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2 years ago

If f(x) = 12 +6, find f(-10) a. -16 b. -4 c. 4 d. 16

Mathematics

1 answer:

MAXImum [283]2 years ago

6 0

Answer:

Step-by-step explanation:

put f of x in to the x spot

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Step-by-step explanation:

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A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is given by a(t) = 6cos(t). At

Rom4ik [11]

a. By the fundamental theorem of calculus, the velocity function is

$v(t)=v(0)+\displaystyle\int_0^ta(u)\,\mathrm du$

The particle starts at rest, so $v(0)=0$ , and we have

$v(t)=\displaystyle\int_0^t6\cos u\,\mathrm du=6\sin u\bigg|_0^t=6\sin t$

Then the position function is

$x(t)=\displaystyle x(0)+\int_0^tv(u)\,\mathrm du$

with $x(0)=6$ , so

$x(t)=6+\displaystyle\int_0^t6\sin u\,\mathrm du=6-6\cos u\bigg|_0^t=12-6\cos t$

b. The particle is at rest whenever $v(t)=0$ ; this happens for

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2 years ago

Suppose you are covering your desk (shape below) with paper and want to know how many square inches of paper you need.

zavuch27 [327]

Answer:

a. Divide the figure into two rectangles, find the area of each rectangle and add them (See the picture attached).

b. $279\ in^2$

c. The total area of the figure is 279 square inches.

Step-by-step explanation:

a. Divide the figure into two rectangles (See the picture attached), then find the area of each rectangle and finally, add the areas calculated in order to get the total area of the given figure,

b. The area of a rectangle can be found using this formula:

$A=lw$

Where "l" is lenght and "w" is the width.

Area of Rectangle A

You can identify that:

$l_A=19\ in\\\\w_A=11\ in$

Then, its area is:

$A_A=(19\ in)(11\ in)=209\ in^2$

Area of Rectangle B

You can identify that:

$l_B=10\ in\\\\w_B=18\ in-11\ in=7\ in$

Then, its area is:

$A_B=(10\ in)(7\ in)=70\ in^2$

Total area

$A_T=209\ in^2+70\ in^2=279\ in^2$

c. The total area of the figure is 279 square inches.

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2 years ago