Answer: There are several information's of immense importance already given in the question. Let us write them down first.
Diameter of the cylinder = 6 inches
Then
Radius of the cylinder = 3 inches.
Height of the cylinder = 3 * radius
= 3 * 3
= 9 inches
Volume of the cylinder = (pi) * (Radius)^2 * Height
= 3.14 * (3)^2 * 9
= 3.14 * 9 * 9
= 254.34 cubic inches
we have
f(x)
and
g(x)=-2f(x)+5
so
step 1
First transformation
Reflection about the x-axis
so
f(x) -----> -f(x)
step 2
Second transformation
A vertical dilation with a scale factor of 2
so
-f(x) ------> -2f(x)
step 3
Third transformation
A translation of 5 units up
so
-2f(x) -------> -2f(x)+5
Answer: 3
Step-by-step explanation:
The 3D vector consists of 3 axes, let's say x, y and z.
Now, a vector P lies in all of them.
So, the angle it makes with x axis is α
The angle it makes with y axis is β
The angle it makes with z axis is γ
So, to determine the Cartesian components or to resolve the vector into it's Cartesian components we need 3 angles with each axis.
Answer:
<em><u>A.10000</u></em>
<em><u>B.25 more trees must be planted</u></em>
Step-by-step explanation:
⇒Given:
- The intial average yield per acre
= 150
- The initial number of trees per acre
= 100
- For each additional tree over 100, the average yield per tree decreases by 1 i.e , if the number trees become 101 , the avg yield becomes 149.
- Total yield = (number of trees per acre)
(average yield per acre)
<em>A.</em>
⇒If the total trees per acre is doubled , which means :
total number of trees per acre 
= 
= 200
the yield will decrease by : -
⇒total yield = 
<em>B.</em>
⇒to maximize the yield ,
let's take the number of trees per acre to be 100+y ;
and thus the average yield per acre = 150 - y;
total yield = 
this is a quadratic equation. this can be rewritten as ,
⇒ 
In this equation , the total yield becomes maximum when y=25;
<u><em>⇒Thus the total number of trees per acre = 100+25 =125;</em></u>
B/ 4 oranges for $1.52 I think.
