600,000 in scientific notation is 6 x 10^5
Answer:
A) dV/dt = the rate of change of the given volume of water in the tank with respect to the time, t.
dH/dt = the rate of change of the height of the water in the tank with respect to the time
B) dV/dt is positive
C) dH/dt is positive
Step-by-step explanation:
We are given that;
V(t) is the volume of water in the tank and H(t) is the height of the water level at time t. Thus;
A) dV/dt = the rate of change of the given volume of water in the tank with respect to the time, t.
dH/dt = the rate of change of the height of the water in the tank with respect to the time
B) When the tank is one-fourth full, dV/dt is positive because the volume water in the tank is increasing with time.
C) when the tank is one-fourth full, dH/dt is positive because the height has increased from zero level to 0.25 times the height of the tank. Thus the height is increasing with time.
Answer:
Give me the equation and I'll tell you
Step-by-step explanation:
Let a, b, c be the measures of the interior angles and x, y, z be the measures of the exterior angles of the triangle. Where x and adjacent to a, y is adjacent to b and z is adjacent to c.
By interior angle sum postulate of a triangle:
a + b + c = 180°... (1)
Therefore, by remote interior angle theorem:
x = b + c.... (2)
y = a + c..... (3)
z = a + b.... (4)
Adding equations (2), (3) & (4)
x + y + z = b + c + a + c + a + b
x + y + z = 2a + 2b + 2c
x + y + z = 2(a + b + c)... (5)
From equations (1) & (5)
Thus, the sum of exterior angles so formed is equal to four right angles.
Proved.
Answer: 33
To maximize the length of the third side, which I'll call x, it needs to be the longest side.
So by the triangle inequality theorem, 19+15>x, meaning the maximum whole number value of x is 33.