What is the rate of change
1 answer:
Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
- Left to Right
<u>Algebra I</u>
- Slope Formula:
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Find points from table.</em>
Point (-1, -1)
Point (0, -5)
<u>Step 2: Find slope </u><em><u>m</u></em>
Simply plug in the 2 coordinates into the slope formula to find slope <em>m</em>. Rate of change and slope are identical.
- Substitute [SF]:
- Add:
- Divide:
You might be interested in
One
Remark
This is very complicate unless you pick the right method. It's very handy o know about substitutions.
Method
Let z = (k + 2)^2
Now the problem becomes
z + 16/z = 92 Multiply through by z
Solution
z^2 + 16 = 92z
That does not look very promising. If you know the quadratic formula, this mess can be solved. If you do not know what the quadratic formula is, then what I've written is the answer.
Worse yet, you have to know what complex numbers are. Is this something you know about? The z form of this equation is fine. It gives answers that are rational. The problem is that both are negative and so in your next step, you will be forced to take the square root of a negative number.
Maybe the answer is just
(x + 3)^ + 16 = 92(x + 3)^2
If all you have to do is expand this then you get
x^2 + 6x + 9 + 16 = 92(x^2 + 6x + 9) Remove the brackets.
x^2 + 6x + 25 = 92x^2 + 552x + 828 Put the left over to the right.
0 = 92x^2 - x^2 + 552x - 6x + 828 - 25
0 = 91x^1 + 546x + 803
It looks that way from the second question. If I'm wrong about that, put a comment down below.
Two
Put over a common denominator and expand
Remark
This is very complicate unless you pick the right method. It's very handy o know about substitutions.
Method
Let z = (k + 2)^2
Now the problem becomes
z + 16/z = 92 Multiply through by z
Solution
z^2 + 16 = 92z
That does not look very promising. If you know the quadratic formula, this mess can be solved. If you do not know what the quadratic formula is, then what I've written is the answer.
Worse yet, you have to know what complex numbers are. Is this something you know about? The z form of this equation is fine. It gives answers that are rational. The problem is that both are negative and so in your next step, you will be forced to take the square root of a negative number.
Maybe the answer is just
(x + 3)^ + 16 = 92(x + 3)^2
If all you have to do is expand this then you get
x^2 + 6x + 9 + 16 = 92(x^2 + 6x + 9) Remove the brackets.
x^2 + 6x + 25 = 92x^2 + 552x + 828 Put the left over to the right.
0 = 92x^2 - x^2 + 552x - 6x + 828 - 25
0 = 91x^1 + 546x + 803
It looks that way from the second question. If I'm wrong about that, put a comment down below.
Two
Put over a common denominator and expand
<h3>Answer: roughly 12.6274 meters</h3>
The more accurate value is 12.6274169979696, though it's not fully exact.
Round this however you need to.
The exact distance 32*sin(45) - 10 meters.
===========================================================
Explanation:
Refer to the diagram below.
I'll use point A in place of point O since the letter 'oh' is very similar looking to the number zero.
Plot point A at the origin (0,0). While at point A, look directly north. Then turn 30 degrees eastward to look at the bearing 030°. Next, move 20 meters along that bearing direction to arrive at point R. Segment AR is 20 meters long.
In the diagram, note how angle RAB is 30 degrees. The side opposite this is BR = m.
We can use the sine ratio to say that
sin(angle) = opposite/hypotenuse
sin(A) = BR/AR
sin(30) = m/20
m = 20*sin(30)
m = 10
-----------------------------------
While still at point A, look directly north and turn 135 degrees clockwise (ie toward the east) and move 32 meters along that bearing. You'll arrive at point S as the diagram shows.
Notice how
angle RAB + angle RAC + angle CAS = 30+60+45 = 135
The remaining angle DAS is 180-135 = 45 degrees.
When focusing on triangle DAS, we can say
sin(A) = DS/AS
sin(45) = n/32
n = 32*sin(45)
n = 22.6274169979696
This value is approximate.
----------------------------------
Subtract the values of m and n
n - m = 32*sin(45) - 10 = exact distance
n - m = 22.6274169979696 - 10
n - m = 12.6274169979696
n - m = 12.6274 = approximate distance
Round it however you need to. I'm choosing to round to four decimal places.
So we see that point S is roughly 12.6274 meters east of point R.
If your teacher wants the exact distance, then stick with 32*sin(45)-10.