(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.
Answer:
8/11
Step-by-step explanation:
2 2/3 = 8/3
8/3 x 3/11 = 24/33
24/33 = 8/11
A. axis of symmetry: vertex: (–0.5, –0.5)
Answer: 35 sweets
Step-by-step explanation:
2:5:2= 9
peter= 2/9 x a= 14
it then turns to
9/2 x 14= 63
so bridget will get:
5/9 x 63
35 sweets
Step-by-step explanation:
Although I cannot find any model or solver, we can proceed to model the optimization problem from the information given.
the problem is to maximize profit.
let desk be x
and chairs be y
400x+250y=P (maximize)
4x+3y<2000 (constraints)
according to restrictions y=2x
let us substitute y=2x in the constraints we have
4x+3(2x)<2000
4x+6x<2000
10x<2000
x<200
so with restriction, if the desk is 200 then chairs should be at least 2 times the desk
y=2x
y=200*2
y=400
we now have to substitute x=200 and y=400 in the expression for profit maximization we have
400x+250y=P (maximize)
80000+100000=P
180000=P
P=$180,000
the profit is $180,000
