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swat32
3 years ago
14

A number y is five times greater than two added to a number x.write an expression for y in terms of x.if x = 3, what is y

Mathematics
1 answer:
Oduvanchick [21]3 years ago
3 0

Answer:

y=5x+10 or y=25 (i'm not sure what they're asking)

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x = c1 cos(t) + c2 sin(t) is a two-parameter family of solutions of the second-order DE x'' + x = 0. Find a solution of the seco
igomit [66]

Answer:

x=-cos(t)+2sin(t)

Step-by-step explanation:

The problem is very simple, since they give us the solution from the start. However I will show you how they came to that solution:

A differential equation of the form:

a_n y^n +a_n_-_1y^{n-1}+...+a_1y'+a_oy=0

Will have a characteristic equation of the form:

a_n r^n +a_n_-_1r^{n-1}+...+a_1r+a_o=0

Where solutions r_1,r_2...,r_n are the roots from which the general solution can be found.

For real roots the solution is given by:

y(t)=c_1e^{r_1t} +c_2e^{r_2t}

For real repeated roots the solution is given by:

y(t)=c_1e^{rt} +c_2te^{rt}

For complex roots the solution is given by:

y(t)=c_1e^{\lambda t} cos(\mu t)+c_2e^{\lambda t} sin(\mu t)

Where:

r_1_,_2=\lambda \pm \mu i

Let's find the solution for x''+x=0 using the previous information:

The characteristic equation is:

r^{2} +1=0

So, the roots are given by:

r_1_,_2=0\pm \sqrt{-1} =\pm i

Therefore, the solution is:

x(t)=c_1cos(t)+c_2sin(t)

As you can see, is the same solution provided by the problem.

Moving on, let's find the derivative of x(t) in order to find the constants c_1 and c_2:

x'(t)=-c_1sin(t)+c_2cos(t)

Evaluating the initial conditions:

x(0)=-1\\\\-1=c_1cos(0)+c_2sin(0)\\\\-1=c_1

And

x'(0)=2\\\\2=-c_1sin(0)+c_2cos(0)\\\\2=c_2

Now we have found the value of the constants, the solution of the second-order IVP is:

x=-cos(t)+2sin(t)

3 0
3 years ago
A bookmark has an area of 14 square centimeters and a perimeter of 18 centimeters. What are the dimensions of the bookmark?
Naily [24]

Answer:

2 x 7

Step-by-step explanation:

a * b = 14

2a + 2b = 18

(a * b)/b  = 14/b Dividing both sides by b

a = 14/b

Substitute a in the perimeter equation

2(14/b) + 2b = 18

28/b + 2b = 18

2b - 18 + 28/b = 0

Multiply both sides by b

2b^2 - 18b + 28 = 0

Divide both sides by two

b^2 - 9b + 14 = 0

The Factors of 14 include -2 and -7 which add up to -9

(b - 2) * (b - 7) = 0

This has two answers because b can be either the side that is 2 long or 7 long, so there's no need to go back and solve for a.

2 x 7

4 0
3 years ago
A basketball player completed ​44.2% of his field goals in the most recent season. He made 287 field goals. How many did he​ att
Andrej [43]

44.2%= 287

Let the total attempt = x

(287/x) ×100 = 44.2

287/x = 44.2/100

287/x = 0.442

x = 287/0.442

<h3>x= <u>649 </u></h3>

Hope this will help...

5 0
3 years ago
Determine the price of a $35 basketball that is on sale for 50% off the regular price.
alexira [117]

Answer:

$17.5

Step-by-step explanation:

50 is 1/2 of 100, so just divide 35 by 1/2

6 0
3 years ago
PLEASE HELP!
meriva

The time taken for the population of the pig to reach 1000 will be almost four years.

<h3>What is a function?</h3>

A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.

Six guinea pigs are released in an area with no natural predators.

The guinea pig population quadruples every year.

Write a function P that represents the guinea pig population at a given time T measured in years.

Then the function will be

\rm P = 6 (4)^T

Then the inverse function of P will be

\rm T = 6 (4)^P\\\\\\P \ln 4 = \ln \left (\dfrac{T}{6} \right )\\\\\\P = \dfrac{\ln (T/6)}{\ln 4}

Then the time taken for the population of the pig to reach 1000 will be

\rm 1000 = 6 (4)^T\\\\\\166.667 = 4^T\\\\\\T = 3.69 \\\\\\T \approx 4 \ years

More about the function link is given below.

brainly.com/question/5245372

#SPJ1

8 0
2 years ago
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