The maximum value can be determined by taking the derivative of the function.
(dh/dt) [h(t)] = h'(x) = -9.8t + 6
Set h'(x) = 0 to find the critical point
-9.8t + 6 = 0
-9.8t = -6
t = 6/9.8
Plug the time back into the function to find the height.
h(6/9.8) = -4.9(6/9.8)^2 + 6(6/9.8) + .6
= 2.4
And I don't understand your second question.
I'm assuming your function is f(x) = -9^(x+1)
So we just have to plug in and see if the function is true.
1) -9^(0+1) = -9^1 = -9
YES
2) -9^(1+1) = -9^2 = -81
NO
3) -9^(-1+1) = -9^0 = -1
YES
Answer: Lattice parameter, a = (4R)/(√3)
Step-by-step explanation:
The typical arrangement of atoms in a unit cell of BCC is shown in the first attachment.
The second attachment shows how to obtain the value of the diagonal of the base of the unit cell.
If the diagonal of the base of the unit cell = x
(a^2) + (a^2) = (x^2)
x = a(√2)
Then, diagonal across the unit cell (a cube) makes a right angled triangle with one side of the unit cell & the diagonal on the base of the unit cell.
Let the diagonal across the cube be y
Pythagoras theorem,
(a^2) + ((a(√2))^2) = (y^2)
(a^2) + 2(a^2) = (y^2) = 3(a^2)
y = a√3
But the diagonal through the cube = 4R (evident from the image in the first attachment)
y = 4R = a√3
a = (4R)/(√3)
QED!!!
Answer:
7.2
Step-by-step explanation:
To reach point D from point C, you need to add 4 to the x-value of point C and take away 6 from the y-value. These numbers are the sides of the hypothetical triangle.
The Pythagorean Theorem states that
. If we plug the side lengths in for a and b, we get
. This can be simplified to
, or
. If we root both sides, we find that c is equal to
, which is slightly more than 7, at around 7.2.
This isnt something I can do... But draw and label a tape diagram that goes from 0 to 30.