Part A.
We are given the total volume of the amount of sand she will want to fill
we are also given the shape and dimensions of the cylinders
Total volume of the sand = 1,000
Cylinder= radius 4 in, and height 8 in
the volume of a cylinder is V=πr^2h
We will solve for the volume of the cylinders
V=πr^2hV=π(4)^2*(10)
V = π (16) * (10)
V = π 160
The volume of the cylinders she wants to fill is 502.65 in^3
How many cylinders will she need
Well,
1000/502.65 <span>≈ 1.98
She will need two cylinder cans to fill with the 1,000 in^3 of sand
Part B.
To see if this is true, we find the half of the original cylinder's radius and height then solve for the volume and compare
</span>V=πr^2h
<span>The height and radius of the original cylinders were 4 r and 8h
we will find half of that which will be : 2 r and 4 h
Now solve for the volume </span>V=πr^2h
V=π(2)^2* (4)
V=π (4)*(4)
V = π 16
V ≈<span> 50.26 inches ^3
The volume of the original cylinders was </span>502.65 in^3 and the volume of the new cylinders is 50.26 in^3... Clearly the volume of the new cylinders is NOT half of the original. Sally is not correct!
<span>
Hope this helps :)
</span>
Answer:
Rectangular area
side a = 3 units
side b = 2.60 units
Step-by-step explanation: See annex
We have an equilateral triangle (3 equal sides, three equal inside angles)
side length = 6
∠ ABC = ∠BCA = ∠CAB = 60⁰
tan 60⁰ = sin 60⁰/cos 60⁰ = √3/2 / 1/2
tan 60⁰ = √3
From annex
tan ∠ ABC = √3 = b/x then b = √3 * x
and a = 6 - 2*x ( by symmetry)
Then
A = a*b
A(x) = ( 6 - 2*x ) * √3 *x
A(x) = 6*√3 *x - 2*√3 *x²
Taking derivatives on both sides of the equation we get:
A´(x) = 6*√3 - 4*√3 *x ⇒ A´(x) = 0 ⇒ 6*√3 - 4*√3 *x = 0
x = 6/4 ⇒ x = 1.5
then a = 6 - 2*x ⇒ a = 6 - 3 ⇒ a = 3 (units)
and b = √3*x = 1.5 *√3 = 2.60 units
We get a rectangle (almost a square)
He made $120.
You divide 1,320 by 22. That gives you 60. Then you times 60 by 2(which equals 120) because 60 represents the packets and he made 2 dollars per packet.
Mathematically the steps look like this:
1,320/22
=60
60(2) or 60 x 2
= 120
so $120
hope this helped!
Answer:
8x^3
Step-by-step explanation:
(2x)^3
=(2x)^3
=2x*2x*2x
=8x^3
Step-by-step explanation:
given
( x³ -64)/ x - 4
= (x³ - 4³) / x - 4
= (x - 4) ( x² + 4x + 16 ) / (x - 4)
( x- 4 ) will be cancelled out then
= x² + 4x + 16
