Answer:
a. -216, 0 real roots
Step-by-step explanation:
The discriminant of ...
ax² + bx + c = 0
is ...
d = b² -4ac
When we put your equation into the standard form shown above, we get ...
7n² +8n +10 = 0
Then we can identify a=7, b=8, c=10. The discriminant is then ...
d = 8² - 4·7·10 = 64 -280 = -216
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The interpretation of the discriminant is ...
- < 0; no real roots (2 complex roots)
- = 0; one real root (multiplicity 2)
- > 0; 2 real roots
Your discriminant is -216, so there are 0 real roots.
124.8 ( money found ) ÷ 2 (gbe & his friend) = 62.4
Answer:
decreasing at 390 miles per hour
Step-by-step explanation:
Airplane A's distance in miles to the airport can be written as ...
a = 30 -250t . . . . . where t is in hours
Likewise, airplane B's distance to the airport can be written as ...
b = 40 -300t
The distance (d) between the airplanes can be found using the Pythagorean theorem:
d^2 = a^2 + b^2
Differentiating with respect to time, we have ...
2d·d' = 2a·a' +2b·b'
d' = (a·a' +b·b')/d
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To find a numerical value of this, we need to find the values of its variables at t=0.
a = 30 -250·0 = 30
a' = -250
b = 40 -300·0 = 40
b' = -300
d = √(a²+b²) = √(900+1600) = 50
Then ...
d' = (30(-250) +40(-300))/50 = -19500/50 = -390
The distance between the airplanes is decreasing at 390 miles per hour.
