if a line intersect x axis at a point (6,0) and y axis at a point (0,-8). then what is equation of a line?​

Answer:

a) the work done in propelling a five-ton satellite to a height of 100 miles above Earth is 487.8 mile-tons  

b) the work done in propelling a five-ton satellite to a height of 300 miles above Earth is 1395.3 mile-tons

Step-by-step explanation:

Given the data in the question;

We know that the weight of a body varies inversely as the square of its distance from the center of the earth.

⇒F(x) = c / x²

given that; F(x) = five-ton = 5 tons

we know that the radius of earth is approximately 4000 miles

so we substitute

5 = c / (4000)²

c = 5 × ( 4000 )²

c = 8 × 10⁷

∴ Increment of work is;

Δw =  [ ( 8 × 10⁷ ) / x² ] Δx

a) For 100 miles above Earth;

W = ₄₀₀₀∫⁴¹⁰⁰ [ ( 8 × 10⁷ ) / x² ] Δx

= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{x}[/tex] [tex]]^{4100}_{4000[/tex]

= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{4100}[/tex] [tex]+\frac{1}{4000}[/tex] [tex]][/tex]

= (8 × 10⁷ ) [ 6.09756 × 10⁻⁶ ]

= 487.8 mile-tons  

Therefore, the work done in propelling a five-ton satellite to a height of 100 miles above Earth is 487.8 mile-tons  

b) For 300 miles above Earth.

W = ₄₀₀₀∫⁴³⁰⁰ [ ( 8 × 10⁷ ) / x² ] Δx

= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{x}[/tex] [tex]]^{4300}_{4000[/tex]

= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{4300}[/tex] [tex]+\frac{1}{4000}[/tex] [tex]][/tex]

= (8 × 10⁷ ) [ 1.744186 × 10⁻⁵ ]

= 1395.3 mile-tons

Therefore, the work done in propelling a five-ton satellite to a height of 300 miles above Earth is 1395.3 mile-tons

Answer:

Step-by-step explanation:

Answer:

third option

Step-by-step explanation:

m(n(x)) =

[tex] \frac{x - 3 + 5}{x - 3 - 1} = \frac{x + 2}{x - 4} [/tex]

the domain of this is R/(4)

so as the third option

The function that has the same domain as (m o n)(x) is

h(x) = 11 / (x - 3)

Option D is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

m(x) = (x + 5)/ (x - 1) and n(x) = x - 3,

Now,

(m o n)(x)

= m (n(x)

= m (x - 3)

= (x - 3 + 5) / (x - 3 - 1)

= (x + 2) / (x - 3)

We can not have x = 3.

So,

The domain can not have x = 3.

From the options,

h(x) = 11 / (x - 3) can not have x = 3.

Thus,

The function that has the same domain as (m o n)(x) is

h(x) = 11 / (x - 3)

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ7

9514 1404 393

Answer:

  (c)  2440

Step-by-step explanation:

The sum of the squares of numbers 1 .. n is ...

  s(n) = n(n +1)(2n +1)/6

You want the sum of squares from 5 to 19. We can compute that from ...

  s(19) -s(4) = (19(20)(39) -4(5)(9))/6 = (14820 -180)/6 = 2440

Answer:

Step-by-step explanation:

hope it helps u too

Answe

SI Si olla amigo lel just spammin here

Step-by-step explanation:

Answer:

Espanol la vecsu

Step-by-step explanation:

Answer:

x = 1

Step-by-step explanation:

The diagonals of a rectangle bisect each other , so

DE = EB , that is

7x - 1 = 2x + 4 ( subtract 2x from both sides )

5x - 1 = 4 ( add 1 to both sides )

5x = 5 ( divide both sides by 5 )

x = 1

5 ÷ 1/2 => 5 x 2/1 => 10/1 => 10

Answer:

10

Step-by-step explanation:

In the pic, it shows ten half squares.  

Answer:

300 computers

Step-by-step explanation:

So I divided 1500 out of a 100 and got 15, then I multiply 15 to 20 and got 300.

