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joja [24]
3 years ago
12

What is the total surface area of the following cylinder?

Mathematics
1 answer:
lilavasa [31]3 years ago
6 0

Answer: 791.28cm^2

Step-by-step explanation:

A=2\pi rh+2\pi r^2

We have the diameter, to calculate the radius, divide by 2.

12/2=6cm

height: 15cm

Plug in the formula.

A=2(3.14)(6cm)(15cm)+2(3.14)(6cm)^2\\A=565.20cm^2+226.08cm^2\\A=791.28cm^2

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A flat circular plate has the shape of the region x squared plus y squared less than or equals 1x2+y2≤1. the​ plate, including t
vredina [299]

You're looking for the extreme values of x^2+3y^2+13x subject to the constraint x^2+y^2\le1.

The target function has partial derivatives (set equal to 0)

\dfrac{\partial(x^2+3y^2+13x)}{\partial x}=2x+13=0\implies x=-\dfrac{13}2

\dfrac{\partial(x^2+3y^2+13x)}{\partial y}=6y=0\implies y=0

so there is only one critical point at \left(-\dfrac{13}2,0\right). But this point does not fall in the region x^2+y^2\le1. There are no extreme values in the region of interest, so we check the boundary.

Parameterize the boundary of x^2+y^2\le1 by

x=\cos u

y=\sin u

with 0\le u. Then t(x,y) can be considered a function of u alone:

t(x,y)=t(\cos u,\sin u)=T(u)

T(u)=\cos^2u+3\sin^2u+13\cos u

T(u)=3+13\cos u-2\cos^2u

T(u) has critical points where T'(u)=0:

T'(u)=-13\sin u+4\sin u\cos u=\sin u(4\cos u-13)=0

(1)\quad\sin u=0\implies u=0,u=\pi

(2)\quad4\cos u-13=0\implies\cos u=\dfrac{13}4

but |\cos u|\le1 for all u, so this case yields nothing important.

At these critical points, we have temperatures of

T(0)=14

T(\pi)=-12

so the plate is hottest at (1, 0) with a temperature of 14 (degrees?) and coldest at (-1, 0) with a temp of -12.

4 0
2 years ago
How to rewrite decimals to fractions before adding
torisob [31]
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7 0
3 years ago
Read 2 more answers
Write the equation of the linear relationship in slope-intercept form, using decimals as needed.
d1i1m1o1n [39]
Ok so look for the change between x and y.
7 0
3 years ago
Read 2 more answers
Which one is at better value and show work
kogti [31]
360/0.96 or 510/1.44

360/0.96

0.96/360

.........3.76
_________
96/36000
......288
___________
.........720
.........672
_________
...........580
............576
_________
.................4

___________
510/1.44

............354
____________
144/ 51000
.........432
________
780
720
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600
576
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24

360g at $0.96 is best deal
4 0
3 years ago
How much money should be invested in an account that earns 8% interest compounded quarterly to yield $10,000 in 4 years? (Round
sweet [91]

Answer:

757,576cents

Step-by-step explanation:

Given

Amount = $10000

Time = 4years

Rate = 8%

n = 1/4 year (compounded quarterly

Using the formula to get the principal

A = P(1+r/n)^nt

10000 = P(1+0.08/0.25)^4(1/4)

10000 = P(1+0.32)

10000= 1.32P

P = 10000/1.32

P = 7575.76

Hence he suppose to invest $7575.76 which is equivalent to 7575.76×100 cents i.e 757,576cents

4 0
2 years ago
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