Answer:
87°
Step-by-step explanation:
If a quadrilateral is inscribed in a circle, then opposite angles are supplementary. That means that z + 93 = 180 and z = 87°
Answer:
It will take 1 hour and 12 minutes for the two trains to be 192 miles apart
Step-by-step explanation:
The total distance between the two trains is the distance traveled by both trains. The distance traveled by the eastbound train is 85 mph * elapsed time and the distance traveled by the westbound train is 75 * elapsed time.
The combined formula is distance traveled = speed of first train * elapsed time + speed of second train * elapsed time.
Since the elapsed time is equal for both trains then the formula is modified as distance traveled = (speed of first train + speed of second train) * elapsed time.
Solving for the elapsed time
distance traveled = (speed of first train + speed of second train) * elapsed time
192 miles = (85mph + 75 mph) * elapsed time
192 miles = 160 mph * elapsed time
elapsed time = 192 miles / 160 mph
elapsed time = 1.2 hours
elapsed time = 1 hour and 12 minutes
It will take 1 hour and 12 minutes for the two trains to be 192 miles apart.
Use the binomial expansions of x - 1/x :
x - 1/x = 4
(x - 1/x)² = x² - 2 + 1/x² = 16
===> x² + 1/x² = 14
(x - 1/x)³ = x³ - 3x + 3/x - 1/x³
===> x³ - 1/x³ = 3 (x - 1/x) = 12
(x - 1/x)⁴ = x⁴ - 4x² + 6 - 4/x² + 1/x⁴
===> x⁴ + 1/x⁴ = 4 (x² + 1/x²) - 6 = 50
0.74 is less than 0.79 0.74<0.79
Answer:
YES
Step-by-step explanation:
-3 times -4 = 12
12 + 2 = 14
14 < 15