(I am a high schooler so I hope this is 3rd grade math because I notice you are a college student and I hope this not some college tricky math, if you get this wrong I am truly sorry)

Answer:

This means the average amount of time is 48 minutes but many people will do it in 45 to 51

Hope This Helps!!!

Answer:

0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation 2.

This means that [tex]\mu = 14, \sigma = 2[/tex]

Sample of 100:

This means that [tex]n = 100, s = \frac{2}{\sqrt{100}} = 0.2[/tex]

What is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2?

This is 1 subtracted by the p-value of Z when X = 14.2. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{14.2 - 14}{0.2}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a p-value of 0.8413.

1 - 0.8413 = 0.1587

0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.

Answer:

Sister's house is 7.5 feet high

Step-by-step explanation:

Given :

     My house = 5  feet

     Sisters house = [tex]1\frac{2}{4}[/tex]  [tex]times[/tex]  [tex]my \ house[/tex]

                           = [tex]\frac{6}{4} \times 5[/tex]

                           [tex]=\frac{30}{4}\\\\=\frac{15}{2}\\\\= 7 . 5 \ feet[/tex]

Answer:

216

Step-by-step explanation:

=>log   36 = -2/3

        m

=>36=(m)^-2/3

=>(root(-36))^3=m

=>m=(root(36))^3

=>m=6^3

=>m=216

Answer:

last step is (2x + 5)(2x + 1)

Step-by-step explanation:

4x^2 + 12x + 5

4x^2 + (10 + 2)x + 5

4x^2 + 10x + 2x + 5

2x(2x + 5) +1(2x + 5)

(2x + 5)(2x + 1)

Answer:

x ≥ 12

Step-by-step explanation:

-3/4x +2 ≤ -7

Subtract 2 from each side

-3/4x +2-2 ≤ -7-2

-3/4x  ≤ -9

Multiply each side by -4/3, remembering to flip the inequality

-3/4x * -4/3 ≥ - 9 *(-4/3)

x ≥ 12

Answer:

x>=12

Step-by-step explanation:

-3/4x + 2<=-7

-3/4x <= -7 -2

-3/4x<=-9

cross multiply

-3x<=-36

dividing throughout by -3

x>=12

Answer:

(a)

Mean

[tex]\bar x_1 = 31.375[/tex]

[tex]\bar x_2 = 41.75[/tex]

[tex]\bar x_3 = 53.00[/tex]

Standard deviation

[tex]\sigma_1 = 8.73[/tex]

[tex]\sigma_2 = 7.65[/tex]

[tex]\sigma_3 = 6.04[/tex]

(b) Yes, there is a difference in the mean

Step-by-step explanation:

Solving (a): The mean and standard deviation of each commercial

This is calculated as:

[tex]\bar x = \frac{\sum x}{n}[/tex]

For clothes:

[tex]\bar x_1 = \frac{43+24+42+35+28+31+17+31}{8}[/tex]

[tex]\bar x_1 = \frac{251}{8}[/tex]

[tex]\bar x_1 = 31.375[/tex]

For food:

[tex]\bar x_2 = \frac{30+38+46+54+47+42+34+43}{8}[/tex]

[tex]\bar x_2 = \frac{334}{8}[/tex]

[tex]\bar x_2 = 41.75[/tex]

For toys:

[tex]\bar x_3 = \frac{52+58+43+49+63+53+48+58}{8}[/tex]

[tex]\bar x_3 = \frac{424}{8}[/tex]

[tex]\bar x_3 = 53.00[/tex]

The sample standard deviation is:

[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]

For clothes:

[tex]\sigma_1 = \sqrt{\frac{(43 - 31.375)^2 +.............+(31 - 31.375)^2}{8-1}}[/tex]

[tex]\sigma_1 = \sqrt{\frac{533.875}{7}[/tex]

[tex]\sigma_1 = \sqrt{76.2678571429}[/tex]

[tex]\sigma_1 = 8.73[/tex]

For food:

[tex]\sigma_2 = \sqrt{\frac{(30 - 41.75)^2 +............+(43 - 41.75)^2}{8-1}}[/tex]

