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3 years ago

Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = ln(x2 + 5x + 12), [−3, 1]

Mathematics

1 answer:

Bezzdna [24]3 years ago

8 0

A graphing calculator shows the minimum to be located at the vertex of the quadratic, x = -2.5, and the maximum to be located at the right end of the interval.

The absolute maximum value of f(x) is ln(18) ≈ 2.89037.
The absolute minimum value of f(x) is ln(5.75) ≈ 1.74920.

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Daniel invests $2,037 in a retirement account with a fixed annual interest rate of 6% compounded 6 times per year. What will the

notka56 [123]

Answer:

$\$5294.72$

Step-by-step explanation:

GIVEN: Daniel invests $\$2,037$ in a retirement account with a fixed annual interest rate of $6\%$ compounded $6$ times per year.

TO FIND: What will the account balance be after $16$ years

SOLUTION:

Amount invested by Daniel $=\$2037$

Annual interest rate $=6\%$

Total amount generated by compound interest is $=P(1+\frac{r}{n})^n^t$

Here Principle amount $P=\$2037$

rate of interest $r=6\%$

number of times compounding done in a year $n=6$

total duration of time $nt=16\text{ years}$

putting values we get

= $2037(1+\frac{6}{6\times100})^1^6$

$=2037(\frac{101}{100})^1^6$

$=\$5294.72$

Hence the total balance after $16\text{ years}$ will be $\$5294.72$

4 0

3 years ago

Which two quadrants have negative x-values?

mart [117]

Answer:

II and III ( 2 and 3)

Step-by-step explanation:

The quadrants are numbered counter clockwise, with the top right being number I

II I

III IV

The ones having negative x values are II and III ( 2 and 3)

3 0

2 years ago

A parallel system functions whenever at least one of its components works. Consider a parallel system of 5 components, and suppo

Aneli [31]

Answer:

Probability that component 4 works given that the system is functioning = 0.434 .

Step-by-step explanation:

We are given that a parallel system functions whenever at least one of its components works.

There are parallel system of 5 components and each component works independently with probability 0.4 .

Let <em>A = Probability of component 4 working properly, P(A) = 0.4 .</em>

<em>Also let S = Probability that system is functioning for whole 5 components, P(S)</em>

Now, the conditional probability that component 4 works given that the system is functioning is given by P(A/S) ;

P(A/S) = {Means P(component 4 working and system also working)

divided by P(system is functioning)}

P(A/S) = {In numerator it is P(component 4 working) and in

denominator it is P(system working) = 1 - P(system is not working)}

Since we know that P(system not working) means that none of the components is working in system and it is given with the probability of 0.6 and since there are total of 5 components so P(system working) = 1 - $0.6^{5}$ .