Answer:
<h2>Approximately 141 malt balls</h2>
Step-by-step explanation:
this problem is on the mensuration of solids shapes.
first we need to calculate the volume of the rectangular prism
volume of prsim= l*b*h
given that
length= 1.5 in
breath=2.5 in
hieght= 6 in
volume= 1.5*2.5*6
volume=22.5 in^3
secondly we then calculate the volume of a malt ball
given that
raduis r= 0.34
volume of sphere = 4/3πr^3
volume of sphere = 4/3*3.124*(0.34)^3
volume of sphere = 1.33*3.142*0.039
volume of sphere = 0.16 in^3
now we can calculate the amount of sphere that can fit into the prism as
= volume of prism/volume of sphere
= 22.5/0.16
=140.6
approximately 141 malt balls
Call the number : x
(1/3)x + 5 = x-6
=> (1/3)x + 5 - (x-6) = 0
=> (1/3)x + 5 - x + 6 = 0
Group (1/3)x with -x, 5 with 6
=> [(1/3)x - x] + (5+6) = 0
=> (-2/3)x + 11 = 0
=> (-2/3)x = -11
=> x = -11 : (-2/3) = 33/2.
Recheck : 1/3 x 33/2 + 5 = 33/6 + 5 = 63/6 = 21/2
33/2 - 21/2 = 12/2 = 6 (21/2 is 6 less than 33/2, satisfied.)
1. Plug in the 3 in all the x’s that are in the equation:
(3)2 + y2 = for x2 + y2
(3)2 - y2 = for x2 - y2
This would get you for both equations..
6 + y2 = for x2 + y2
6 - y2 = for x2 - y2
2. Now let’s plug in the value of y which is -4:
6 + (-4)2 = for x2 + y2
6 - (-4)2 = for x2 + y2
This would get you for both equations...
-2 = x2 + y2
14 = x2 - y2
Hope this helped, have an awesome day!
Answer:
Step-by-step explanation:
we know that
In the right triangle DEF
----> by TOA (opposite side divided by adjacent side)
substitute the given values
solve for EF
