Answer:
dt/dx = -0.373702
dt/dy = -1.121107
Explanation:
Given data
T(x, y) = 54/(7 + x² + y²)
to find out
rate of change of temperature with respect to distance
solution
we know function
T(x, y) = 54 /( 7 + x² + y²)
so derivative it x and y direction i.e
dt/dx = -54× 2x / (7 +x² + y²)² .........................1
dt/dy = -54× 2y / (7 + x² + y²)² .........................2
now put the value point (1,3) as x = 1 and y = 3 in equation 1 and 2
dt/dx = -54× 2(1) / (7 +(1)² + (3)²)²
dt/dx = -0.373702
and
dt/dy = -54× 2(3) / (7 + (1)² + (3)²)²
dt/dy = -1.121107
On question 30, that is a displacement- time graph (DT). On this type of graph the gradient is equal to the velocity. B has the steepest gradient, then A and finally C
Now velocity is a vector quantity so it has a direction and speed ( speed doesn't have a fixed direction.)
on the DT graph im going to assume that movement B is a positive velocity with A and C being negative.
So by ranking these: A is the most negative, C is the least negative and B has to be the greatest as it is the only positive velocity.
Q31, The same type of graph is present, by looking at the gradients we can rank the largest and smallest velocities- speeds in the case of the question.
i'll skip my working out as its the same as before:
C, B, A and then D
the same idea as on Q30 applies to Q31 part b,
D,C,B then A
I’m so sorry, I need more information. Good luck and I’m sorry I couldn’t help you :(
Answer:
the time at which it passes through the equilibrum position is:
t = 0.1 second
Explanation:
given
w= 4pounds
k(spring constant) = 2lb/ft
g(gravitational constant) = 10m/s² = 32ft/s²
β(initial point above equilibrum) = 1
velocity = 14ft/s
attached is an image showing the calculations, because some of the parameters aren't convenient to type.
Answer:
8962.5 N
Explanation:
From fundamental kinematics equations, acceleration, a is given by 
where v is final velocity, u is initial velocity and t is time
We also know that force is a product of mass and acceleration of an object and substituting in the formula F=ma we obtain
where m is the mass of the body
Therefore, the force is 8962.5 N
