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gizmo_the_mogwai [7]
3 years ago
6

If f(1) = 10 and f '(x) ≥ 3 for 1 ≤ x ≤ 6, how small can f(6) possibly be?

Mathematics
2 answers:
Hoochie [10]3 years ago
7 0

Answer:

25

Step-by-step explanation:

Our "best" case is when f'(x) = 3 everywhere - if it changes it means f(x) will grow faster. But if f'(x) is constant, it means f(x) is the straight line [tex] y-10 = 3 (x-1) [tex], which passes through the point (6, 25)

Natalka [10]3 years ago
6 0

Answer:

f'( x ) =  \frac{f(b) - f(a)}{b - a}  \\  = \frac{f(6) -f(a)}{6 - 1} \\  3\leqslant \frac{f(6) - 10}{5} \\  15\leqslant f(6) - 10 \\ f(6) \geqslant 15 + 10 \\ f(6) \geqslant 25

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We have that

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7 0
4 years ago
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Is (x + 2) a factor of 3x3 + 4x2 - 4 ?
nordsb [41]

Answer:

No it is not a factor

Step-by-step explanation:

Reason for not being a factor is 3x^3-4x^2-4x. 3x3−4x2−4x 3 x 3 - 4 x 2 - 4 x. Factor x x out of 3x3−4x2−4x 3 x 3 - 4 x 2 - 4 x

5 0
3 years ago
Give the rate in miles per hour. Round to the nearest tenth.<br> Rachel jogs 20 feet in 3 seconds.
Tanya [424]

Answer:

Rate of jogging is 4.6 miles per hour.

Step-by-step explanation:

Rachel jogs 20 feet in 3 seconds and we have to find the rate of jogging in miles per hour.

Since 1 feet = 0.000189394 miles

Therefore, 20 feet = 0.0037879 miles

Similarly, 1 second = \frac{1}{3600} hour

Therefor, 3 seconds = \frac{3}{3600}

                                  = \frac{1}{1200} hours

Formula to calculate the rate = \frac{\text{Total distance of jogging}}{\text{Time taken to cover the distance}}

                                                = \frac{0.0037879}{\frac{1}{1200} }                                                        

                                                = 1200 × 0.0037879

                                                = 4.545

                                                ≈ 4.6 miles per hour

Therefore, rate of jogging is 4.6 miles per hour.

6 0
3 years ago
Suppose that a single die with 9 sides (numbered 1, 2, 3, ... , 9) is rolled twice. What is the probability that the sum of the
Darina [25.2K]

Answer:

<h2>2/81</h2>

Step-by-step explanation:

Probability is defines as the likelihood or chance that an event will occur.

Probability = expected outcome of event/total outcome.

Since a single die with 9 sides was rolled, the total event outcome will be 9*9 = 81

Expected outcome will be the event that the sum of the two rolls equals 3. The possible outcomes are {(1,2), (2,1)}. The expected outcome is 2

Probability that the sum of the two rolls equals 3 = 2/81

8 0
3 years ago
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pashok25 [27]
Go over it again ! Look closely and restart. If u didn’t use pencil and paper do that.!
5 0
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