Answer:
x = (-5 ± 2√10) / 3
Step-by-step explanation:
5 − 10x − 3x² = 0
Write in standard form:
-3x² − 10x + 5 = 0
Solve with quadratic formula:
x = [ -b ± √(b² − 4ac) ] / 2a
x = [ -(-10) ± √((-10)² − 4(-3)(5)) ] / 2(-3)
x = [ 10 ± √(100 + 60) ] / -6
x = (10 ± 4√10) / -6
x = (-5 ± 2√10) / 3
D2x/dt2=-g (which we'll approximate as a constant -32ft/s^2)
d2x/dt2=-32 integrating we get:
dx/dt=-32t+C, where C is the initial velocity which we are told is 128ft/s so
dx/dt=-32t+128, integrating again we get:
h(t)=-16t^2+128t+C, where C is the initial height of the object..which we are told is 136 ft so
h(t)=-16t^2+128t+136 if we factor the first two terms we get:
h=-16(t^2-8t)+136
Answer:
b = -16.77
Step-by-step explanation:
We could get a quick estimate from b/8 = -2: b is approximately -16.
For an exact answer, multiply both sides by 7.8: b = -16.77
Plug in x = -4 and then use PEMDAS to simplify
f(x) = 5(3-x)^2
f(x) = 5*(3-x)^2
f(-4) = 5*(3-(-4))^2 ... replace every x with -4
f(-4) = 5*(3+4)^2
f(-4) = 5*(7)^2
f(-4) = 5*(49)
f(-4) = 245
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Final Answer: 245