[tex]\sigma_2 = \sqrt{\frac{409.5}{7}}[/tex]

[tex]\sigma_2 = \sqrt{58.5}[/tex]

[tex]\sigma_2 = 7.65[/tex]

For toys:

[tex]\sigma_3 = \sqrt{\frac{(52-53.00)^2+...................+(58-53.00)^2}{8}}[/tex]

[tex]\sigma_3 = \sqrt{\frac{292}{8}}[/tex]

[tex]\sigma_3 = \sqrt{36.5}[/tex]

[tex]\sigma_3 = 6.04[/tex]

Solving (b): Difference in mean in the commercials;

In (a), we have:

[tex]\bar x_1 = 31.375[/tex]

[tex]\bar x_2 = 41.75[/tex]

[tex]\bar x_3 = 53.00[/tex]

[tex]\bar x_1 \ne \bar x_2 \ne \bar x_3[/tex]

Hence, there is a difference in their means

Answer:

The last one!

Step-by-step explanation:

Answer:

Your options are not clear

Step-by-step explanation:

[tex]\sqrt[3]{-1000 \times p^{12} \times q^3} \\\\(-1 \times 10^3 \times p^{12} \times q^3)^{\frac{1}{3} }\\\\(-1^3)^{\frac{1}{3} }\times 10^{3 \times \frac{1}{3} } \times p^{12 \times \frac{1}{3}} \times q^{3 \times \frac{1}{3}} \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ (-1)^3 = - 1 \ ] \\\\- 1 \times 10 \times p^4 \times q\\\\-10p^4q[/tex]

Answer:

8[tex]v^{-3}[/tex]z - [tex]\frac{5}{3}[/tex] vz

Step-by-step explanation:

Answer:

[tex]cos \theta = \frac{11}{12}[/tex]

Step-by-step explanation:

[tex]sin \theta = \frac{\sqrt{23}}{12} \ , \ tan \theta = \frac{\sqrt{23}}{11}\\\\tan \theta = \frac{sin \theta }{cos \theta }\\\\ \frac{\sqrt{23}}{11} = \frac{\frac{\sqrt{23}}{12} }{cos \theta}\\\\cos \theta = \frac{\frac{\sqrt{23}}{12} }{\frac{\sqrt{23}}{11} }\\\\cos \theta = \frac{\sqrt{23}}{12 } \times \frac{11}{\sqrt{23}}\\\\cos \theta = \frac{11}{12}[/tex]

Answer:

Because we know that here we have an oscillation, we can model this with a sine or cosine function.

P = A*cos(k*t) + M

where:

k is the frequency

A is the amplitude

M is the midline

We know that at t = 0, we have the lowest population.

We know that the mean is 129, so this is the midline.

We know that the population oscillates 25 above and below this midline,

And we know that for t = 0 we have the lowest population, so:

P = A*cos(k*0) + 129 = 129 - 25

P = A + 129 = 129 - 25

A = -25

So, for now, our equation is

P = -25*cos(k*t) + 129

Because this is a yearly period, we should expect to see the same thing for t = 12 (because there are 12 months in one year).

And remember that the period of a cosine function is 2*pi

Then:

k*12 = 2*pi

k = (2*pi)/12 = pi/6

Finally, the equation is:

P = -25*cos(t*pi/6) + 129

Now we want to find the lowest population was in April instead:

if January is t = 0, then:

February is t = 2

March is t = 3

April is t = 4

Then we would have that the minimum is at t = 4

If we want to still use a cosine equation, we need to use a phase p, such that now our equation is:

P = -25*cos(k*t + p) + 129

Such that:

cos(k*4 + p) = 1

Then:

k*4 + p = 0

p =  -k*4

So our equation now is:

P = -25*cos(k*t  - 4*k) + 129

And for the periodicity, after 12 months, in t = 4 + 12 = 16, we should have the same population.

Then, also remembering that the period of the cosine function is 2*pi:

k*12 - 4*k = 2*pi

k*8 = 2*pi

k = 2*pi/8 = pi/4

And remember that we got:

p = -4*k = -4*(pi/4) = -pi

Then the equation for the population in this case is:

P = -25*cos( t*pi/4 - pi) + 129

Answer:

It will take him 5.85 seconds.

