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3 years ago

Solving polynomial equations

x}^{2} = 48x" alt="6 {x}^{2} = 48x" align="absmiddle" class="latex-formula">

Mathematics

1 answer:

Vaselesa [24]3 years ago

7 0

$6x^2=48x\qquad\text{subtract 48x from both sides}\\\\6x^2-48x=0\qquad\text{divide both sides by 6}\\\\x^2-8x=0\\\\x(x-8)=0\iff x=0\ \vee\ x-8=0\\\\\boxed{x=0\ \vee\ x=8}$

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2 years ago

If y=e5t is a solution to the differential equation

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Answer:

k = 30, $y(t) = C_1e^{5t}+C_2e^{6t}$

Step-by-step explanation:

Since $y=e^{5t}$ is a solution, then it must satisfy the differential equation. So, we calculate the derivatives and replace the value in the equation. We have that

$\frac{d^2y}{dt^2} = 25 e^{5t},\frac{dy}{dt} = 5e^{5t}$

Then, replacing the derivatives in the equation we have:

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Since $e^{5t}$ is a positive function, we have that

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$Ae^{rt}(r^2-11r+30)=0$

We already know that r=5 is a solution of the equation, then we can divide the polynomial by the factor (r-5) to the get the other solution. If we do so, we get that (r-6)=0. So the other solution is r=6.

Therefore, the general solution is

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2 years ago

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2 years ago

Write the exponential function.

sertanlavr [38]

Answer:

$f(x) = 10*(b)^x$

Step-by-step explanation:

exponential function : $y=a*(b)^x$

where a = y intercept and b = factor ( what you multiply by )

looking at the table the y intercept is at (0,10) so a = 10

so we now have y = 10 * (b)^x

to find the factor we simply plug in one of the ordered pairs.

note that the ordered pair chosen does not effect the outcome

i chose (2,250)

we have y = 10 * (b)^x

(x,y) = (2,250)

250 = 10 * (b)^2

divide both sides by 10

25 = b^2

take the square root of both sides

5 = b

the final equation would be f(x) = 10 * (b)^x

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2 years ago