Using division, you will find that -1/9 continues on and on forever with no end, so you can mark this by drawing a line over the last repeating number
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>
its 15=T/5 I think.
the "is no more than a number" is kinda throwing me off.
if its no more it cant really be no less giving the numbers
.
Answer:
where are the options?
Step-by-step explanation:
SOLUTION:
To begin with, let's establish that the formula of this line is in slope-intercept form as follows:
y = mx
The formula for this line isn't:
y = mx + b
This is as this line doesn't have a y-intercept ( b ) as it passes through the origin instead. This means that ( b ) would be rendered useless in this formula as it would just bring us back to the y = mx formula as displayed below:
y = mx + b
y = mx + 0
y = mx
Moving on, for ( m ), we need to find the gradient of the line as displayed below:
m = gradient
m = rise / run
m = 10 / 2
m = 5
Now, we must simply substitue ( m ) into the formula in order to obtain the equation for this line as displayed below:
y = mx
y = 5x
Therefore, the answer is:
A. y = 5x
