Using the first derivative test, it is found that the graph is increasing on the interval is (-5, ∞).
<h3>What is Function?</h3>
A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B.
Here, the function is given by:
f(x) = x²/2 + 5x + 6
On differentiating both sides, with respect to x we get
f'(x) = x + 5
Then, we test the signal of the derivative, which is the first derivative test.
x + 5 ≥ 0
x ≥ -5
Thus, It is found that the Function is increasing on the interval is (-5, ∞).
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Answer:
Step-by-step explanation:
<u>Given </u><u>:</u><u>-</u><u> </u>
- A quadratic equation is given to us.
- The equation is 2x² + 7x +6=0
And we need to find out the roots of the given equation. We can use the middle term splitting method to find out the roots as ,
<u>Given </u><u>equation</u><u> </u><u>:</u><u>-</u>
Step 1: <u>Find</u><u> out</u><u> the</u><u> </u><u>factors</u><u> </u><u>of </u><u>1</u><u>2</u><u> </u><u>:</u><u>-</u><u> </u>
We will choose the two factors such that their sum equals to the coefficient of x i.e. 7 .The factors are , 1×12 , 2×6 , 3×4 .
- And 3 + 4 = 7. So we will break the middle term into 3x and 4x .
Step 2 :<u> Breaking</u><u> the</u><u> </u><u>middle</u><u> term</u><u> </u><u>:</u><u>-</u><u> </u>
Step 3: <u>Take </u><u>out </u><u>common</u><u> </u><u>from </u><u>terms </u><u>:</u><u>-</u>
Step 4 : <u>Equate </u><u>them </u><u>with </u><u>0</u><u> </u><u>:</u><u>-</u><u> </u>
<u>Hence </u><u>the</u><u> </u><u>correct</u><u> </u><u>options </u><u>are </u><u>C </u><u>and </u><u>D </u><u>.</u>
Volume of large prism: 8 x 4 x 2 1/4 = 72 cubic inches
volume of small prism: 1/4 ^3 = 0.15625 cubic inches
72 / 0.15625 = 4,608 cubes
The top number is 4 and t =1, so you need to replace t with 1, find the answer, then replace t with 2 through 4, then find the sum of all of them:
6^1-1 = 6^0 = 1
6^2-1 = 6^1 = 6
6^3-1 - 6^2 = 36
6^4-1 = 6^3 = 216
Sum = 1 + 6 + 36 + 216 = 259
The answer is B.
Step-by-step explanation:
3 gal = 900 ft
... gal = 1100 ft
So, each gal is used for cover 300 ft,
Then,
![\sf \frac{1100}{900} \times 3 = \frac{11}{3} = \boxed{ \bold{ \red{3 \frac{2}{3} \: gal}}}](https://tex.z-dn.net/?f=%20%5Csf%20%5Cfrac%7B1100%7D%7B900%7D%20%20%5Ctimes%203%20%3D%20%20%5Cfrac%7B11%7D%7B3%7D%20%20%3D%20%20%5Cboxed%7B%20%5Cbold%7B%20%5Cred%7B3%20%5Cfrac%7B2%7D%7B3%7D%20%20%5C%3A%20gal%7D%7D%7D)
We need <u>3 2/3 gal</u> to cover 1100 ft.
Hope it helps!