Ask question

Ask question

All categories

3 years ago

14

What is the exact value of

1" title=" \sin(\frac{5\pi}{12} ) " alt=" \sin(\frac{5\pi}{12} ) " align="absmiddle" class="latex-formula">?

1 answer:

Sergeeva-Olga [200]3 years ago

3 0

The answer is: 0.02274421908

You might be interested in

Use the polar representation to write the following in the form a + bi (a) (-1+ i)^7 (b) (1+v3i)^10

ira [324]

Answer with Step-by-step explanation:

For any complex number x+iy the polar form is represented as

$z=re^{i\theta }$

where

$r^{2}=x^2+y^2\\\\tan(\theta )=\frac{y}{x}$

Part a) x+iy = -1+i

Thus $r=\sqrt{-1^2+1^2}=\sqrt{2}\\\\ \theta _{1}=tan^{-1}(\frac{-1}{1})=\frac{-\pi }{4}$

Thus using De-Morvier's theorem

$(-1+i)^7=(\sqrt{2}e^{i\frac{-\pi }{4}})^7\\\\\therefore (-1+i)^7=2^{7/2}\cdot e^{\frac{i-\pi }{28}}$

Part 2) x+iy = 1+3i

Thus $r=\sqrt{1^2+3^2}=\sqrt{10}\\\\ \theta _{1}=tan^{-1}(\frac{3}{1})=1.25$

Thus using De-Morvier's theorem

$(1+3i)^{10}=(\sqrt{10}e^{1.25i})^{10}\\\\\therefore (1+3i)^{10}=10^{5}\cdot e^{12.5i}$

3 0

3 years ago

Can u pls give a clear explanation & word it out how u got the answer without using big words. Thank u

gizmo_the_mogwai [7]

A.

We can rewrite the squared in two ways.

The first way is to rewrite it as a multiplication, this is:

$(y-6)^2=(y-6)(y-6)$

The second way to rewrite the squared is by using the formula for this kind of product:

$(y-6)^2=y^2+2(-6)(y)+(-6)^2$

B.

Once again we can find the final result using each of the options given in part A, for the first option we have:

$\begin{gathered} (y-6)^2=(y-6)(y-6) \\ =y^2-6y-6y+36 \\ =y^2-12y+36 \end{gathered}$

For the second option we have:

$\begin{gathered} (y-6)^2=y^2+2(-6)(y)+(-6)^2 \\ =y^2-12y+36 \end{gathered}$

No matter which way we choose the answer for the squared is:

$y^2-12y+36$

3 0

1 year ago

You are considering the purchase of a closed circuit TV monitoring system for your store. The quarterly physical inventory has s

Tcecarenko [31]

If quarterly shrinkage (every 3 months) is 2.5%, then multiplying by $875,495 gives a value of 21887.38, or an average monthly shrinkage of 21887.38 / 3 = $7,295.79.For an employee to monitor the CCTV, it would cost ($7.5/h)(11 h/d)(30 d/m) = $2,475/month. Therefore, it is much cheaper (around 2/3 cheaper) to have an employee monitor CCTV rather than to allow the high shrinkage rate.

7 0

4 years ago

For the point P(21, 24) and Q(26, 27) , find the distance d(P, Q) and the coordinates of the midpoint M of the segment PQ

aleksley [76]

Answer:

d(P,Q) = 5.83 units

Mid-point = (23.5,25.5)

Step-by-step explanation:

Given points are:

P(21,24) = (x1,y1)

Q(26,27) = (x2,y2)

The distance formula is given by:

$d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Here (x1,y1) are the coordinates of first point and (x2,y2) are coordinates of second point.

Putting the given values in the formula

$d(P,Q) = \sqrt{(26-21)^2+(27-24)^2}\\= \sqrt{(5)^2+(3)^2}\\=\sqrt{25+9}\\=\sqrt{34}$

$= 5.830952$

Rounding off: 5.83 units

The mid-point of two points is given by the formula:

$M = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})$

Putting the values:

$M = (\frac{21+26}{2} , \frac{24+27}{2})\\=(\frac{47}{2} , \frac{51}{2})\\=(23.5, 25.5)$

Hence,

d(P,Q) = 5.83 units

Mid-point = (23.5,25.5)

3 0

3 years ago

Math Homework Jim Thompson June 13th

Fittoniya [83]

Answers:

3. E) -0.8
4. True
5. True
6. True
7. D) 17.62%

=========================================

Explanations:

3. We have negative correlation because the regression line is going downhill (move from left to right). The points are fairly close to the same regression line, so I'd say we have either moderate or fairly strong negative correlation. That means r is fairly close to -1. It's not -1 exactly since that would have to mean all points are on the same line.

-----------------

4. Negative correlation goes with negative r values. Refer to problem 3. Positive correlation goes to positive r values. The r value will most likely not equal the slope value, but they share the same sign.

----------------

5. If r is close to +1, then we have fairly strong positive linear correlation. If r is close to -1, then we have fairly strong negative linear correlation. If r = 0 or close to it, then we should use some other kind of regression tool. Or perhaps the data points are simply randomly scattered about and they have no pattern at all.

-----------------

6. Refer to problem 5.

-----------------

7. Plug in x = 15 and you should find that y = -0.632(15)+27.1 = 17.62, which means that the estimated tip is roughly 17.62% of the bill.

8 0

3 years ago