All categories

3 years ago

Y= 175÷x+z when x=17 and z=8

Mathematics

1 answer:

denpristay [2]3 years ago

3 0

18.29
175 divided by 17 plus 8, use PEMDAS

You might be interested in

Z^4-5(1+2i)z^2+24-10i=0

mixer [17]

Using the quadratic formula, we solve for $z^2$ .

$z^4 - 5(1+2i) z^2 + 24 - 10i = 0 \implies z^2 = \dfrac{5+10i \pm \sqrt{-171+140i}}2$

Taking square roots on both sides, we end up with

$z = \pm \sqrt{\dfrac{5+10i \pm \sqrt{-171+140i}}2}$

Compute the square roots of -171 + 140i.

$|-171+140i| = \sqrt{(-171)^2 + 140^2} = 221$

$\arg(-171+140i) = \pi - \tan^{-1}\left(\dfrac{140}{171}\right)$

By de Moivre's theorem,

$\sqrt{-171 + 140i} = \sqrt{221} \exp\left(i \left(\dfrac\pi2 - \dfrac12 \tan^{-1}\left(\dfrac{140}{171}\right)\right)\right) \\\\ ~~~~~~~~~~~~~~~~~~~~= \sqrt{221} i \left(\dfrac{14}{\sqrt{221}} + \dfrac5{\sqrt{221}}i\right) \\\\ ~~~~~~~~~~~~~~~~~~~~= 5+14i$

and the other root is its negative, -5 - 14i. We use the fact that (140, 171, 221) is a Pythagorean triple to quickly find

$t = \tan^{-1}\left(\dfrac{140}{171}\right) \implies \cos(t) = \dfrac{171}{221}$

as well as the fact that

$0$

$\sin\left(\dfrac t2\right) = \sqrt{\dfrac{1-\cos(t)}2} = \dfrac5{\sqrt{221}}$

(whose signs are positive because of the domain of $\frac t2$ ).

This leaves us with

$z = \pm \sqrt{\dfrac{5+10i \pm (5 + 14i)}2} \implies z = \pm \sqrt{5 + 12i} \text{ or } z = \pm \sqrt{-2i}$

Compute the square roots of 5 + 12i.

$|5 + 12i| = \sqrt{5^2 + 12^2} = 13$

$\arg(5+12i) = \tan^{-1}\left(\dfrac{12}5\right)$

By de Moivre,

$\sqrt{5 + 12i} = \sqrt{13} \exp\left(i \dfrac12 \tan^{-1}\left(\dfrac{12}5\right)\right) \\\\ ~~~~~~~~~~~~~= \sqrt{13} \left(\dfrac3{\sqrt{13}} + \dfrac2{\sqrt{13}}i\right) \\\\ ~~~~~~~~~~~~~= 3+2i$

and its negative, -3 - 2i. We use similar reasoning as before:

$t = \tan^{-1}\left(\dfrac{12}5\right) \implies \cos(t) = \dfrac5{13}$

$1 < \tan(t) < \infty \implies \dfrac\pi4 < t < \dfrac\pi2 \implies \dfrac\pi8 < \dfrac t2 < \dfrac\pi4$

$\cos\left(\dfrac t2\right) = \dfrac3{\sqrt{13}}$

$\sin\left(\dfrac t2\right) = \dfrac2{\sqrt{13}}$

Lastly, compute the roots of -2i.

$|-2i| = 2$

$\arg(-2i) = -\dfrac\pi2$

$\implies \sqrt{-2i} = \sqrt2 \, \exp\left(-i\dfrac\pi4\right) = \sqrt2 \left(\dfrac1{\sqrt2} - \dfrac1{\sqrt2}i\right) = 1 - i$

as well as -1 + i.

So our simplified solutions to the quartic are

$\boxed{z = 3+2i} \text{ or } \boxed{z = -3-2i} \text{ or } \boxed{z = 1-i} \text{ or } \boxed{z = -1+i}$

3 0

1 year ago

#1.) What is the slope between point C and Point D? *Please Show All Work*

ANTONII [103]

Answer:

1. $m = slope = \frac{12}{7}$

2. $y = \frac{12}{7}x$

3. Domain: 0≤x≤7

Range: 0≤y≤12

Step-by-step explanation:

1. Assuming 1 unit = 1 box on the grid, therefore, coordinates of C and D would be:

C(0, 0),

D(7, 12)

$Slope = m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{12 - 0}{7 - 0} = \frac{12}{7}$

2. Equation of the using the slope-intercept formula, $y = mx + b$ , where,

$m = slope = \frac{12}{7}$

b = y-intercept, which is where the line CD cuts the y-axis = 0

Plug in the values for m and b into the formula to get the equation of the line:

$y = \frac{12}{7}x + 0$

$y = \frac{12}{7}x$

3. The domain for C to D part = all x-values = 0≤x≤7

The range = all y-values = 0≤y≤12

3 0

4 years ago

An analyst for a large credit card company is going to conduct a survey of customers to examine their household characteristics.

zheka24 [161]

Answer:

We can conclude that the value of 1732 is a statistic who represent the sample selected. And the value of 1622 represent the population mean from all the customers with the previous data.

Step-by-step explanation:

Previous concepts

A statistic or sample statistic "is any quantity computed from values in a sample", for example the sample mean, sample proportion and standard deviation

A parameter is "any numerical quantity that characterizes a given population or some aspect of it".

Solution to the problem

For this case the analyst knows that from previous records that the mean for all the customers (that represent the population of interest) is $\mu = 1622$

He have a random sample of n =500 customers from the previous month and he knows that 1732 represent the sample mean for the selected customers calculated from the following formula:

$\bar X = \frac{\sum_{i=1}^{500} X_i}{500}= 1732$

So on this case we can conclude that the value of 1732 is a statistic who represent the sample selected. And the value of 1622 represent the population mean from all the customers with the previous data.

6 0

3 years ago

Please help me!! Lots of love!!

Marizza181 [45]

Answer:

D) 2

Step-by-step explanation:

write 8 in exponential form which is 2^3

now simplyfy the root which equals 2

2 is the answer.

4 0

3 years ago

Erica solved the equation −5x − 25 = 78; her work is shown below. Identify the error and where it was made.

Alja [10]

Answer:

Step 1: She should have added 25 to both sides

6 0

3 years ago