F1 . . . 100% of it = 900N is in the +x direction.
F2 . . . 70.7% of it (cos45°, 530.3N) is in the +x direction,
and 70.7% of it (sin45°, 530.3N) is in the +y direction.
F3 . . . 80% of it (520N) is in the -x direction,
and 60% of it (390N) is in the +y direction.
Total x-component: 900 + 530.3 - 520 = 1,950.3 N
Total y-component: 530.3 + 390 = 920.3 N
Magnitude of the resultant = √ (x² + y²)
= √(1950.3² + 920.3²)
= √4,650,070.09
= 2,156.4 N .
Angle of the resultant, measured counterclockwise
from the +x axis, is
tan⁻¹ (y / x)
= tan⁻¹ (920.3 / 1950.3)
= tan⁻¹ (0.4719)
= about 25.3° .
Caution:
The same fatigue that degrades my ability to READ the question accurately
may also compromise the accuracy of my solutions. Before you use this
answer for anything, check it, check it, check it !
Answer:
e^(ln x) is just plain x
Step-by-step explanation:
The functions f(x) = e^x and g(x) = ln x are inverses of one another. In other words, one "undoes" the other.
Thus, as the rule goes, e^(ln x) is just plain x.
Here, e^(ln x) = 4 simplifies to x = 4.
We're given that 
and 
, and want to find 
.
By the chain rule, we have
and
Then
(because the point 
corresponds to 
)
The answer is 30 cubic inches.
If <span>5 chocolate candies are in 1 cubic inch, 150 </span><span>chocolate candies will be in x cubic inches:
</span>5 chocolate candies : 1 cubic inch = 150 chocolate candies : x<span> cubic inches
</span>5 : 1 = 150 : x
5 = 150 : x
x = 150 : 5
x = 30
So, if <span>150 chocolate candies are in a jar, the volume of the jar is 30 cubic inches.</span>
Answer:
3,500,000
Step-by-step explanation:
(1×7)×500000 or 7×500000
