the maximum of A=6/2(x-3)2+3
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the maximum value of \(\frac{\left(x^2+15\right)}{x^2+3}\)
\(\frac{x^2+15}{x^2+3}\)
\(=\frac{x^2+3+12}{x^2+3}\)
\(=\frac{x^2+3}{x^2+3}+\frac{12}{x^2+3}\)
\(=1+\frac{12}{x^2+3}\)
\(x^2\ge0\)
\(x^2+3\ge3\)
\(\frac{12}{x^2+3}\le4\)
\(1+\frac{12}{x^2+3}\le5\)
ĐS: 5
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The maximum value of (2x-3)(5-x)is..
if x/3-1/y=1/6( with x and y are two integer numbers)
then the maximum value of y-x is ....
the maximum value of C=x2+8/(2(x2+2)
Exercise 2: Give the correct form of the verbs in brackets.1. The news about Mr Hogan (be) ___________surprising.2. Fifty minutes (be)___________the maximum length of the time allowed for the exam.3. Many people in the world (not have) ___________enough food to eat.4. The poor (need)___________ help from the community.5. Listening to loud music at rock concerts (cause)_______ hearing loss in some teenagers these days.6. There (be) ___________a lot of sheep in the field.7. Ten miles (be) _______...
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Exercise 2: Give the correct form of the verbs in brackets.
1. The news about Mr Hogan (be) ___________surprising.
2. Fifty minutes (be)___________the maximum length of the time allowed for the exam.
3. Many people in the world (not have) ___________enough food to eat.
4. The poor (need)___________ help from the community.
5. Listening to loud music at rock concerts (cause)_______ hearing loss in some teenagers these days.
6. There (be) ___________a lot of sheep in the field.
7. Ten miles (be) ___________ too far to walk.
8. Not only John but also his friends (want) ___________ to buy this race horse.
9. A number of students (recently participate) ___________ in intensive language programs abroad.
10. Sarah, along with 20 students, (plan) ___________a party now.
11. The number of students who (withdraw) ___________from class since the term began
(be) ___________quite high.
12. There (be) at least one window in every room.
13. A lot of students in my class (speak) ___________ and (undrstand) ___________ Spanish.
14. The trousers Lan’s bought (not, go) ___________ best with her shirt.
15. The information she gave me (be not) ___________valuable.
16. The number of days in a week (be) ___________seven.
17. Either you or he (have) ___________to do the task.
18. Two years without a job (be) ___________too long to be.
19. Every girl and boy (be) ___________required to have certain immunizations before enrolling in public school.
20. Neither of John’s parents (be)___________ English.
1 is
2 is
3 don't have
4 need
5 causes
6 are
7 is
8 want
9 have recently participated
10 is planning
11 withdraw - to be
12 is
13 speak - understand
14 don't go
15 wasn't
16 is
17 has
18 is
19 is
20 is
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Find the maximum value of:
a) \(-3x^2-9x-25\)
b) \(x-x^2\)
c) \(-x^2+7x+12\)
a: \(=-3\left(x^2+3x+\dfrac{25}{3}\right)\)
\(=-3\left(x^2+3x+\dfrac{9}{4}+\dfrac{73}{12}\right)\)
\(=-3\left(x+\dfrac{3}{2}\right)^2-\dfrac{73}{4}< =-\dfrac{73}{4}\)
Dấu '=' xảy ra khi x=-3/2
b: \(=-\left(x^2-x+\dfrac{1}{4}-\dfrac{1}{4}\right)=-\left(x-\dfrac{1}{2}\right)^2+\dfrac{1}{4}< =\dfrac{1}{4}\)
Dấu '=' xảy ra khi x=1/2
c: \(=-\left(x^2-7x-12\right)\)
\(=-\left(x^2-7x+\dfrac{49}{4}-\dfrac{97}{4}\right)\)
\(=-\left(x-\dfrac{7}{2}\right)^2+\dfrac{97}{4}< =\dfrac{97}{4}\)
Dấu '=' xảy ra khi x=7/2
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Given that x and y satisfy x2 + y2 = 7 . Find the maximum of x2 + 2y2 + 2x - 4
Let \(A=x^2+2y^2+2x-4\)
From condition, we have: \(y^2=7-x^2\)
Therefore: \(A=x^2+2\left(7-x^2\right)+2x-4\)
\(\Rightarrow A=-x^2+2x+10=-\left(x-1\right)^2+11\le11\)
\(\Rightarrow A_{max}=11\) when \(\left\{{}\begin{matrix}x=1\\y^2=6\end{matrix}\right.\)
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1. People alleged that the man had robbed the store of $4,000 in cash
It ...
The man ...
2. It is reported that the damage is extensive.
The damage ...
3. People alleged that two prisoners had escaped from the maximum security prison
It ...
Two prisoners...
What is the maximum possible area, in , of a rectangle with a perimeter of 20cm?
Coi 2 cạnh của hình chữ nhật là a và b, a+b=10.Sử dụng BĐT Cauchy: \(ab\le\frac{a^2+b^2}{2}\)Dấu "=" xảy ra khi a=b=5 tức là max(ab)=25
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