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3 years ago

I need help with this..

Mathematics

1 answer:

Misha Larkins [42]3 years ago

8 0

Answer:

a0) 2

x<0

a1) x

0≤x<3

a2) 3

x≥3

Step-by-step explanation:

As shown in the given graph

function of y is a straight line at y=2 line till x=0

hence a0:

y= 2 for x<0

Then function becomes linear line from x=0 till x=3

hence a1:

y= x for 0≤x<3

Now after that graph of function y again shift to straight line from x=3 onward with y-axis value of 3

hence a2:

y= 3 for x≥3 !

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Write the equation of the line that passes through the points (3, 6) and (5, 18) using function notation.

faust18 [17]

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This line passes through both given points.

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3 years ago

Read 2 more answers

Consider the differential equation <img src="https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D6%20y%5E%7

Nutka1998 [239]

As a Bernoulli equation:

$x^2\dfrac{\mathrm dy}{\mathrm dx}=6y^2+6xy\iff x^2y^{-2}\dfrac{\mathrm dy}{\mathrm dx}-6xy^{-1}=6$

Let $z=y^{-1}\implies\dfrac{\mathrm dz}{\mathrm dx}=-y^{-2}\dfrac{\mathrm dy}{\mathrm dx}$ . The ODE becomes

$-x^2\dfrac{\mathrm dz}{\mathrm dx}-6xz=6$
$x^6\dfrac{\mathrm dz}{\mathrm dx}+6x^5z=-6x^4$
$\dfrac{\mathrm d}{\mathrm dx}[x^6z]=-6x^4$
$x^6z=-6\displaystyle\int x^4\,\mathrm dx$
$x^6z=-\dfrac65x^5+C$
$z=-\dfrac6{5x}+\dfrac C{x^6}$
$y^{-1}=-\dfrac6{5x}+\dfrac C{x^6}$
$y=\dfrac1{\frac C{x^6}-\frac6{5x}}$
$y=\dfrac{5x^6}{C-6x^5}$

With $y(3)=6$ , we get

$6=\dfrac{5(3)^6}{C-6(3)^5}\implies C=\dfrac{4131}2$

so the solution is

$y=\dfrac{5x^6}{\frac{4131}2-6x^5}=\dfrac{10x^6}{4131-12x^5}$

which is valid as long as the denominator is not zero, which is the case for all $x\neq\sqrt[5]{\dfrac{4131}{12}}$ .

8 0

3 years ago

I would really appreciate it if this would get answered thank you

Maksim231197 [3]

Answer: I'll simplify the inequality

11. x≤8

12. y<8

13. z>2

14. b≥12

15. c<1.8

16. already solved a≤0

5 0

3 years ago

If f(x) = 3x – 2 and g(x) = 2x + 1, find (f + g)(x).

Mariulka [41]

Answer:

D. 5x - 1

Step-by-step explanation:

(f+g)(x) ➡ f(x) + g(x)

3x -2 + 2x + 1 = 5x -1

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3 years ago