<h2>
Answer:</h2>
The term speed is used to denote distance traveled divided by time. The speed is the magnitude of instantaneous velocity and so can never be negative. In this problem, we have a boat’s velocity measured in meter per second, described by vector:
![b=(3,-4)](https://tex.z-dn.net/?f=b%3D%283%2C-4%29)
1. Therefore, the magnitude of this vector, which is also the speed of the boat can be found as:
![\left|b\right|=\sqrt{3^2+(-4)^2}=5m/s](https://tex.z-dn.net/?f=%5Cleft%7Cb%5Cright%7C%3D%5Csqrt%7B3%5E2%2B%28-4%29%5E2%7D%3D5m%2Fs)
2. On the other hand, the direction the boat is traveling is the angle that this vector makes with the horizontal. So this can be found as:
![\theta = tan^{-1}(\frac{3}{-4})=-36,86^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20tan%5E%7B-1%7D%28%5Cfrac%7B3%7D%7B-4%7D%29%3D-36%2C86%5E%7B%5Ccirc%7D)
The representation of this problem is shown below.
Answer:
y=kx
subst y=10 and x=20 into the above
<em>1</em><em>0</em><em>=</em><em>k20</em>
<em>k</em><em>=</em><em>1</em><em>0</em><em>/</em><em>2</em><em>0</em>
<em>k</em><em>=</em><em>1</em><em>/</em><em>2</em>
<em>therefore</em><em> </em><em>relationship</em><em>:</em><em> </em><em>y</em><em>=</em><em>1</em><em>/</em><em>2</em><em>x</em>
<em>subst</em><em> </em><em>x</em><em>=</em><em>1</em><em>5</em><em> </em><em>into</em><em> </em><em>the</em><em> </em><em>relationship</em>
<em> </em><em>y</em><em>=</em><em>1</em><em>/</em><em>2</em><em>(</em><em>1</em><em>5</em><em>)</em>
<em>y</em><em>=</em><em>7</em><em>,</em><em>5</em>
Step by step explanation:
- Step 1: when they say y varies directly with x they mean<em> y is proportional to x</em>
- step 2: so y=kx where <em>k is the constant</em>
- step 3: is to substitute <em>y=10</em> and <em>x=20</em> into the above equation y=kx
- step 4: you will end up with <em>10=k20</em> then divide both sides by 20 so that <em>k becomes the subject of the formula </em>
- step 5: your answer from the above will be <em>k=10/20 </em>so the relationship is <em>y is directly proportional to 1/2 x </em>what you did here is that you substituted k for 1/2 in the equation in step 3
- step 6: is to finally substitute x=15 into the equation <em>y=1/2x</em> to finally get your answer <em>y</em><em>=</em><em>7</em><em>,</em><em>5</em><em>.</em>
Step 1. Identify the variable.
Step 2. Write an algebraic equation.
Step 3. Solve the equation.
Step 4. Answer the equation.
Step 5. Check answer.
Hope this helps...?
Answer:
3/2
Step-by-step explanation:
Answer:
(a) 34.
(b) Yes.
Step-by-step explanation:
The first term is 3(1)^2 + 1 = 4 ( where k = 1).
The sum of 2 terms = 3(2)^2 + 2 = 14.
The sum of 3 terms = 3(3)^2 + 3 = 30.
The sum of 4 terms = 3(4)^2 + 4 = 52.
So the first 4 terms are 4, 10, 16 and 22 . - increasing by 6.
The common difference is 6 so it is an arithmetic sequence.
The 6th term = a1 + d(n - 1)
= 4 + 6(6-1)
= 34.