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.
9514 1404 393
Answer:
Step-by-step explanation:
Let a and s represent the prices of adult and student tickets, respectively.
13a +12s = 211 . . . . . . ticket sales the first day
5a +3s = 65 . . . . . . . ticket sales the second day
Subtracting the first equation from 4 times the second gives ...
4(5a +3s) -(13a +12s) = 4(65) -(211)
7a = 49 . . . . . . . simplify
a = 7 . . . . . . . divide by 7
5(7) +3s = 65 . . . . substitute into the second equation
3s = 30 . . . . . . . subtract 35
s = 10 . . . . . . . divide by 3
The price of one adult ticket is $7; the price of one student ticket is $10.
42
It’s 42 since if you would convert this
The circumference of the drain to the nearest tenth is 15.10 inches.
<h3>What is the circumference?</h3>
The circumference of the drain is the distance round the drain. Since the drain has the shape of a circle, the formula used to determine the circumference of a circle would be used to determine the circumference of the drain.
Circumference of the drain = πd
3.14 x 4.8 =15.10 inches
To learn more about how to determine the circumference of a circle, please check: brainly.com/question/14351152
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