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bixtya [17]
3 years ago
12

18,31, 44.. Find the 84th term of the arithmetic sequence

Mathematics
1 answer:
Lilit [14]3 years ago
3 0
The answer is 1092
:)
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A graphing calculator is recommended. A grain silo consists of a cylindrical main section and a hemispherical roof. If the total
eimsori [14]

Answer:

11.28 ft

Step-by-step explanation:

The volume of a cylinder can be written as;

Volume V1 = πr^2 h

The volume of an hemisphere can be written as;

Volume V2 = (2/3)πr^3

The total volume of the silo is;

V = V1 + V2

V = πr^2 h + (2/3)πr^3

Given;

Volume of silo V= 15000 ft^3

Height of cylinder part h = 30 ft

Substituting the values;

V = πr^2 h + (2/3)πr^3

15000 = 30πr^2 + (2/3)πr^3

15000/π = 30r^2 + (2/3)r^3

2r^3 + 90r^2 - (15000×3/π) = 0

Solving the equation, we have;

r = 11.28 ft or -15.61 ft or -40.67 ft

Since the radius cannot be negative;

Radius r = 11.28 ft

3 0
3 years ago
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
3 years ago
two runners are saving money to attend a marrathon. the first runner has $112 in savings, received a $45 gift from a friend, and
Arturiano [62]
112+45+25m=50+60m
Both sides should be qual to each other once they both hit a certain number of months. I hope this helps!
5 0
3 years ago
Read 2 more answers
Y = 7/2x + 10 y = -7/2x - 1/10 these lines have perpendicular slopes. True or false?
forsale [732]

Answer: This is False because they don't go together and it doesn't make sense.

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
The vertices of a triangle are located at X(-2,-1), Y(2,5) and Z(4,3). What is the perimeter of this triangle?
Lana71 [14]
If you plot the points you will find you have to use the distance formula. Pick out 2 pairs label them (x1,y1) (x2,y2) then plug it into the distance formula. The repeat for the other sides. So you should get (2,5) (4,3) plug into distance formula what is get it distance between those two points, then (4,3) (-2,-1) plug into distance formula to get an answer, lastly (-2,-1) (2,5) plug in. Now you have three answers add all together and here is your perimeter of a triangle.
3 0
3 years ago
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