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3 years ago

For f(x) = 2x + 1 find each value. f(6) f(3) f(−5)

Mathematics

1 answer:

sertanlavr [38]3 years ago

7 0

F(6) = 2(6) + 1
= 12 +1
= 13

f(3) = 2(3) + 1
= 6 + 1
= 7

f(-5) = 2(-5) + 1
= -10 + 1
= -9

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Determine the slope of the line that has the points (-5, 8) and (-5, 3).

Anuta_ua [19.1K]

Answer:

Option D : Undefined

Step-by-step explanation:

Given points (-5,8) and (-5,3) lies on a line.

Slope of a line is given by:

m = $\frac{y_2-y_1}{x_2-x_1}$

$m = \frac{3-8}{-5-(-5)}\\\\m=\frac{-5}{0}$

Anything divided by zero is undefined.

Therefore,

Option D is the correct answer.

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3 years ago

First-order linear differential equations

kkurt [141]

Answer:

$(1)\ logy\ =\ -sint\ +\ c$

$(2)\ log(y+\dfrac{1}{2})\ =\ t^2\ +\ c$

Step-by-step explanation:

1. Given differential equation is

$\dfrac{dy}{dt}+ycost = 0$

$=>\ \dfrac{dy}{dt}\ =\ -ycost$

$=>\ \dfrac{dy}{y}\ =\ -cost dt$

On integrating both sides, we will have

$\int{\dfrac{dy}{y}}\ =\ \int{-cost\ dt}$

$=>\ logy\ =\ -sint\ +\ c$

Hence, the solution of given differential equation can be given by

$logy\ =\ -sint\ +\ c.$

2. Given differential equation,

$\dfrac{dy}{dt}\ -\ 2ty\ =\ t$

$=>\ \dfrac{dy}{dt}\ =\ t\ +\ 2ty$

$=>\ \dfrac{dy}{dt}\ =\ 2t(y+\dfrac{1}{2})$

$=>\ \dfrac{dy}{(y+\dfrac{1}{2})}\ =\ 2t dt$

On integrating both sides, we will have

$\int{\dfrac{dy}{(y+\dfrac{1}{2})}}\ =\ \int{2t dt}$

$=>\ log(y+\dfrac{1}{2})\ =\ 2.\dfrac{t^2}{2}\ + c$

$=>\ log(y+\dfrac{1}{2})\ =\ t^2\ +\ c$

Hence, the solution of given differential equation is

$log(y+\dfrac{1}{2})\ =\ t^2\ +\ c$

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4 years ago

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nalin [4]

right answer is a.

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3 years ago

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lys-0071 [83]

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Step-by-step explanation:

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3 years ago

Which equation is a point slope form equation for line AB ?

zepelin [54]

(-2,3)(4,-1)
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equation
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4 years ago