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IrinaK [193]
2 years ago
7

The diameter of a circle is 8 inches. What is the area? 8 pi iThe diameter of a circle is 8 inches. What is the area? 8 pi inche

s squared 16 pi inches squared 32 pi inches squared 64 pi inches squarednches squared 16 pi inches squared 32 pi inches squared 64 pi inches squared
Mathematics
2 answers:
Aleksandr [31]2 years ago
9 0

Answer:

16pi inches squared is the answer

Step-by-step explanation:

nlexa [21]2 years ago
5 0

16 say I'll but is2 2+ what know even don't i

A

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Archy [21]

(a) If the particle's position (measured with some unit) at time <em>t</em> is given by <em>s(t)</em>, where

s(t) = \dfrac{5t}{t^2+11}\,\mathrm{units}

then the velocity at time <em>t</em>, <em>v(t)</em>, is given by the derivative of <em>s(t)</em>,

v(t) = \dfrac{\mathrm ds}{\mathrm dt} = \dfrac{5(t^2+11)-5t(2t)}{(t^2+11)^2} = \boxed{\dfrac{-5t^2+55}{(t^2+11)^2}\,\dfrac{\rm units}{\rm s}}

(b) The velocity after 3 seconds is

v(3) = \dfrac{-5\cdot3^2+55}{(3^2+11)^2} = \dfrac{1}{40}\dfrac{\rm units}{\rm s} = \boxed{0.025\dfrac{\rm units}{\rm s}}

(c) The particle is at rest when its velocity is zero:

\dfrac{-5t^2+55}{(t^2+11)^2} = 0 \implies -5t^2+55 = 0 \implies t^2 = 11 \implies t=\pm\sqrt{11}\,\mathrm s \imples t \approx \boxed{3.317\,\mathrm s}

(d) The particle is moving in the positive direction when its position is increasing, or equivalently when its velocity is positive:

\dfrac{-5t^2+55}{(t^2+11)^2} > 0 \implies -5t^2+55>0 \implies -5t^2>-55 \implies t^2 < 11 \implies |t|

In interval notation, this happens for <em>t</em> in the interval (0, √11) or approximately (0, 3.317) s.

(e) The total distance traveled is given by the definite integral,

\displaystyle \int_0^8 |v(t)|\,\mathrm dt

By definition of absolute value, we have

|v(t)| = \begin{cases}v(t) & \text{if }v(t)\ge0 \\ -v(t) & \text{if }v(t)

In part (d), we've shown that <em>v(t)</em> > 0 when -√11 < <em>t</em> < √11, so we split up the integral at <em>t</em> = √11 as

\displaystyle \int_0^8 |v(t)|\,\mathrm dt = \int_0^{\sqrt{11}}v(t)\,\mathrm dt - \int_{\sqrt{11}}^8 v(t)\,\mathrm dt

and by the fundamental theorem of calculus, since we know <em>v(t)</em> is the derivative of <em>s(t)</em>, this reduces to

s(\sqrt{11})-s(0) - s(8) + s(\sqrt{11)) = 2s(\sqrt{11})-s(0)-s(8) = \dfrac5{\sqrt{11}}-0 - \dfrac8{15} \approx 0.974\,\mathrm{units}

7 0
2 years ago
Tam has picked up 5 different books that interest
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Answer:

ujn uzun g ne bu bu http TV fy ve g CD ve de c TT vcxcxc TR TRT TT ttgrsxfgzfggfxvzgrstgygfdfdzvsdcvzdcgz TR

4 0
2 years ago
Read 2 more answers
Anthony bought an 8-foot board. He cut off 3/4 of the board to build a shelf and gave 1/3 of the rest to his brother for an art
AleksAgata [21]
I’m pretty sure the answer is 8 inches, mark as brainleist pls :)
6 0
2 years ago
What are the names of three planes that contain Point G ​
belka [17]

Answer:

Points L, J, and K are collinear.

Step-by-step explanation:

brinlest plz

8 0
2 years ago
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A triangle has one side that measures 5 ft, one side that measures 6 ft, and one side that measures 9 ft.
pochemuha

Area= 14.142

Perimeter=20

Height=3.14

5 0
2 years ago
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