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butalik [34]
3 years ago
15

What are the solutions of the equation x2 – 1 = 15?

Mathematics
2 answers:
raketka [301]3 years ago
7 0
X^2-1=15
x^2=16
x=-4,4
Mila [183]3 years ago
7 0

Answer:

C

Step-by-step explanation:

NEXTQUESTION ALSO C

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Please help! whats 15 divided by 12
katrin2010 [14]

Answer:

1.25

Step-by-step explanation:

4 0
3 years ago
Answer options <br><br> 2<br><br> 3<br><br> 4<br><br> 5
777dan777 [17]

Answer:

k = 5

Step-by-step explanation:

given f(x) then f(x) + k represents a vertical translation of f(x)

• If k > 0 then a shift of k units up

• If k < 0 then a shift of k units down

f(x) crosses the y- axis at - 2

g(x) crosses the y- axis at 3

Thus g(x) is 5 units vertically up from f(x)

since g(x) = f(x) + k → then k = 5

7 0
3 years ago
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
If f(x) = 2x-12, evaluate -2f(3) <br><br> PLEASE HELP!!!!!!
mel-nik [20]
I think that’s it f(x)=2x−12
6 0
2 years ago
Read 2 more answers
What's greater 4 yards or 13 feet
ELEN [110]
That would be 13 feet because each yard is 3 feet so 3x4=12 (feet)
so the correct answer would be 13 feet.
3 0
3 years ago
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