As you progress in math, it will become increasingly important that you know how to express exponentiation properly.
y = 2x3 – x2 – 4x + 5 should be written <span>y = 2^x3 – x^2 – 4^x + 5. The
" ^ " symbol denotes exponentiation.
I see you're apparently in middle school. Is that so? If so, are you taking calculus already? If so, nice!
Case 1: You do not yet know calculus and have not differentiated or found critical values. Sketch the function </span>y = 2x^3 – x^2 – 4^x + 5, including the y-intercept at (0,5). Can you identify the intervals on which the graph appears to be increasing and those on which it appears to be decreasing?
Case 2: You do know differentiation, critical values and the first derivative test. Differentiate y = 2x^3 – x^2 – 4^x + 5 and set the derivative = to 0:
dy/dx = 6x^2 - 2x - 4 = 0. Reduce this by dividing all terms by 2:
dy/dx = 3x^2 - x - 2 = 0 I used synthetic div. to determine that one root is x = 2/3. Try it yourself. This leaves the coefficients of the other factor, (3x+3); this other factor is x = 3/(-3) = -1. Again, you should check this.
Now we have 2 roots: -1 and 2/3
Draw a number line. Locate the origin (0,0). Plot the points (-1, 0) and (2/3, 0). This subdivides the number line into 3 subintervals:
(-infinity, -1), (-1, 2/3) and (2/3, infinity).
Choose a test number from each interval and subst. it for x in the derivative formula above. If the derivative comes out +, the function is increasing on that interval; if -, the function is decreasing.
Ask all the questions you want, if this explanation is not sufficiently clear.
Answer:
Radius - 30 feet
Area - 2826 feet²
Step-by-step explanation:
I'm pretty sure that's the answer
Answer:
I think the answer is 0.28 or 7/25
Step-by-step explanation:
Answer:
The equation to represent total number of pencils p that Rafael bought is 15 n .
Step-by-step explanation:
Given as :
The total numbers of pencils packs bought by Rafael = n
The number of pencils in each pack = 15 pencils
Let The total number of pencil does Rafael bought = p
<u>Now, According to question</u>
The total number of pencil does Rafael bought = total numbers of pencils packs bought by Rafael × number of pencils in each pack
i.e p = n × 15
So, The total number of pencil does Rafael bought = p = 15 n
Hence, The equation to represent total number of pencils p that Rafael bought is 15 n . Answer
Answer:
Tank A is filling quicker
Step-by-step explanation:
You can tell this by looking at the slope of each line. Since the slope of line A is larger and going up faster, that tells you that tank A is filling faster than tank B