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Mathematics

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docker41 [41]3 years ago

3 0

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How do you do f(x)=12x+3 2units left g(x)= please help I'm confused

Mkey [24]

Answer:

g(x) = 12x + 27

Step-by-step explanation:

Take a point in the f(x).

f(0) = 12(0) + 3

f(0) = 3

A point on f(x) is (0,3).

Move the point 2 units left. It will make the x-coordinate decrease by 2.

0 - 2 = -2

A point on g(x) is (-2,3).

Substitute the point and the same slope into the equation of a line. The slope did not change.

y = mx + b

3 = 12(-2) + b

3 = -24 + b

b = 3 + 24

b = 27

Rewrite g(x) using b = 27 and the same slope, m = 12.

g(x) = 12x + 27

7 0

3 years ago

How do you write algebraic expressions to model quantities?

Natali5045456 [20]

Let's say you are walking down the street and you see a lemonade stand. One of the workers tell you that if you buy a lemonade you will have to buy 5 times that amount to sit down and a lemonade cost $2. you order 2 lemonades. after grabbing your drink you feel like sitting down. so you go up to the stand and and attempt to purchase a seat.
5($2x2)=x
(THIS IS JUST AN EXAMPLE)

3 0

3 years ago

Read 2 more answers

Evaluate using integration by parts

PolarNik [594]

Rather than carrying out IBP several times, let's establish a more general result. Let

$I(n)=\displaystyle\int x^ne^x\,\mathrm dx$

One round of IBP, setting

$u=x^n\implies\mathrm du=nx^{n-1}\,\mathrm dx$

$\mathrm dv=e^x\,\mathrm dx\implies v=e^x$

gives

$\displaystyle I(n)=x^ne^x-n\int x^{n-1}e^x\,\mathrm dx$

$I(n)=x^ne^x-nI(n-1)$

This is called a power-reduction formula. We could try solving for $I(n)$ explicitly, but no need. $n=5$ is small enough to just expand $I(5)$ as much as we need to.