quadratic formula:
x = <u>-b ± √(b² - 4ac)</u>
2a
7x² - x = 7
subtract 7 from both sides:
7x² - x - 7 = 0
plug values into the quadratic formula:
x = <u>-(-1) ± √((-1)²- 4(7)(-7))</u>
2(7)
simplify:
x = <u>1 ± √(197)</u>
14
13d-(-9d-4)
Transfer minus sign to all numbers in parenthesis. = 13d +9d +4 =
Answer: 22d+4
is conservative if we can find a scalar function 
such that 
. This would require
Integrating both sides of the first equation wrt 
gives
Differentiating both sides of this wrt 
gives
but we assumed 
was a function of and 
, independent of . So there is no such and 
is not conservative.
To find the work, first parameterize the path (call it 
) by
for 
. Then
and the work is given by the line integral,
Answer:
The solutions are -3 and -1
Step-by-step explanation:
∵ y = -x² - 2x + 8
∵ y = 2x + 11
∴ -x² - 2x + 8 = 2x + 11
∴ -x² - 2x - 2x + 8 - 11 = 0
∴ -x² - 4x - 3 = 0 ⇒ divide both sides by -1
∴ x² + 4x + 3 = 0
∴ (x + 3)(x + 1) = 0
∴ x + 3 = 0 ⇒ x = -3
∴ x + 1 = 0 ⇒ x = -1
∴ The solutions are -3 and -1
2m + 4s = 66.
4m + 3s = 84.
(Double the 2 glass of milk and 4 snack bars)
4m + 8s = 132.
4m + 3s = 84.
(Take away the second equation from the first equation)
5s= 48.
s = 48/5.
s = 9.6.
4m + 3(9.6) = 84.
4m + 28.8 = 84.
4m = 84 - 28.8.
4m = 55.2.
4m/4 = 55.2/4.
m = 13.8.
In a glass of milk, there are 13.8 carbs, and in a snack bar, there are 9.6 carbs.
2(13.8) + 4(9.6) = 66.
