In this item, we let x be the rate of the boat in still water and y be the rate of the current.
Upstream. When the boat is going upstream, the speed in still water is deducted by the speed of the current because the boat goes against the water. The distance covered is calculated by multiplying the number of hours and the speed.
(x - y)(3) = 144
Downstream. The speed of the boat going downstream is equal to x + y because the boat goes with the current.
(x + y)(2) = 144
The system of linear equations we can use to solve for x is,
3x - 3y = 144
2x + 2y = 144
We use either elimination or substitution.
We solve for the y of the first equation in terms of x,
y = -(144 - 3x)/3
Substitute this to the second equation,
2x + 2(-1)(144 - 3x)/3 = 144
The value of x from the equation is 60
<em>ANSWER: 60 km/h</em>
Answer:
a) (0, -33, 12)
b) area of the triangle : 17.55 units of area
Explanation:
<h2>
a) </h2>
We know that the cross product of linearly independent vectors 
and 
gives us a nonzero, orthogonal to both, vector. So, if we can find two linearly independent vectors on the plane through the points P, Q, and R, we can use the cross product to obtain the answer to point a.
Luckily for us, we know that vectors 
and 
are living in the plane through the points P, Q, and R, and are linearly independent.
We know that they are linearly independent, cause to have one, and only one, plane through points P Q and R, this points must be linearly independent (as the dimension of a plane subspace is 3).
If they weren't linearly independent, we will obtain vector zero as the result of the cross product.
So, for our problem:
<h2>B)</h2>
We know that and are two sides of the triangle, and we also know that we can use the magnitude of the cross product to find the area of the triangle:
so:
Answer:
C. Waves transfer energy, but not matter.
Explanation: hope this helps :)
Answer:
Explanation:
Speed of light is the product of its wavelength and frequency, expressed as
S=fw
Where s represent speed, f is frequency while w is wavelength
Making f the subject of the formula then
f=s/w
Substituting 2.99x10^8 m/s for s and 3.012x10^-12 m for w then
Therefore, the frequency equals to
