A. A numberis greater than an - 8 and less than or equal to 4.

denpristay [2]

The person HAD homework 75/100 or 75%

the remaining days he did NOT have homework , which is 25/100 or 25%

8 0

3 years ago

Solve the following initial-value problem, showing all work, including a clear general solution as well as the particular soluti

Vikki [24]

Answer:

General Solution is $y=x^{3}+cx^{2}$ and the particular solution is $y=x^{3}-\frac{1}{2}x^{2}$

Step-by-step explanation:

$x\frac{\mathrm{dy} }{\mathrm{d} x}=x^{3}+3y\\\\Rearranging \\\\x\frac{\mathrm{dy} }{\mathrm{d} x}-3y=x^{3}\\\\\frac{\mathrm{d} y}{\mathrm{d} x}-\frac{3y}{x}=x^{2}$

This is a linear diffrential equation of type

$\frac{\mathrm{d} y}{\mathrm{d} x}+p(x)y=q(x)$ ..................(i)

here $p(x)=\frac{-2}{x}$

$q(x)=x^{2}$

The solution of equation i is given by

$y\times e^{\int p(x)dx}=\int e^{\int p(x)dx}\times q(x)dx$

we have $e^{\int p(x)dx}=e^{\int \frac{-2}{x}dx}\\\\e^{\int \frac{-2}{x}dx}=e^{-2ln(x)}\\\\=e^{ln(x^{-2})}\\\\=\frac{1}{x^{2} } \\\\\because e^{ln(f(x))}=f(x)]\\\\Thus\\\\e^{\int p(x)dx}=\frac{1}{x^{2}}$

Thus the solution becomes

$\tfrac{y}{x^{2}}=\int \frac{1}{x^{2}}\times x^{2}dx\\\\\tfrac{y}{x^{2}}=\int 1dx\\\\\tfrac{y}{x^{2}}=x+c$ $y=x^{3}+cx^{2$

This is the general solution now to find the particular solution we put value of x=2 for which y=6

we have $6=8+4c$

Thus solving for c we get c = -1/2

Thus particular solution becomes

$y=x^{3}-\frac{1}{2}x^{2}$

5 0

4 years ago

How many rectangular faces does a pentagonal pyramid have?

Evgen [1.6K]

My best answer 5 faces.

7 0

3 years ago

Read 2 more answers

Can someone answer this for me pls

bezimeni [28]

Answer: Lin is the most consistent and I would want to have them on my team.

Why is this? Because their dots are more clustered together compared to the other distributions. Elena may have made the most shots (9) at one point, but her data set is very spread out and more unpredictable. The more spread out a data set is, the higher the variance and standard deviation. The range is also affected by how spread out the data set is since

range = max - min

So in a rough sense, the range can be used to estimate the variance and standard deviation. Though more accurate formulas are usually the better way to go.

5 0

3 years ago

If you are smart in ranges, graphs, and functions, pls help me out. Look at the screenshot below!

jeka94

Answer:

Graph of the equation y = 2/5x - 1

Please check the attached graph of the equation where:

The point (0, -1) represents the y-intercept, it is the point where the line crosses the y-axis.

The point (2.5, 0) represents the x-intercept, it is the point where the line crosses the x-axis.

Step-by-step explanation:

Given the equation

y = 2/5x - 1

Determining the y-intercept:

We know that the value of the y-intercept can be determined by setting x = 0 and determining the corresponding value of y.

As the equation is given such as

y = 2/5x - 1

substitute x = 0

y = 2/5(0) - 1

y = 0 - 1

y = -1

so the ordered pair (0, -1) represents the y-intercept.

Thus, the y-intercept is: -1

Determining the x-intercept:

We know that the value of the x-intercept can be determined by setting x = y and determining the corresponding value of x.

As the equation is given such as

y = 2/5x - 1

substitute y = 0

0 = 2/5x - 1

2/5x = 1

x = 5/2

x = 2.5

so the ordered pair (2.5, 0) represents the x-intercept.

Graph of the equation y = 2/5x - 1

Please check the attached graph of the equation where:

The point (0, -1) represents the y-intercept, it is the point where the line crosses the y-axis.

The point (2.5, 0) represents the x-intercept, it is the point where the line crosses the x-axis.

6 0

3 years ago