Answer:
The velocity of the hail relative to the cyclist is 
The angle at which hailstones falling relative to the cyclist is 
Step-by-step explanation:
Given : On a cold day, hailstones fall with a velocity of 
. If a cyclist travels through the hail at 
.
To find : What is the velocity of the hail relative to the cyclist and At what angle are the hailstones falling relative to the cyclist?
Solution :
The velocity of the hailstone falls is 
The velocity of the cyclist travels through the hail is 
The velocity of the hail relative to the cyclist is given by,
Substitute the value in the formula,
So, The velocity of the hail relative to the cyclist is
Now, The angle of hails falling relative to the cyclist is given by
So, The angle at which hailstones falling relative to the cyclist is
1. As you can see in the figure attached, the <span> line "t" is the perpendicular bisector of JK, and divides the triangle in two equal right triangles. This means that both triangles are congruent. Therefore, both have equal dimensions. Keeping this on mind, you have the followiig:
2. Both triangles are congruents, then:
GK=GJ
3. So if the lenght GK is 8.25, the length GJ has the same length:
GJ=8.25
4. Therefore, the answer is:
GJ=8.25</span>
Answer:
Step-by-step explanation:
There are a few algebraic, geometric, and trig relations you are expected to remember. These come into play in this set of questions.
- vertex form for equation of a parabola: y = a(x -h)² +k, has vertex at (h, k)
- Sine Law relates triangle sides and their opposite angles: a/sin(A) = b/sin(B)
- Cosine Law relates triangle sides and the angle between two of them: c² = a² +b² -2ab·cos(C)
- SOH CAH TOA reminds you of trig relations in a right triangle
- relationships of corresponding sides and angles in congruent and similar triangles: angles are congruent; sides are congruent or proportional.
When solving any problem, the first step is to understand what is being asked. The second step is to identify the relevant information and relationships that can help you answer.
<h3>1)</h3>
You are asked for the equation of a parabola with a given vertex. The vertex form equation will be useful. We can assume a scale factor ('a') of 1.
For vertex (h, k) = (1, -4) and a=1, the vertex form equation is ...
y = a(x -h)² +k
y = 1(x -1)² +(-4)
y = (x -1)² -4
<h3>2)</h3>
You are given 3 sides and want to find an angle. The useful relation in this case is the Cosine Law. (If you wanted to use the Sine Law, you would already need to know an angle.)
<h3>3) </h3>
The mnemonic SOA CAH TOA reminds you that the cosine relation is ...
Cos = Adjacent/Hypotenuse
The side adjacent to angle C is marked 4; the hypotenuse is marked 5. The desired ratio is ...
cos(C) = 4/5
<h3>4)</h3>
The measure x is also the measure of side AB. The similarity statement lists those letters as the first two. It also lists the letters DE as the first two. The other given side in ΔABC is BC, corresponding to side EF in the smaller triangle. Corresponding sides are proportional, so we have ...
AB/DE = BC/EF
x/6 = 10/4
We can find the value of x by multiplying this equation by 6:
x = 6(10/4) = 60/4
x = 15
Please note that BC is the shortest side in ΔABC. This means x > 10. There is only one such answer choice. (No math necessary.)
