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3 years ago

HELP ME QUICK: Suppose AB has one endpoint at A(0, 0). If (5, 3) is the midpoint of AB, what are the coordinates of point B?

Mathematics

1 answer:

DiKsa [7]3 years ago

5 0

Answer:

Step-by-step explanation:

If P is midpoint of AB and: $A(0,\,0)\,,\quad P(5,\,3)\,,\quad B(x_B,\,y_B)$

then:

$x_P-x_A=x_B - x_P\qquad\quad\ \wedge\qquad y_P-y_A=y_B - y_P\\\\ 5-0=x_B-5\qquad\quad\wedge\qquad 3-0=y_B -3\\\\ x_B=5+5\qquad\qquad\wedge\qquad\ \ y_B=3+3 \\\\ {}\quad x_B=10\qquad\qquad\wedge\qquad\qquad \ y_B=6$

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3 years ago

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3 years ago

Find a solution x = x(t) of the equation x′ + 2x = t2 + 4t + 7 in the form of a quadratic function of t, that is, of the form x(

Temka [501]

The particular quadratic solution to the ODE is found as follows:

$x=at^2+bt+c$
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Note that there's also the fundamental solution to account for, which is obtained from the characteristic equation for the ODE:

$x'+2x=0\implies r+2=0\implies r=-2$

so that $x_c=Ce^{-2t}$ is a characteristic solution to the ODE, and the general solution would be

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3 years ago

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dlinn [17]

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<em><u>We'll use the distributive property to simplify this.</u></em>

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<u><em>Combine like terms</em></u>

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3 years ago