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antilog  3.2

We have

log 3.2  = x     ⇒  x  ≈   .505

In exponential form we have

10^.505  =  3.2

b  =10

x  = .505

n  = N  = 3.2

can you explain why please, thanks

Thank you so much!

That's the trajectory.

Thank You, Cphill

11)Let ABCDEFGH be a rectangular prism, as shown, where AB = 2, AD = 3, and AE = 5. Find the volume of pyramid ACFH.

Ln N  =  3

In  exponential form, we have

e^3  =   N

b  =  e

x  = 3

n  = N  

antilog  ≈ 20.09

Since we can use any scale factor for the square that we desire, we can derive an algebraic solution

Let  A  = (0, 0)

B  =  (0, a)

C  =   (a, a)

D  = (a, 0)

E  =  (a/2, a)

F  = (a, a/2)

AB  = a

The slope  of AE  is  (a)  / ( a/2 - 0 )  =  a / (a/2)  =  2

The slope of BF  is  ( a - a/2)   / ( 0 - a)  =  -(1/2)a  / a  =  -1/2 

The equation  of  the line containing segment   AE  is    y  = 2x

The equation  of the line containing segment FB  y = (-1/2)x  + a

Set these equal  to find the x coordinate of G

2x  = (-1/2)x + a

(5/2)x  = a

x  = (2/5)a

And the y coordinate  is y  = 2[(2/5)a]  =  4/5a

So....G  =  (2/5 a, 4/5 a)

And DG  =  √ [ (2/5 a - a)^2  + (4/5 a)^2 ]  = √ [ ( 3/5 a)^2  + (4/5  a)^2 ] =

a√[ 3^2  + 4^2  ] / 5  =   a √25 / 5  = (5 / 5 )  a  = a   =  AB

C  =  [  2 + ( 5 -2)*3  ,  3 + (9 - 3)*3 ]  =  [ 2 + 9, 3 + 18 ]  =  ( 11, 21 )

You need 45 pancakes for that dog house

LOL  MUST BE!

10)Let ABCDE be a pyramid, where the base ABCD is a square of side length 10. The total surface area of pyramid ABCDE (including all five faces) is 260.
Let M, N, P, and Q be the midpoints of AE, BE, CE, and DE, respectively. Find the total surface area of frustum ABCDMNPQ.

This can be rearranged as (x+1)^2 = -2y^2/(y^2+5)

The right hand side is negative unless y is zero, whereas the left hand side is positive unless x = -1.

The only way to achieve equality is for both sides to be zero, which means the only ordered pair of real numbers to satisfy the equation is (x,y) = (-1,0)

9)Each of the eight edges of a regular square pyramid has length 2. The volume of the pyramid is V. Find V^2.

8)Three face diagonals of a rectangular prism have lengths sqrt19, sqrt23 and sqrt30. Find the length of its space diagonal.

I just wrote up a table for each of the possible startpoints, there are 10 of them, and then just worked out all the possible paths.

the ones that end in a multiple of 3 are

123           P(1,2,3) = \(\frac{1}{10}\times\frac{2}{3}\times\frac{2}{3}=\frac{4}{90} \)

343

456

543

656

676

789

876

989

9 10 9

 I have done the first one, work out the probs for all of them and add the probs together for your answer.

You need to check what I have done as well :)

y  = sin  ( x - 2pi)

This the sine graph  shifted to  the right by  2pi rads......however.....since the normal peiod is 2pi, it will not appear different from the normal sine graph

Here's the graph  :  https://www.desmos.com/calculator/z4edgadelv

y  = 2cos (x/4 + pi/2)

Write this as :

y  = 2cos(1/4) (x - 2pi)

This is the normal cosine graph with a period 4 times as long as normal, vertically stretched by a factor of 2  and with a phase shift of 2pi rads to the right

Here's  the parent graph and this one  on the same axis

https://www.desmos.com/calculator/u4qjyniuu7

h  = -16t^2  +  72t

The time that the ball is at the max height can be found as

-72 / [ 2 (-16) ]  =  -72 / -32  =  9/4 sec  = 2.25 sec

And the  max height is

-16(9/4)^2   +  72 (9/4)   =   81 ft

The ball wil fall back to the ground  at  2(9/4)  =  18/4  = 9/2 sec = 4.5 sec

So.....the domain   is  from 0 seconds to 4.5 seconds

And the range is from  0 ft  to   81 ft

Hre's a graph  :   https://www.desmos.com/calculator/i1dbl46fd9

7)A pyramid and a prism share the same base. The prism has 99 edges. How many faces does the pyramid have?

99 : 3 = 33

33 *2 = 66

6)Two cubes of volumes 8 and 27 are glued together at their faces to form a solid with the smallest possible surface area. What is the surface area of the resulting solid?

5)A rectangular prism has dimensions 8, 12, and 16. What is the length of its longest face diagonal?

C

c.y=2x

4)A right pyramid has a regular hexagon as a base. The slant height is 20, and the perimeter of its base is 10. What is the lateral surface area of the pyramid?