaing decimals, or any other type of irrational number

a. The solution for x - 3 ≥ 0  is x ≥ 3

b. The solution for 2x + 11 < 3  is x < -4

c. The solution for the quadratic equation is  -1  ≥ x ≥ 2

d. The solution is x < -4/3 or x > 1

a. x - 3 ≥ 0

isolating the variable x

x - 3 ≥ 0

x ≥ 3

b. 2x + 11 < 3

isolating variable x

2x + 11 < 3

2x < 3 - 11

2x < -8

x < -4

c. x² ≥ x + 2

rearranging the quadratic equation

x² - x - 2 ≥ 0

factorizing

(x - 2)(x + 1) ≥ 0

d. x + 4 > 3x²

rearranging the quadratic equation

3x² - x - 4 < 0

factorizing

(x - 1)(3x + 4) < 0

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Answer:

( 14 , 0 )

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 3*x+6*y-(42)= Pull out like factors :

  3x + 6y - 42  =   3 • (x + 2y - 14)

Equations which are never true:   Solve :    3   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Answer:

Step-by-step explanation:

\( \sqrt{49 {x}^{12} {y}^{8} } \)

\( \sqrt{ {7}^{2} } \sqrt{ {x}^{12} } \sqrt{ {y}^{8} } \)

\(7 ^{ \frac{1}{2} \times 2 } \times {x}^{ \frac{1}{2} \times 12 } \times {y}^{ \frac{1}{2} \times 8 } \)

\(7 {x}^{6} {y}^{4} \)

Answer:

Step-by-step explanation:

(x+6)(x+3)=9+(x+1)

= x^2+3x+6x+18

=x^2+9x+18=9(x+1)

=x^2+9x+18=9x+9

tbs = to both sides

(-9x tbs)= 9x-9x=0 so x^2+18=9

(-18tbs) = x^2=9-18 becomes x^2=-9

x=\(\sqrt{-9}\)

Answer:

Nina can run:

13 1/2 km in 1 hour

Step-by-step explanation:

4 1/2 = 4 + 1/2 = 8/2 + 1/2 = 9/2

proportions:

9/2 hours ⇔  1/3 hour

N hours ⇔ 1 hour

N = (9/2)*1 / (1/3)

N = (9/2) / (1/3)

N = (9*3) / (2*1)

N = 27/2

27/2 = 26/2 + 1/2 = 13 + 1/2 = 13 1/2

Nina can run:

13 1/2 km/h

13 1/2 km in 1 hour

Answer:

13.5

Step-by-step explanation:

Step 1:

4 1/2 × 3 = 13 1/2

Answer:

13.5 kilometers

Hope This Helps :)

The solution to the system of equations is (2. -3/4)

From the question, we have the following parameters that can be used in our computation:

Y = 1/8x - 1

-5x + 4y = -13

Substitute the first equation in the second

So, we have

-5x + 4(1/8x - 1) = -13

Multiply through by 8

-40x + 4(x - 8) = -104

So, we have

-40x + 4x - 32 = -104

Evaluate the like terms

-36x = -72

This gives

x = 2

So, we have

Y = 1/8x - 1

Y = 1/8(2) - 1

Evaluate

y = -3/4

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The main difference between the centers of the distributions of crocodiles and alligators is that crocodiles generally have shorter lengths compared to alligators.

Crocodiles tend to have a lower average or median length compared to alligators, indicating that the center of the distribution for crocodiles is shifted towards shorter lengths. This can be observed by comparing the positions of the central points or measures of central tendency, such as the median, in the dot plots for crocodiles and alligators.

In terms of the spreads of the distributions, one possible difference could be that the spread of the crocodile distribution is smaller than the spread of the alligator distribution. This means that the lengths of crocodiles might have less variability or be more tightly clustered around the center compared to alligators. This can be inferred by examining the overall dispersion of the data points in the dot plots. If the dots for crocodiles are more closely packed together or exhibit less variability in their positioning along the length axis, it suggests a narrower spread for crocodile lengths compared to alligator lengths.

To summarize, the center difference between the distributions is that crocodiles have shorter lengths than alligators, and the spread difference is that the lengths of crocodiles may exhibit less variability or have a narrower range compared to alligators.

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Answer:

y + 0.30x = fee charged

Answer:

Thanks for points though.

Step-by-step explanation:

Hope this helps

Have a great day ahead

Answer:

D

Step-by-step explanation:

because it makes sense75 would be what he deposits in his bank account each month because x is the number of deposits

and 50 would be his birthday money he received

The parametric function for your location on the Ferris wheel at any given time:
x(t) = 80 * sin(2π * (t/2))
y(t) = 80 * cos(2π * (t/2)) + 3

To create a parametric function that models your location on the Ferris wheel at a given time, we need to come up with equations that describe your horizontal and vertical positions as functions of time.

Let's start with the horizontal position. Since the Ferris wheel rotates counter-clockwise, we know that your position on the wheel will increase as time goes on. We can express this as:

x(t) = 80cos(2πt/120)

Here, t represents time in seconds, and the factor of 2π/120 ensures that the function completes one full cycle (i.e. one trip around the wheel) in 120 seconds, or 2 minutes. The cosine function gives us a smooth, periodic curve that oscillates between -80 and 80, corresponding to your position on either side of the wheel's center.

