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timama [110]
3 years ago
14

This is the 3rd of 14.

Mathematics
2 answers:
Brut [27]3 years ago
8 0
Let the height of the triangle be x then the base becomes as 4+x
now area of triangle in a plane surface is given by
1/2*base*height
thus
1/2*(4+x)*x= 16
4x+x^2 = 32
x^2 +4x -32 = 0
x^2+8x-4x-32
x(x+8)-4(x+8)
therefore x is equal to -8 or +4
hence it can't be in negative so it is +4
thus base becomes +8
the height is 4 cm and base is 8cm
Snezhnost [94]3 years ago
4 0
The height is 4 cm and the base is 8 cm.
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3 years ago
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:

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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

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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
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8 0
3 years ago
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lina2011 [118]

Answer:

(-1/3; 4)

Step-by-step explanation:

(-2, -1) , (-1, 6 ) and (2, 7).​

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=> (-1/3; 4)

7 0
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