Answer:0
Step-by-step explanation:0
It would take 1.5 seconds for the diver standing on a spring board 24 feet above the pool to hit the water.
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more numbers and variables.
Given that d represent the height of the diver above the water and t is the time in seconds.
d(t) = -16(2t - 3)(t + 1)
The diver hit the water at d(t) = 0, hence:
0 = -16(2t - 3)(t + 1)
2t - 3 = 0; or t + 1 = 0
t = 1.5 seconds
It would take 1.5 seconds for the diver standing on a spring board 24 feet above the pool to hit the water.
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Answer:
a. 235°
b. 146.03 km
c. 105 km
d. 193 km
Step-by-step explanation:
a. The bearing of E from A is given as 55°. The bearing in the opposite direction, from E to A, is this angle with 180° added:
bearing of A from E = 55° +180° = 235°
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b. The internal angle at E is the difference between the external angle at C and the internal angle at A:
∠E = 134° -55° = 79°
The law of sines tells you ...
CE/sin(∠A) = CA/sin(∠E)
CE = CA(sin(∠A)/sin(∠E)) = (175 km)·sin(55°)/sin(79°) ≈ 146.03 km
CE ≈ 146 km
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c. The internal angle at C is the supplement of the external angle, so is ...
∠C = 180° -134° = 46°
The distance PE is opposite that angle, and CE is the hypotenuse of the right triangle CPE. The sine trig relation is helpful here:
Sin = Opposite/Hypotenuse
sin(46°) = PE/CE
PE = CE·sin(46°) = 146.03 km·sin(46°) ≈ 105.05 km
PE ≈ 105 km
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d. DE can be found from the law of cosines:
DE² = DC² +CE² -2·DC·CE·cos(134°)
DE² = 60² +146.03² -2(60)(146.03)cos(134°) ≈ 37099.43
DE = √37099.43 ≈ 192.6 . . . km
DE is about 193 km
Answer:
0.1057
Step-by-step explanation:
We solve using z score formula.
z = (x-μ)/σ, where
x is the raw score = 57mm
μ is the population mean = 52mm
σ is the population standard deviation = 4mm
z = 57 - 52/4
z = 1.25
Probability value from Z-Table:
P(x<57) = 0.89435
P(x>57) = 1 - P(x<57)
1 - 0.89435
= 0.10565
Approximately = 0.1057
The probability that the diameter of a selected bearing is greater than 57 millimeters is 0.1057
