If you drew the two vectors for the velocity you find a triangle rectangle since the two directions East and North form an angle of 90°. I drew first the vector towards East and second the vector towards North.
Therefore, to get the speed relative to the surface you have to sum the two vectors, which means you can apply the Pythagorean theorem to find the hypotenuse, having the two legs.
h = √(4² + 12²) = √160 = 4√10 = 12.65mph
In order to find the direction, you need to use trigonometry:
- the sine of an angle is given by the ratio between the opposite side divided the hypotenuse;
- the cosine of an angle is given by the ratio between the adjacent side divided by the hypotenuse.
You can use either one, I will show you both:
sinα = O / H
inverting the formula: α = arcsin (O / H) = sin⁻¹ <span>(O / H)
these two forms are equivalent.
Similarly:
cos</span>β = A / H
β = arccos (A / H) = cos⁻¹ <span>(A / H).
Substituting your numbers:
</span>α = sin⁻¹ (12 / 12.65) = <span>sin⁻¹ (0.9486) = 1.25rad
</span>β = cos⁻¹ (4 / 12.65) = cos⁻¹<span> (0.3162) = 1.25rad
As you can see, </span>α = β so you can use either formula.
Your answer will then be: the child is moving relative to the surface of the water with a speed of 12.65mph at a direction of 1.25rad from East towards North.
ATTENTION!
If you drew first the vector towards North and then the one towards East, you get an equivalent triangle, which is rotated by 180° respect to the previous one. This way, what you earlier called Opposite is now Adjacent and vice-versa, but the formulas are still valid.
You will get:
α = sin⁻¹ (4 / 12.65) = <span>sin⁻¹ (0.3162) = 0.32rad
</span>β = cos⁻¹ (12 / 12.65) = cos⁻¹<span> (0.9486) = 0.32rad
And your answer will be: </span><span>the child is moving relative to the surface of the water with a speed of 12.65mph at a direction of 0.32rad from North towards East.</span>
Answer:
28
Step-by-step explanation:
substitute 4 in for p in the equation
64-9p=
64-9(4)=
64-36=
28
Answer:
NANIIIIIIIIIIII?
Step-by-step explanation:
Answer:
A) The indicated values of F(x) for x=-3 and x=5 are 
and 
B) The domain of f is the set of all real numbers
Step-by-step explanation:
Given that the function F is defined by
for x=-3,5
A) To find F(x) for the indicated values of x :
Given for x=-3,5
- Put x=-3 in the given function
Therefore
- Put x=5 in the given function
Therefore
The indicated values of F(x) for x=-3 and x=5 are and
B) To find the domain of f :
The domain of the f in the given expression is the set of all real numbers except where the expression 
is undefined. In this case, there is no real number that makes the expression undefined.
The domain of f is the set of all real numbers
