x=27+360n,153+360n, for any integer n
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Answer:
The time it will take Natalie to pick the forty bushels alone is 10 hours
Step-by-step explanation:
The time it takes Kali to pick forty bushels of apples alone = 15 hours
The time it takes Kali and Natalie to pick forty bushels = 6 hours
The rate at which Kali picks bushels = 40/15 bushels per hour = 8/3 bushels per hour
Let x represents the rate at which Natalie picks bushels, we have;
8/3 × 6 + x × 6 = 40
x × 6 = 40 - 8/3 × 6 = 24
x = 24/6 = 4
Therefore;
The rate at which Natalie picks the bushels of apples = 4 bushels/hour
The time it will take Natalie to pick the forty bushels alone = (40 bushels)/(4 bushels/hour) = 10 hours.
49x^2 + 64y^2 = 3136 . . . (1)
y - 6 = (1/4)x^2 . . . (2)
From (2), x^2 = 4(y - 6) = 4y - 24 . . . (3)
Putting (3) into (1) gives
49(4y - 24) + 64y^2 = 3136
196y - 1176 + 64y^2 = 3136
64y^2 + 196y - 4312 = 0
y = 6.819
x = sqrt(4(6.819) - 24)
x = 1.81
The possible point of collision is (1.81, 6.819)
Answer:
Real values of x where x < -1
Step-by-step explanation:
Above the x-axis, the function is positive.
The function is decreasing when the gradient is negative.
The function has a positive
coefficient, therefore the vertex is a local minimum;
This means the gradients are negative before the vertex and positive after it;
To meet the conditions therefore, the function must be before the vertex and above the x-axis;
This will be anywhere before the x-intercept at x = -1;
Hence it is when x < -1.
The consecutive integers are i, i+1, i+2, i+3.
3 less than sum of the integers
= i + i +1 + i + 2 + i + 3 - 3 = 4i + 3
