(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.
2/8 is greater because 5/8 is lesss
Answer:
a. $1360
b. $8.50 per hour
Step-by-step explanation:
a.
5 couches upholstered, each 105 equals 5 * 105 = 525
6 loveseats upholstered, each 85 equals 6 * 85 = 510
5 chairs upholstered, each 65 equals 5 * 65 = 325
Hence, total pay = 525 + 510 + 325 = $1360
b.
To find hourly rate, we take total amount and divide it by number of hours.
1360/160 = $8.5 per hour
Hence, hourly rate is $8.50 per hour
Answer:
14
Step-by-step explanation:
A = 1/2 BH
B = 5H
A = 490
490 = 5/2 * H^2
H = 14
Answer:
6c^2(-40 + 5c^3 + 3c^2)
Step-by-step explanation:
These three terms have the common factor c^2. Thus:
-240c^2+ 30c^5+ 18c^4 = c^2(-240+ 30c^3+ 18c^2).
Recognizing that 6 is common to all three terms inside the parentheses, we get:
6c^2(-40 + 5c^3 + 3c^2) This is as far as factoring of this expression can be taken.
