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Gnom [1K]
1 year ago
14

Find the set of values of k for which the equation 3x² - 12x + k >. 0 has no real roots.​

Mathematics
1 answer:
anzhelika [568]1 year ago
3 0

Answer:

k > 12

Step-by-step explanation:

If a quadratic equation has no real roots the values of b^2 - 4ac

( for the general form ax^2 + bx + c = 0) is negative,

So we have the inequality:

(-12)^2  - 4*3* k < 0

144 - 12k < 0

12k > 144

k > 12

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(sec x - tan x)^2 \\  \\ = sec^2x - 2 sec x tan x + tan^2 x \\  \\ =(1+tan^2 x) - 2 sec x tan x +tan^2 x \\  \\ =1 - 2 sec x tan x + 2 tan^2 x \\  \\ = 1 - 2tan x(sec x - tan x) \\  \\ =1 - \frac{2 sin x}{cos x} (\frac{1-sin x}{cos x}) \\  \\ = 1 - \frac{2 sin x (1-sin x)}{cos^2 x} \\  \\ =1 - \frac{2 sin x (1-sin x)}{1-sin^2 x} \\  \\ =1 - \frac{2 sin x (1-sin x)}{(1-sin x)(1+sin x)} \\  \\ =1-\frac{2 sin x}{1+sin x}
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2 years ago
Michael bought a shirt with 2/5 of his money. Then he bought a jacket that cost $5 more than the shirt. He spent $105 altogether
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Answer:

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Step-by-step explanation:

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3 years ago
You have $18 to buy peppers. Peppers cost $1.50 each. Write and solve and inequality that represents the number of peppers you c
IrinaVladis [17]

Answer:

1.50x=18

Step-by-step explanation:

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3 years ago
Read 2 more answers
A survey of the whole United States shows that 75% of 6th grade students like sports that involve running, that 60% of boys like
slamgirl [31]

Answer: 75% of 6th Grade Students

Step-by-step explanation:

This sample makes the most sense because it is a majority of everyone, not just a majority of certain people. Also, Mountain School would get fewer complaints from other people if they went with a majority of 75%. Finally, running sports usually cost less then other sports.

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2 years ago
Paul,Linda,and Aaron make homemade cards. Paul can make 1 card for every 3 cards Linda makes. Linda can make 3 cards for every 2
dimaraw [331]

Answer:

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Here, we want to know how many cards Linda makes than Paul during the week.

We proceed as follows;

From the question;

If Paul makes 1 card, then Linda has made three

Now let’s get their relationship with Aaron;

If Aaron makes 2 cards , Linda has made three

Now since Aaron made 72 cards, Let’s say Linda has made x cards

Let’s get the value of x now

To get the value of x, we simply cross multiply;

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So the number of cards Paul will make if Linda makes 108 will be 108/3 = 36

So the number of more cards that Linda makes than Paul during the week will be ; 108 -36 = 72 cards

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3 years ago
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