Answer:
Step-by-step explanation:
The given quadratic equation is
2x^2+3x-8 = 0
To find the roots of the equation. We will apply the general formula for quadratic equations
x = -b ± √b^2 - 4ac]/2a
from the equation,
a = 2
b = 3
c = -8
It becomes
x = [- 3 ± √3^2 - 4(2 × -8)]/2×2
x = - 3 ± √9 - 4(- 16)]/2×2
x = [- 3 ± √9 + 64]/2×2
x = [- 3 ± √73]/4
x = [- 3 ± 8.544]/4
x = (-3 + 8.544) /4 or x = (-3 - 8.544) / 4
x = 5.544/4 or - 11.544/4
x = 1.386 or x = - 2.886
The positive solution is 1.39 rounded up to the nearest hundredth
Answer:
2000 players will complete the game with a perfect score.
Step-by-step explanation:
The testing phase tells us that 
is the probability that a person will finish with a perfect score.
This means 1 out of 500 people will be able to finish with perfect score.
Now,
the game is given to 1,000,000 (1 million) people and how much do we expect to finish with perfect score?? Simple! It would be the of 1 million!
We do the calculation shown below:
So, 2000 players will complete the game with a perfect score.
Answer:
Step-by-step explanation:
Answer:
a) y-8 = (y₀-8) , b) 2y -5 = (2y₀-5)
Explanation:
To solve these equations the method of direct integration is the easiest.
a) the given equation is
dy / dt = and -8
dy / y-8 = dt
We change variables
y-8 = u
dy = du
We replace and integrate
∫ du / u = ∫ dt
Ln (y-8) = t
We evaluate at the lower limits t = 0 for y = y₀
ln (y-8) - ln (y₀-8) = t-0
Let's simplify the equation
ln (y-8 / y₀-8) = t
y-8 / y₀-8 =
y-8 = (y₀-8)
b) the equation is
dy / dt = 2y -5
u = 2y -5
du = 2 dy
du / 2u = dt
We integrate
½ Ln (2y-5) = t
We evaluate at the limits
½ [ln (2y-5) - ln (2y₀-5)] = t
Ln (2y-5 / 2y₀-5) = 2t
2y -5 = (2y₀-5)
c) the equation is very similar to the previous one
u = 2y -10
du = 2 dy
∫ du / 2u = dt
ln (2y-10) = 2t
We evaluate
ln (2y-10) –ln (2y₀-10) = 2t
2y-10 = (2y₀-10)
Answer:
she walked 6 miles.
Step-by-step explanation:
We know that Ruth walks at a speed of 4 mph and it took her 1.5 hours to walk from her home to the library (from 9 to 10.30).
We can solve this using a rule of three:
If she walks 4 miles in 1 hour, how many hours did she walk in 1.5 hours?
1 hour 4 miles
1.5 hours x miles
Solving for x we get:
miles
Thus, she walked a distance of 6 miles
Answer:
Two dogs and three ducks
Step-by-step explanation:
Dogs have four legs and ducks have two, to find the answer, you add the number to get your answer.
In this case, two dogs would make a total of 8 legs and three ducks would make a total of 6 legs. Adding 8 and 6 together, you get 14.
