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3 years ago

A) What is the derivative of x^2 - 6x +36.

Mathematics

2 answers:

Aleks04 [339]3 years ago

5 0

Answer:

2x-6

Step-by-step explanation:

ivolga24 [154]3 years ago

5 0

Answer:

$2x - 6$

$x=3 \rightarrow \ minimum \ point$

Step-by-step explanation:

$f(x) = x^2 - 6x +36$

The derivative is: $f'(x)= 2x - 6$

To calculate the max/min point of the function, we use the first derivative and put it equal to zero (if needed)

$f'(x) = 2x - 6 = 0\\2x - 6 = 0\\2x = 6\\x = 3$

To check whether this point is max or min, we substitute the value of x in the second derivative of the function. If the answer is positive, the value is minimum. If the answer is negative, the value is minimum.

$f''(x) = 2$

The second derivative is positive, hence $x = 3$ is minimum.

You might be interested in

Three equivalent forms of a quadratic function are given. Select the form which reveals the zeros of f(x) without needing to alt

Vanyuwa [196]

Answer:

Read explanation and apply it

Step-by-step explanation:

The vertex form of a quadratic equation is $f(x)=a(x-h)^2+k$

The general form of a quadratic equation is $f(x)=ax^2+bx+c$

The factored form of a quadratic equation is $f(x)=a(x-p)(x-q)$

The one which reveals the zeros of f(x) without needing to alter the equation is the factored form $f(x)=a(x-p)(x-q)$ .

When f(x)=0, we have $a(x-p)(x-q)=0$

The values of x are $x=p$ and $x=q$ .

I hope this guides you to choose the correct answer.

4 0

3 years ago

Let n be the smallest positive integer that is a multiple of 75 and has exactly 75 positive integral divisors, including itself

Juli2301 [7.4K]

Answer:

$n=2^4 3^4 5^2 =32400$ and then we have:

$\frac{n}{75}=\frac{2^4 3^4 5^2}{3 5^2}=432$

Step-by-step explanation:

From the info given by the problem we need an integer defined as the smallest positive integer that is a multiple of 75 and have 75 positive integral divisors, and we are assuming that 1 is one possible divisor.

Th first step is find the prime factorization for the number 75 and we see that

$75=3 5^2$

And we know that 3 =2+1 and 5=3+2 and if we replace we got:

$75 = (2+1)(4+1)^2 = (2+1)(4+1)(4+1)$

And in order to find 75 integral divisors we need to satisify this condition:

$n= a^{r_1 -1}_1 a^{r_2 -1}_2 *......$ such that $a_1 *a_2*....=75$

For this case we have two prime factors important 3 and 5. And if we want to minimize n we can use a prime factor like 2. The least common denominator between 2 and 4 is LCM(2,4) =4. So then the need to have the prime factors 2 and 3 elevated at 4 in order to satisfy the condition required, and since 5 is the highest value we need to put the same exponent.

And then the value for n would be given by:

$n=2^4 3^4 5^2 =32400$ and then we have:

$\frac{n}{75}=\frac{2^4 3^4 5^2}{3 5^2}=432$

8 0

4 years ago

A basketball coach kept stats for his team in free throw percentage and steals (among others). At the last game, Erin's free thr

Setler79 [48]

Answer:

Due to the higher z-score, she did better in the free throw category.

Step-by-step explanation:

Z-score:

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

She did better in the category that she had the higher z-score:

Free-throws:

Her free throw percentage was 79%, which means that $X = 79$