I need the answer for 90 please its due tommorow!
2 answers:
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This is adding two vectors, one magnitude 300 direction east, and one magnitude 100 direction 30 degrees northeast.
For the resulting sum we can use the Law of Cosines or just add up the components. Let's try it both ways.
Components first. In the east direction we have
300 + 100 cos 30° = 300 + 100(√3/2) = 386.60 miles per hour
In the north direction we have
0 + 100 sin 30° = 100 (1/2) = 50 miles per hour
So a total speed of
sqrt{386.6^2 + 50^2} = 389.82 miles per hour
Answer: 389.82
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OK let's try the Law of Cosines. We have sides 300 and 100 and included angle 150°.
Answer:
The tangent line to the given curve at the given point is .
Step-by-step explanation:
To find the slope of the tangent line we to compute the derivative of and then evaluate it for
.
Differentiate the equation.
Differentiate both sides.
Sum/Difference rule applied:
Constant multiple rule applied:
Applied power rule:
Simplifying and apply constant rule:
Simplify.
Evaluate y' for x=4:
is the slope of the tangent line.
Point slope form of a line is:
where is the slope and
is a point on the line.
Insert 9 for and (4,10) for
:
The intended form is which means we are going need to distribute and solve for
.
Distribute:
Add 10 on both sides:
The tangent line to the given curve at the given point is .
------------Formal Definition of Derivative----------------
The following limit will give us the derivative of the function at
(the slope of the tangent line at
):
We are given f(4)=10.
Let's see if we can factor the top so we can cancel a pair of common factors from top and bottom to get rid of the x-4 on bottom:
Let's check this with FOIL:
First:
Outer:
Inner:
Last:
---------------------------------Add!
So the numerator and the denominator do contain a common factor.
This means we have this so far in the simplifying of the above limit:
Now we get to replace x with 4 since we have no division by 0 to worry about:
2(4)+1=8+1=9.