a rectangular prism has a volume of 10 cubic units. If the length width and height of the prism are all each made 3 times as lon
1 answer:
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Answer:
The rate of change of temperature is 1.29 degree Celsius per second.
Step-by-step explanation:
We are given the following information in the question:
The temperature at a point (x, y) is T(x, y), measured in degrees Celsius where x and y are measured in centimeters.
We have to find the rate at which the temperature is rising on the bug's path after 14 seconds.
At t = 14 seconds, we have,
To find rate of change of temperature, we differentiate,
Thus, the rate of change of temperature is 1.29 degree Celsius per second.
Answer:
The coordinates of B is (3, - 5)
Step-by-step explanation:
A(6, 1)
C(2, -7)
Coordinates of point B such that AB = 1/3 × BC
Hence we have;
Therefore BC = 3/4 × AC
Hence, AB = 1/3 × BC = 1/3 × 3/4 × AC = 1/4 × AC
AC = √((6 - 2)² + (1 - (-7))²) = √(16 + 64) = √80 = 4·√5
AB = 1/4 × 4·√5 = √5
Therefore;
AB² = (x - 6)² + (y - 1)² = 5
Slope = (1 - (-7))/(6 - 2) = 2
Hence the y coordinate of B = -7 + sin(tan⁻¹(2)) ×√5 = -5
The x coordinate of B = 2 + cos(tan⁻¹(2)) ×√5 = 3
The coordinates of B = (3, - 5)