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
Answer:
meters
Explanation:The question ask for the maximum value of the function f(t) which can be find by find the maxima of the function
The maxima of the function occurs when the slope is zero. i.e.
Hence the maxima occurs at t=1.63 seconds
The maximum value of f is
hence maximum height is found to be
meters
Answer:
Approximately .
Explanation:
The refractive index of the air is approximately .
Let denote the refractive index of the glass block, and let denote the angle of refraction in the glass. Let denote the angle at which the light enters the glass block from the air.
By Snell's Law:
.
Rearrange the Snell's Law equation to obtain:
.
Hence:
.
In other words, the angle of refraction in the glass would be approximately .
Answer:
25 m/s
Explanation:
Given that:
Initial speed, u = 4 m/s
Final velocity, V = 11 m/s
Time, t = 8 seconds
t2, = 16 seconds
Acceleration, a= (change in velocity) / time interval
a = (11 - 4) / 8
a = 7 / 8 = 0.875m/s²
Final velocity, v2 ;
Acceleration * t2
0.875 * 16 = 14
V2 = 14 m/s
Final speed : v + v2 = (11 + 14)m/s = 25m/s