Answer:
-1
Step-by-step explanation:
To solve this without L'Hopital's rule, multiply by the conjugate, (1 − cos n + sin n) / (1 − cos n + sin n).
The numerator becomes:
(1 − cos n + sin n) (1 − cos n + sin n)
(1 − cos n + sin n) − cos n (1 − cos n + sin n) + sin n (1 − cos n + sin n)
1 − cos n + sin n − cos n + cos² n − sin n cos n + sin n − sin n cos n + sin² n
2 − 2 cos n + 2 sin n − 2 sin n cos n
2 − 2 cos n + sin n (2 − 2 cos n)
(1 + sin n) (2 − 2 cos n)
The denominator becomes:
(1 − cos n − sin n) (1 − cos n + sin n)
(1 − cos n)² − sin² n
1 − 2 cos n + cos² n − sin² n
1 − 2 cos n + cos² n − 1 + cos² n
2 cos² n − 2 cos n
-cos n (2 − 2 cos n)
Dividing, the 2 − 2 cos n factors cancel out, leaving us with:
(1 + sin n) / -cos n
The limit as n approaches 0 is therefore:
(1 + 0) / -1
-1
Answer:
$81.5475 or to round it $81.55
Step-by-step explanation:
Simple steps:
1) Add the 2 items
2) Multiply by 0.75. because 25% discount = 75% of item
($72.49+$36.24)x0.75 = $81.5475 or $81.55
Answer:
The magnitude of the given vector is 40.72 units.
Step-by-step explanation:
The given vector is ![v=-3\widehat{i}+40\widehat{j}+7\widehat{k}](https://tex.z-dn.net/?f=v%3D-3%5Cwidehat%7Bi%7D%2B40%5Cwidehat%7Bj%7D%2B7%5Cwidehat%7Bk%7D)
We know that for any vector 'r'
the magnitude is given by
![|r|=\sqrt{x^{2}+y^{2}+z^{2}}](https://tex.z-dn.net/?f=%7Cr%7C%3D%5Csqrt%7Bx%5E%7B2%7D%2By%5E%7B2%7D%2Bz%5E%7B2%7D%7D)
Comparing with the given vector we have
x = -3
y = 40
z = 7
Thus the magnitude equals
![|v|=\sqrt{(-3)^{2}+40^{2}+7^{2}}](https://tex.z-dn.net/?f=%7Cv%7C%3D%5Csqrt%7B%28-3%29%5E%7B2%7D%2B40%5E%7B2%7D%2B7%5E%7B2%7D%7D)
![|v|=40.72](https://tex.z-dn.net/?f=%7Cv%7C%3D40.72)
Answer:
down
Step-by-step explanation:
Answer:
12^2 + 43x + 35
Step-by-step explanation:
(3x+7)(4x+5)
=(3x+7)(4x+5)
=(3x)(4x)+(3x)(5)+(7)(4x)+(7)(5)
=12x2+15x+28x+35
=12x2+43x+35