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Anna007 [38]
2 years ago
6

What are the solutions to the system of the equations graphed below?

Mathematics
2 answers:
xz_007 [3.2K]2 years ago
8 0
A (2,0) and (0,-8) because it’s shown in the picture that’s the red line indicates the place it needs to be in
Zigmanuir [339]2 years ago
4 0

Answer:

D

Step-by-step explanation:

Where the graphs intersect each other is where the solution is. The graphs intersect each other at the points (0,-8) and (4,8). Hope this helps!

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Solve for x in the equation x^2-10x+25=35.
KatRina [158]
So, this is too vague but I'll solve for both quadratic formula and find the discriminant.

Quadratic formula: <span>x=<span>5+<span><span><span>√35 OR</span><span> </span></span>x</span></span></span>=<span>5−<span>√<span>35
Finding the discriminant: 141</span></span></span>
3 0
3 years ago
Read 2 more answers
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
What is the product of -1/2 x 1/8 in simplest form
hjlf

Answer: Edit: -0.0625

Step-by-step explanation:

3 0
3 years ago
How do I solve this?
bogdanovich [222]

Answer:

<h2>5(x + 7)²</h2>

Step-by-step explanation:

5(x+7)^4=\boxed5\cdot\boxed{(x+7)}\cdot\boxed{(x+7)}\cdot(x+7)\cdot(x+7)\\\\35(x+7)^2=\boxed5\cdot7\cdot\boxed{(x+7)}\cdot\boxed{(x+7)}\\\\15(x+7)^3=\boxed5\cdot3\cdot\boxed{(x+7)}\cdot\boxed{(x+7)}\cdot(x+7)\\\\GCF\bigg(5(x+7)^4,\ 35(x+t)^2,\ 15(x+7)^3\bigg)=\boxed5\cdot\boxed{(x+7)}\cdot\boxed{(x+7)}\\\\=5(x+7)^2

5 0
3 years ago
Please someone help me answer this!!
jekas [21]

Answer:

a^10

Step-by-step explanation:

5*2=10

3 0
3 years ago
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