Next, let's consider your vertical position. We know that you start at a height of 3 feet above the ground, and as the wheel rotates, your height will vary sinusoidally over time. We can express this as:

y(t) = 80sin(2πt/120) + 3

Here, the sine function gives us a smooth, periodic curve that oscillates between 77 and 83 feet (i.e. the radius of the wheel plus or minus 3 feet).

So, putting it all together, our parametric function for your location on the Ferris wheel at a given time t is:

(r(t), θ(t)) = (80cos(2πt/120), 80sin(2πt/120) + 3)

Here, r(t) and θ(t) represent your radial distance from the center of the wheel and the angle you've rotated from the starting position, respectively. This parametric function describes a smooth, periodic curve that traces out your path on the Ferris wheel as it rotates counter-clockwise.

Given the information, we know the Ferris wheel has a radius of 80 feet, the bottom is 3 feet above the ground, it rotates counter-clockwise, and has a period of 2 minutes.

To create a parametric function, we need two equations, one for the x-coordinate (horizontal) and one for the y-coordinate (vertical). Let's denote the time variable as t, measured in minutes.

1. X-coordinate (horizontal position):
Since the Ferris wheel rotates counter-clockwise, we can use the following equation for the x-coordinate:
x(t) = 80 * sin(2π * (t/2))

2. Y-coordinate (vertical position):
To account for the bottom of the Ferris wheel being 3 feet above the ground, we need to add 3 to the vertical equation:
y(t) = 80 * cos(2π * (t/2)) + 3

Now, we have the parametric function for your location on the Ferris wheel at any given time:
x(t) = 80 * sin(2π * (t/2))
y(t) = 80 * cos(2π * (t/2)) + 3

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Answer:

Step-by-step explanation:

H

Answer:

because they have straight lines and they are regular

Step-by-step explanation:

Answer:

D is on the number line, which point is closest to /-/

Answer:

It well be D

Step-by-step explanation:

Answer:

The answer is 17.58

How much a statistic varies from one sample to another is known as the sampling variability of a statistic.

Testing variability arises due to the reality that exceptional samples of the same size can produce special values of a statistic, although the samples are described from the same populace. the quantum of slice variability depends on the scale of the sample, the variety of the populace, and the unique statistic being calculated.

The end of statistical conclusion is to apply the data attained from a sample to make consequences about the population, while counting for the slice variability of the statistic. ways similar as thesis checking out and tone belief intervals do not forget the sampling variability of a statistic to make redundant accurate consequences about the populace.

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Answer:-3

Step-by-step explanation: -3 because when you do it I really don't know how to explain it srry

perimeter is the total length of a boundary of a figure.

1/2 as a decimal becomes 0.5

Answer:

.50

Step-by-step explanation:

Answer:

8 in

Step-by-step explanation:

Area of a square = l×w

Since it is a square then l and w are equal to each other.

So we can instead just say l^2 = A

l^2 = 68.2

l = square root of 68.2

l = 8.26

Using the P-value method of testing hypotheses with a significance level of 0.05, the sample provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.

To test the claim that the mean score of job applicants from the university is greater than 160, we will perform a one-sample t-test using the P-value method. The null hypothesis (H0) assumes that the mean score is equal to 160, while the alternative hypothesis (Ha) assumes that the mean score is greater than 160.

First, we calculate the test statistic, which is the t-value. The formula for the t-value is:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

Plugging in the given values, we have:

t = (183 - 160) / (12 /   √(25))

  = 23 / (12 / 5)

  = 23 * (5 / 12)

  ≈ 9.58

Next, we find the P-value associated with the test statistic. The P-value represents the probability of obtaining a test statistic as extreme as the observed value, assuming the null hypothesis is true. Since the alternative hypothesis is one-sided (greater than 160), we calculate the P-value by finding the probability of the t-distribution with 24 degrees of freedom being greater than the calculated t-value.

Consulting statistical tables or using software, we find that the P-value is very small (less than 0.0001).

Since the P-value (less than 0.0001) is less than the significance level (0.05), we reject the null hypothesis. This provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.

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The average change in elevation of the object in meters per second is -69/10.

Find the change in elevation of the object. The object started at an elevation of 0 meters and fell to an elevation of -4.9 meters. Therefore, the total change in elevation was -4.9 meters.

The time elapsed was 0.71 seconds.

Calculate the average change in elevation per second. Divide -4.9 meters by 0.71 seconds to get -6.90 meters per second. Express the answer as a rational number. -6.90 meters per second can be expressed as -69/10 meters per second. Therefore, the average change in elevation of the object, in meters per second, is -69/10.

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Answer:

Step-by-step explanation:

In the arithmetic sequence \(t_1\), \(t_2\), \(t_3\), ..., \(t_n\), \(t_1=23\) and \(t_n= t_{n-1} - 3\) for each n > 1. What is the value of n when \(t_n = -4\)?

A. -1

B. 7

C. 10

D. 14

E. 20

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Best Regards,

E.

MGMAT 1 --> 530

MGMAT 2--> 640

MGMAT 3 ---> 610

GMAT ==> 730

Answer:

4 + 3(n-1)

Step-by-step explanation:

Sequences start from n=1,2,3....

In this case

4 + 3(1-1)= 4

4 + 3(2-1) =7

And continue the pattern