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Note that

When n = 1 to n = 3....the sum   = (1) *3  = 3

When n =  4 to n = 8, the sum  = (2)* 5 =  10

When n = 9 to n =15, the sum  = (3) * 7  =  21

So....generalizing this we have the sum

(1)*3 + (2)*5 + (3)*7  + ( 4)*9 +(5)*(11)  + (6)*13 + (7)*15  + (8)*17 + (9)*19 +  10   =  625

= 1/2 ln(x+37)  = ln {(x^2-25)/(x+5)}

1/2 ln (x+37)= ln (x-5)

ln (x+37)^1/2 =ln(x-5)

sqrt (x+37 ) = x-5

x+37 = x^2 -10x+25

x^2 -11x-12   = 0

(x-12)(x+1) = 0      x = 12    or -1  (throw out....would result in  ln  of negative number)  

When x  = -3,  then f(-3)  = - (-3)^2 + 4   =   - 9 + 4    =  -5

And from the table, when x  = - 3, then g(-3)  = 1

So  when x = -3, 

f(-3) < g(-3)

Sumfor(n, 1, 100, floor(sqrt(n)) = 625

C. When the pile is changing at a rate of 1.5 feet per minute, how tall is the pile?

dh/ dt  =  4pi h^2

1.5 =  4 pi h^2

(1/5) / ( 4pi)  = h^2

√[ 1.5 / (4 pi) ]  = h ≈   .345 ft 

B. When the  pile is 5 feet high, how fast is the height of the  pile changing

dv / dh  = 4pi h^2

So......

dV / dt   =  dV/ dh * dh /dt

8 ft^3   = 4pi h^2 * dh/dt

8 ft^3  = 4pi (5ft)^2  * dh/dt

8 ft^3 = 100pi ft^2 * dh /dt

8 / [ 100pi ]  = dh/dt

.08/pi  ft /min  = dh/dt

No figure is shown.....

A.  

v(t)  = 4t(t - 7) (t - 1)     simplify

v(t)  = 4t  ( t^2 - 8t + 7)

v(t)  =  4t^3 - 32t^2 + 28t

The acceleration at any time  is the derivative of this  = v'(t)  = 12t^2 - 64t + 28

B.  Set the derivative to 0  and solve for t

12t^2 - 64t + 28  = 0        divide through by 4

3t^2 - 16t + 7     =  0         

The minimum acceleration on [0,3 ] occurs at  t  =    (16)/ (2 * 3)  =  16/6 =  8/3  sec

And the minimum acceleration is   3(8/3)^2  - 16(8/3) + 7   =  -43/3

C. See the graph here :  https://www.desmos.com/calculator/70cdiunnem

The max velocity on [0, 2 ] occurs at about .481 s   and is  ≈ 6.51

Grain is falling into from a conveyor into a conical pile at a rate of 8 cubic feet per minute. The diameter of the pile is four times the height of the pile.

A. Write an equation for the volume of the pile in terms of the height.

B. When the pile is 5 feet high, how has is the height of the pile changing?

C. When the pile is changing at a rate of 1.5 cubic feet per minute, how tall is the pile????

 y-2x  = -3.5  

-2y+x = -14     or   x = 2y-14     Use this value of x to sub into first equation

y - 2(2y-14) = - 3.5

y - 4y + 28 = - 3.5

-3y = -31.5

y = 10.5                     Substitute this value of y into one of th equations to find x

x = 2y-14

x = 2(10.5) -14

x = 7

0.33333333=33.333333%

but

0.33333333....= 33 1/3%

33.3333 %

MS.....I told you it was A     the question says 'choose all that apply'

A   C   D      is the answer......You should look at the diagram and UNDERSTAND why.....just pasting your answer does you no good whatsoever...you are not learning anything and will soon  (if not already) be in over your head.....

A toy is in the form of a cone mounted on a hemisphere the diameter of the base of the cone is 18 cm and its height is 12 centimetre calculate the surface area of toy​

answer is D ?

Yes !  

the answer is B ?

See N on the number line.......close to -3       between  -3 and -4......which answer fits?

Trig is a shortcut for "Trigonometry"

Trigonometry is a branch of mathematics which mostly deals with triangles. You need trigonometry for any further studies in mathematics (E.g. calculus) 

I assume you are referring to basic trigonometry, so, the basic trigonometry deals with right angle triangles as well as general triangles(Triangles not right), but let's start with right angle triangle

We have 3 main functions called trigonometric functions

First: In a right angle triangle, we already know that the side opposite (I.e. in front of the 90-degree angle) is called the hypotenuse. Now pick any other angle from this triangle let's say the upper one (Above the 90-degree angle) we don't know its value (assume) so let's label it \(\theta \) (theta, greek letter usually used for unknown angles). Now the side in front of this angle is called "Opposite side" of this angle, the side next to it (Other than the hypotenuse of course) is called adjacent, with that known and we know the length of the 3 or 2 sides, we can use the following functions to find the value of this angle:

\(sin(\theta) =\frac{opposite}{hypotenuse}\)

\(cos(\theta )=\frac{adjacent}{hypotenuse}\)

\(tan(\theta )=\frac{opposite}{adjacent}\)

Where \(\theta \) is the angle you are trying to find the value of or that you already have.

These laws apply only in right-angle triangles.

I already told you it is A      What about  C   or   D  ?

Bingo !

It would be  A

Triangle ABC is a right angled triangle,AB is perpendicular to BC,E is a point on BC,D is a point on AB ,intersection of AE and CD is F, AD=10,DB=8 BE=6,EC=10, Then find the area of quadrilateral DBEF.

It is BETWEEN  -1 and -2           NOT between   0 and -1 .......

is it A or D ?