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sp2606 [1]
3 years ago
13

Y - 660 = 80(X – 7)?

Mathematics
2 answers:
asambeis [7]3 years ago
5 0

Answer:

Answer:

y=80x + 100

Step-by-step explanation:

y - 660 = 80(X – 7)

y-660= 80 x - 560

y-660+660= 80 x - 560+660

y= 80x + 100

Step-by-step explanation:

just read it g

Murljashka [212]3 years ago
3 0

Answer:

y=80x + 100

Step-by-step explanation:

y - 660 = 80(X – 7)

y-660= 80 x - 560

y-660+660= 80 x - 560+660

y= 80x + 100

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Find the function y1 of t which is the solution of 121y′′+110y′−24y=0 with initial conditions y1(0)=1,y′1(0)=0. y1= Note: y1 is
strojnjashka [21]

Answer:

Step-by-step explanation:

The original equation is 121y''+110y'-24y=0. We propose that the solution of this equations is of the form y = Ae^{rt}. Then, by replacing the derivatives we get the following

121r^2Ae^{rt}+110rAe^{rt}-24Ae^{rt}=0= Ae^{rt}(121r^2+110r-24)

Since we want a non trival solution, it must happen that A is different from zero. Also, the exponential function is always positive, then it must happen that

121r^2+110r-24=0

Recall that the roots of a polynomial of the form ax^2+bx+c are given by the formula

x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}

In our case a = 121, b = 110 and c = -24. Using the formula we get the solutions

r_1 = -\frac{12}{11}

r_2 = \frac{2}{11}

So, in this case, the general solution is y = c_1 e^{\frac{-12t}{11}} + c_2 e^{\frac{2t}{11}}

a) In the first case, we are given that y(0) = 1 and y'(0) = 0. By differentiating the general solution and replacing t by 0 we get the equations

c_1 + c_2 = 1

c_1\frac{-12}{11} + c_2\frac{2}{11} = 0(or equivalently c_2 = 6c_1

By replacing the second equation in the first one, we get 7c_1 = 1 which implies that c_1 = \frac{1}{7}, c_2 = \frac{6}{7}.

So y_1 = \frac{1}{7}e^{\frac{-12t}{11}} + \frac{6}{7}e^{\frac{2t}{11}}

b) By using y(0) =0 and y'(0)=1 we get the equations

c_1+c_2 =0

c_1\frac{-12}{11} + c_2\frac{2}{11} = 1(or equivalently -12c_1+2c_2 = 11

By solving this system, the solution is c_1 = \frac{-11}{14}, c_2 = \frac{11}{14}

Then y_2 = \frac{-11}{14}e^{\frac{-12t}{11}} + \frac{11}{14} e^{\frac{2t}{11}}

c)

The Wronskian of the solutions is calculated as the determinant of the following matrix

\left| \begin{matrix}y_1 & y_2 \\ y_1' & y_2'\end{matrix}\right|= W(t) = y_1\cdot y_2'-y_1'y_2

By plugging the values of y_1 and

We can check this by using Abel's theorem. Given a second degree differential equation of the form y''+p(x)y'+q(x)y the wronskian is given by

e^{\int -p(x) dx}

In this case, by dividing the equation by 121 we get that p(x) = 10/11. So the wronskian is

e^{\int -\frac{10}{11} dx} = e^{\frac{-10x}{11}}

Note that this function is always positive, and thus, never zero. So y_1, y_2 is a fundamental set of solutions.

8 0
3 years ago
The circle graph shows a family budgets it’s annual income.if the total annual income is 140,000, what amount is budgeted for au
emmasim [6.3K]

Answer: The amount budgeted for Auto Expenses is $18,200

Step-by-step explanation:

13 Percent of $140,000 is $18,200

0.13 times 140,000 :-)

5 0
3 years ago
Abril earned a total of $60 mowing lawns around her neighborhood. she charges $8 an hour and received $20 in tips .use the equat
zmey [24]

Answer:

She spent 5 hours mowing lawns.

Step-by-step explanation:

To solve, we will just use some algebra

8h + 20 = 60 | Subtract 20 from both sides

8h = 40 | Divide both sides by 8

h = 5

We can confirm this by plugging it back into the original formula.

8(5) + 20 = 60

40 + 20 = 60

60 = 60

5 0
3 years ago
10) Solve the equation for the variable "a":<br> 2(x + a) = 4b
masya89 [10]

Answer:

a= 2b-x

Step-by-step explanation:

You have to isolate the variable by dividing each side of the factors that does not contain the variable "a".

3 0
3 years ago
Solve for X <br> PLEASE HELP ITS URGENT
almond37 [142]
With pythagorean theorem and working backwards, you do 8100-1225 to get 6875, you then get the square root of that to get x=82.91 or rounded to 82.92
6 0
3 years ago
Read 2 more answers
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