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3 years ago

Can someone plz help me solved this problem! I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!

Mathematics

1 answer:

sergeinik [125]3 years ago

4 0

Answer:

a). 8(x + a)

b). 8(h + 2x)

Step-by-step explanation:

a). Given function is, f(x) = 8x²

For x = a,

f(a) = 8a²

Now substitute these values in the expression,

$\frac{f(x)-f(a)}{x-a}$ = $\frac{8x^2-8a^2}{x-a}$

= $\frac{8(x^2-a^2)}{(x-a)}$

= $\frac{8(x-a)(x+a)}{(x-a)}$

= 8(x + a)

b). $\frac{f(x+h)-f(x)}{h}$ = $\frac{8(x+h)^2-8x^2}{h}$

= $\frac{8(x^2+h^2+2xh)-8x^2}{h}$

= $\frac{8x^2+8h^2+16xh-8x^2}{h}$

= (8h + 16x)

= 8(h + 2x)

You might be interested in

Natalia solved the problem 74.4/12=6.2. complete the model with partial products check Natalia's work using multiplication

tia_tia [17]

Answer:

Natalia's work is wrong.

Step-by-step explanation:

Natalia divided a decimal number by an entire number. Since division is a operation derived from multiplication, the best approach to check if work was good is multiplying the given result by denomination, that is:

1) $x = 6.2\times 12$ Given.

2) $x = \left(6+0.2\right)\times 12$ Definition of addition.

3) $x = 6\times 12 + 0.2\times 12$ Distributive property.

4) $x = 72 + \frac{2}{10}\times 12$ Definitions of multiplication and decimal number.

5) $x = 72 +[2\cdot (10)^{-1}]\cdot 12$ Definition of division/Associative property.

6) $x = 72 + [2\cdot 12]\cdot (10)^{-1}$ Associative property.

7) $x = 72 + 24\cdot 10^{-1}$ Definition of multiplication.

8) $x = 72 + \frac{24}{10}$ Definition of divsion.

9) $x = 72 + 2.4$ Defintion of decimal number.

10) $x = 74.4$ Definition of addition/Result

Natalia's work is wrong.

5 0

2 years ago

Assume that there is a 4% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive wit

kap26 [50]

Answer:

a) 99.84% probability that during a year, you can avoid catastrophe with at least one working drive

b) 99.999744% probability that during a year, you can avoid catastrophe with at least one working drive

Step-by-step explanation:

For each disk drive, there are only two possible outcomes. Either it works, or it does not. The disks are independent. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

4% rate of disk drive failure in a year.

This means that 96% work correctly, $p = 0.96$

a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive?

This is $P(X \ geq 1)$ when $n = 2$

We know that either none of the disks work, or at least one does. The sum of the probabilities of these events is decimal 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$ . So

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{2,0}.(0.96)^{0}.(0.04)^{2} = 0.0016$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0016 = 0.9984$

99.84% probability that during a year, you can avoid catastrophe with at least one working drive

b. If copies of all your computer data are stored on four independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive?

This is $P(X \ geq 1)$ when $n = 4$