Answer:
The measure of arc SQ is 95° ⇒ (1)
Step-by-step explanation:
- The measure of any circle is 360°
- The measure of the subtended arc to an inscribed angle is twice the measure of this angle
In the given circle
∵ S lies on the circumference of the circle
∴ ∠QSR is an inscribed angle
∵ ∠QSR is subtended by arc QR
→ By using the 2nd rule above
∴ m arc QR = 2 × m∠QSR
∵ m∠QSR = 95°
∴ m arc QR = 2 × 95
∴ m arc QR = 190°
→ By using the 1st rule above
∵ m of the circle = m arc QR + m arc SQ + m arc SR
∵ m arc SR = 75° and m arc QR = 190°
→ Substitute them in the equation above
∴ 360 = 190 + m arc SQ + 75
→ Add the like term in the right side
∴ 360 = 265 + m arc QS
→ Subtract 265 from both sides
∵ 360 - 265 = 265 - 265 + m arc SQ
∴ 95° = m arc SQ
∴ The measure of arc SQ is 95°
Answer:
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Step-by-step explanation:
HOPE it HELPS
You never told us how much money he has
Answer:
a) see the plots below
b) f(x) is exponential; g(x) is linear (see below for explanation)
c) the function values are never equal
Step-by-step explanation:
a) a graph of the two function values is attached
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b) Adjacent values of f(x) have a common ratio of 3, so f(x) is exponential (with a base of 3). Adjacent values of g(x) have a common difference of 2, so g(x) is linear (with a slope of 2).
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c) At x ≥ 1, the slope of f(x) is greater than the slope of g(x), and the value of f(x) is greater than the value of g(x), so the curves can never cross for x > 1. Similarly, for x ≤ 0, the slope of f(x) is less than the slope of g(x). Once again, f(0) is greater than g(0), so the curves can never cross.
In the region between x=0 and x=1, f(x) remains greater than g(x). The smallest difference is about 0.73, near x = 0.545, where the slopes of the two functions are equal.
Answer:
The dimensions of the can that will minimize the cost are a Radius of 3.17cm and a Height of 12.67cm.
Step-by-step explanation:
Volume of the Cylinder=400 cm³
Volume of a Cylinder=πr²h
Therefore: πr²h=400

Total Surface Area of a Cylinder=2πr²+2πrh
Cost of the materials for the Top and Bottom=0.06 cents per square centimeter
Cost of the materials for the sides=0.03 cents per square centimeter
Cost of the Cylinder=0.06(2πr²)+0.03(2πrh)
C=0.12πr²+0.06πrh
Recall: 
Therefore:



The minimum cost occurs when the derivative of the Cost =0.






r=3.17 cm
Recall that:


h=12.67cm
The dimensions of the can that will minimize the cost are a Radius of 3.17cm and a Height of 12.67cm.