We are given with:
Average height of plants to be at least 73 inches
Three plants with heights of
70, 71, 72
The inequality that can be used to determine the possible heights of the fourth plant is:
(70 + 71 + 72 + x) / 4 ≥ 73
Solving for x
x ≥ 79
(a) Yes all six trig functions exist for this point in quadrant III. The only time you'll run into problems is when either x = 0 or y = 0, due to division by zero errors. For instance, if x = 0, then tan(t) = sin(t)/cos(t) will have cos(t) = 0, as x = cos(t). you cannot have zero in the denominator. Since neither coordinate is zero, we don't have such problems.
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(b) The following functions are positive in quadrant III:
tangent, cotangent
The following functions are negative in quadrant III
cosine, sine, secant, cosecant
A short explanation is that x = cos(t) and y = sin(t). The x and y coordinates are negative in quadrant III, so both sine and cosine are negative. Their reciprocal functions secant and cosecant are negative here as well. Combining sine and cosine to get tan = sin/cos, we see that the negatives cancel which is why tangent is positive here. Cotangent is also positive for similar reasons.
Given equations are;<span>
2a + 3b = -1 ..................equation 1
3a + 5b = -2 ....................equation 2</span>
Now multiply equation 1 with (-3)
The equation will be;
-6a -9b = 3 …………………..equation 3
Now multiply equation 2 with (2)
The equation will be;
6a + 10b = -4 ……………..equation 4
Now add equation 3 and equation 4
-6a – 9b = 3
<span>6a + 10b = -4</span>
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0a + b = -1
b = -1
Now put the value of b in equation 1
2a + 3(-1) = -1
2a -3 = -1
2a = -1+3
2a = 2
a=1
Thus the solution is (a,b) = (1,-1)
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Answer:
Step-by-step explanation:
We are given that
Differentiate w.r.t x
By using formula
Hence, the derivative of function
V=w•h•l
w=2 1/2=5/2=2.5 m
h=1 3/4=7/4=1.75 m
l= 2 1/4=9/4=2.25 m
V= 2.5 •1.75 •2.25
V=9.84 m^3
