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3 years ago

What is the nth term of the sequence 3 , 4.5 , 6 , 7.5

Mathematics

1 answer:

Alisiya [41]3 years ago

6 0

Nx1.5+1.5

+1.5 +1.5 +1.5
3, 4.5, 6, 7.5

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Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 3 at x = −3 and a local minimum value of 0 at

Amiraneli [1.4K]

Answer:

The cubic function is f(x) = (27/32)·x - 3/32·x³ - -9/32·x² - 9/32

Step-by-step explanation:

The given function is f(x) = a·x³ + b·x² + c·x + d

By differentiation, we have;

3·a·x² + 2·b·x + c = 0

3·a·(-3)² + 2·b·(-3) + c = 0

3·a·9 - 6·b + c = 0

27·a - 6·b + c = 0

3·a·(1)² + 2·b·(1) + c = 0

3·a + 2·b + c = 0

a·(-3)³ + b·(-3)² + c·(-3) + d = -3

-27·a + 9·b - 3·c + d = -3...(1)

a + b + c + d = 0...(2)

Subtracting equation (1) from equation (2) gives;

28·a - 8·b + 4·c = 3

Therefore, we have;

27·a - 6·b + c = 0

3·a + 2·b + c = 0

28·a - 8·b + 4·c = 0

Solving the system of equations using an Wolfram Alpha gives;

a = -3/32, b = -9/32, c = 27/32 from which we have;

a + b + c + d = 0 3 × (-3/32) + 2 × (-9/32) + (27/32) + d = 0

d = 0 - (0 3 × (-3/32) + 2 × (-9/32) + (27/32)) = -9/32

The cubic function is therefore f(x) = (-3/32)·x³ + (-9/32)·x² + (27/32)·x + (-9/32).

4 0

2 years ago

a. A 2017 poll found that 56% of college students were very confident that their major will lead to a good job. If 15 college s

lesya [120]

Answer:

0.01083 or 1.083%

Step-by-step explanation:

This problem can be modeled as a binomial probability model with probability of success p = 0.56.

The probability of x=13 successes (a college student being very confident their major would lead to a good job) in a number of trials of n=15 is:

$P(X=x) = \frac{n!}{(n-x)!x!} *p^x*(1-p)^{n-x}\\P(X=13) = \frac{15!}{(15-13)!13!} *0.56^{13}*(1-0.56)^{15-13}\\P(X=13) = 0.01083=1.083\%$

The probability is 0.01083 or 1.083%.

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2 years ago

5x-7=118 solve for the variable x

myrzilka [38]

X=25 ...... ................

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3 years ago

Read 2 more answers

What are the solutions of x^2-2x+5=0

Damm [24]

Answer:

1 + 2i and 1 – 2i

3 0

3 years ago

What is the factored form of 3x^2 + 23x - 36?

alex41 [277]

The factored form is (3x-4)(x+9)

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3 years ago