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.
The answer is <span>C. 94 ´ 94 ; 8836 ft.
There are 4 possible gardens, each with different areas. From the biggest area to the smallest one:
8836 ft (C.) > 8835 ft (D.) > 8832 ft (B.) > 8811 ft (A.)
Thus, the </span>greatest possible area for a garden will be 8836 ft (choice B.). It should also be taken into consideration that this is a square ( 94 <span>´ 94 ) which is for surely rectangle. </span>
Answer: let the hours they both have equal amount of water be X
130+10x=280-5x
10x+5x=280-130
15x=150
x=10hrs
Step-by-step explanation:
Answer:
The measure of <u>Angle G is 41</u>
Step-by-step explanation:
We know that in a parallelogram, opposite angles are congruent, therefore let's solve for x-value first;
3x + 11 = 5x - 9
11 = 5x - 3x - 9
11 = 2x - 9
11 + 9 = 2x
20 = 2x
20/2 = x
10 = x
Now that we have x-value, we can substitute it in the equation for Angle G to find it's angle measure;
5(10) - 9 = ∠G
50 - 9 = ∠G
41 = ∠G
So the final answer = <u>The measure of Angle G is 41</u>
Hope this helps!
Given: Mean μ = 61.2 and standard deviation σ =21.4
The Z score of the value x=45 is given by
Z = 
Z = 
Z = 
Z = -0.757
The z-score value for 45 rounded to nearest tenth is -0.8
