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2 years ago

If P > Q is true and Q is true then p is

Mathematics

1 answer:

Illusion [34]2 years ago

7 0

q>p

Step-by-step explanation:

im sorry if its wrong im only in 7th grade i think its right.... :)

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If mn, solve for x. (3x + 9) (x + 21)

Sloan [31]

3x. + 63x + 9x + 189

Step-by-step explanation:

Use distributive law, in other words multiply the first bracket terms by the second bracket terms 

6 0

2 years ago

Use the definition of a Taylor series to find the first three non zero terms of the Taylor series for the given function centere

Ket [755]

Answer:

$e^{4x}=e^4+4e^4(x-1)+8e^4(x-1)^2+...$

$\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n$

Step-by-step explanation:

Taylor series expansions of f(x) at the point x = a

$\text{f}(x)=\text{f}(a)+\text{f}\:'(a)(x-a)+\dfrac{\text{f}\:''(a)}{2!}(x-a)^2+\dfrac{\text{f}\:'''(a)}{3!}(x-a)^3+...+\dfrac{\text{f}\:^{(r)}(a)}{r!}(x-a)^r+...$

This expansion is valid only if $\text{f}\:^{(n)}(a)$ exists and is finite for all $n \in \mathbb{N}$ , and for values of x for which the infinite series converges.

$\textsf{Let }\text{f}(x)=e^{4x} \textsf{ and }a=1$

$\text{f}(x)=\text{f}(1)+\text{f}\:'(1)(x-1)+\dfrac{\text{f}\:''(1)}{2!}(x-1)^2+...$

$\boxed{\begin{minipage}{5.5 cm}\underline{Differentiating $e^{f(x)}$}\\\\If $y=e^{f(x)}$, then $\dfrac{\text{d}y}{\text{d}x}=f\:'(x)e^{f(x)}$\\\end{minipage}}$

$\text{f}(x)=e^{4x} \implies \text{f}(1)=e^4$

$\text{f}\:'(x)=4e^{4x} \implies \text{f}\:'(1)=4e^4$

$\text{f}\:''(x)=16e^{4x} \implies \text{f}\:''(1)=16e^4$

Substituting the values in the series expansion gives:

$e^{4x}=e^4+4e^4(x-1)+\dfrac{16e^4}{2}(x-1)^2+...$

Factoring out e⁴:

$e^{4x}=e^4\left[1+4(x-1)+8}(x-1)^2+...\right]$

Taylor Series summation notation:

$\displaystyle \text{f}(x)=\sum^{\infty}_{n=0} \dfrac{\text{f}\:^{(n)}(a)}{n!}(x-a)^n$

Therefore:

$\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n$

7 0

1 year ago

A bank loans you $5000 for school to be repaid with 4% interest how much do you owe after 2 years? 4 years? and 7 years?

Gemiola [76]

After 2 years-$4608
After 4 years-$4246.73
After 7 years-$3757.24

8 0

2 years ago

certain computer virus can damage any file with probability 35%, independently of other files. Suppose this virus enters a folde

Ksivusya [100]

Answer:

0.623 is the probability that between 800 and 850 files get damaged.

Step-by-step explanation:

We are given the following information:

We treat virus can damage computer as a success.

P( virus can damage computer) = 35% = 0.35

The conditions for normal distribution are satisfied.

By normal approximation:

$\mu = np = 2400(0.35) = 840\\\sigma = \sqrt{np(1-p)} = \sqrt{2400(0.35)(1-0.35)} = $$23.36$

We have to evaluate probability that between 800 and 850 files get damaged.

$P(800 \leq x \leq 850) = P(\displaystyle\frac{800 - 840}{23.36} \leq z \leq \displaystyle\frac{850-840}{23.36}) = P(-1.712 \leq z \leq 0)\\\\= P(z \leq 0.428) - P(z < -1.712)\\= 0.666 - 0.043 = 0.623 = 62.3\%$

$P(800 \leq x \leq 850) = 62.3\%$

0.623 is the probability that between 800 and 850 files get damaged.

8 0

2 years ago

A triangle has side lengths of 11 cm and 7 cm. Which could be the value of the third side, 19 cm or 17 cm ?

9966 [12]

Answer:

By the triangle side length theorem, the sum of the two shorter sides has to be equal to or larger than the third side. Thus, we can write the following inequation.

≥

, where a and b are the shorter sides and c the longest.

11, 9 and 15 satisfies this inequality while 11, 9 and 20 doesn't.

Justification:

The reason for this rule is simple; it's because if the longest side is longer than the sum of the two shorter sides, this means that the shorter sides aren't long enough to connect with the longest side, thus rendering the shape a collection of lines and disqualifying the possibility of having a triangle, which was our objective.

Practice exercises:

Which of the following triangles is possible?

a) 4,6 and 14

b) 5,11 and 16

c) 1,3,6

D). 12,19 and 26

Find the smallest possible value of a to make the following an actual triangle :

Hopefully this helps:

Step-by-step explanation:

8 0

3 years ago