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3 years ago

What is the slope of a line perpendicular to the line: y = -2/3x + 5

Mathematics

1 answer:

Rus_ich [418]3 years ago

5 0

1.5

Opposite reciprocal of -2/3

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X+3/2 + (x-1) = 4/5

tester [92]

Answer:

x = $\frac{3}{20}$

Step-by-step explanation:

Given

x + $\frac{3}{2}$ + (x - 1) = $\frac{4}{5}$

Multiply through by 10 ( the LCM of 2 and 5 ) to clear the fractions

10x + 15 + 10(x - 1) = 8

10x + 15 + 10x - 10 = 8

20x + 5 = 8 ( subtract 5 from both sides )

20x = 3 ( divide both sides by 20 )

x = $\frac{3}{20}$

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3 years ago

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3 years ago

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For a data set of weights (pounds) and highway fuel consumption amounts (mpg) of eleven types of automobile, the linear corre

Zina [86]

Answer:

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Step-by-step explanation:

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3 years ago

Write 7/3,41/9,9/5 in simplest form

Soloha48 [4]

Answer:

$\frac{7}{3}$ = 2 1/3 ← Mixed Fraction
$\frac{41}{9}$ = 4 5/9
$\frac{9}{5}$ = 1 4/5

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3 years ago

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Find the solution of the given initial value problem. ty' + 2y = sin t, y π 2 = 9, t > 0 y(t) =

Helen [10]

For the ODE

$ty'+2y=\sin t$

multiply both sides by t so that the left side can be condensed into the derivative of a product:

$t^2y'+2ty=t\sin t$

$\implies(t^2y)'=t\sin t$

Integrate both sides with respect to t :

$t^2y=\displaystyle\int t\sin t\,\mathrm dt=\sin t-t\cos t+C$

Divide both sides by $t^2$ to solve for y :

$y(t)=\dfrac{\sin t}{t^2}-\dfrac{\cos t}t+\dfrac C{t^2}$

Now use the initial condition to solve for C :

$y\left(\dfrac\pi2\right)=9\implies9=\dfrac{\sin\frac\pi2}{\frac{\pi^2}4}-\dfrac{\cos\frac\pi2}{\frac\pi2}+\dfrac C{\frac{\pi^2}4}$

$\implies9=\dfrac4{\pi^2}(1+C)$

$\implies C=\dfrac{9\pi^2}4-1$

So the particular solution to the IVP is

$y(t)=\dfrac{\sin t}{t^2}-\dfrac{\cos t}t+\dfrac{\frac{9\pi^2}4-1}{t^2}$

$y(t)=\dfrac{4\sin t-4t\cos t+9\pi^2-4}{4t^2}$

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3 years ago