Step-by-step explanation:

12.5 (0.2t - 1) + 21t = 150

Use Distributive Property:

2.5t - 12.5 + 21t = 150

Combine like terms:

23.5t - 12.5 = 150

Subtract 12.5 from both sides:

23.5t = 137.5

Divide both sides by 23.5 to isolate variable t:

5.851063.....

Round to two decimal places (hundredths place):

5.85

Answer:

Since acceleration is the derivative of velocity, velocity is the antiderivative of acceleration. If you know the acceleration for all time, and if you know the starting velocity, you can figure out the velocity for all time.

Step-by-step explanation:

Answer:

Since acceleration is the derivative of velocity, velocity is the antiderivative of acceleration. If you know the acceleration for all time, and if you know the starting velocity, you can figure out the velocity for all time.

Given:

Line A goes through (0,y) and (-2,0).

Line B goes through (1,2) and (3,10).

To find:

The value of y for which the system of given linear equation (equation of line A and line B) has no solutions.

Solution:

Two linear equation has no solutions if they are parallel line.

Slope formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We know that the slopes of two parallel lines are the same.

So, the given system of given linear equation has no solutions if

Slope of line A = Slope of line B

[tex]\dfrac{0-y}{-2-0}=\dfrac{10-2}{3-1}[/tex]

[tex]\dfrac{-y}{-2}=\dfrac{8}{2}[/tex]

[tex]\dfrac{y}{2}=4[/tex]

Multiply both sides by 2.

[tex]\dfrac{y}{2}\times 2=4\times 2[/tex]

[tex]y=8[/tex]

Therefore, the required value of y is 8.

11%

Hope this helps! :)

______________

Answer:

[tex] \frac{195.80}{220} \times 100 \% \\ = 0.89\%[/tex]

Answer:

C)  The graph rises to the left and rises to the right.

Step-by-step explanation:

The highest expone tis even and it's coefficient is positive

therefor

The graph rises to the left and rises to the right.

Answer:

y = -3x + 13

Step-by-step explanation:

First, find the slope:

[tex]m=\frac{y_1-y_2}{x_1-x_2}\\\\m=\frac{4-10}{3-1}\\\\m=\frac{-6}{2}\\\\m=-3[/tex]

Finally, find the equation:

[tex]y-y_1=m(x-x_1)\\\\y-4=-3(x-3)\\\\y-4=-3x+9\\\\y=-3x+13[/tex]

let the number be b

62.5/100 x b = 25

0.625 x b = 25

b =25/0.625

b=40

half of b= 40/2 = 20

Answer:

i guess its 1...

Step-by-step explanation:

Answer:

79 numbers

Step-by-step explanation:

39 x 39 = 1521 ( Find the square of 39)

40 x 40 = 1600 (Find the square of 40)

1600 - 1521 = 79 ( Finding the difference of the two squares)

Answer:

x^2+2x-5 - 1/x

Step-by-step explanation:

f(x)=1/x

g(x)=x^2+2x-5

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

Answer:

c. x² + 2x - 5 - 1 / x

Step-by-step explanation:

f ( x) = 1 / x.

g ( x) = x² + 2x - 5

so,

( g - f) ( x) = x² + 2x - 5 - 1 / x

Answer:

Correct answers= 18

Incorrect answers=30-18= 12 answers

Step-by-step explanation:

total questions=30

correct answers= x

incorrect answers= 30-x

given: 5 marks for each correct answer

therefore, marks for correct answers = 5*x = 5x

Given: 1 mark deducted for every incorrect answer

therefore, marks deducted = 1(30-x) = 30-x

Total marks scored= 78

★  The Difference of Marks scored for Correct Answers and Marks deducted for Incorrect Answers should be equal to 78

5x- (30-x) =78

5x-30+x=78

5x+x=78+30

6x= 108

x=108/6 = 18

Correct answers= 18

Incorrect answers=30-18= 12 answers