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marshall27 [118]
3 years ago
14

Find the exact value. cos225°

Mathematics
2 answers:
Free_Kalibri [48]3 years ago
8 0

Answer:

cos(225$^{\circ}$) = -\sqrt{2} /2 \approx-0.707

Step-by-step explanation:

We can use the next table which show you the simplest algebraic values of trigonometric functions. As you can see:

cos(45)=\frac{\sqrt{2}}{2}

And actually:

cos(45+n90)=\pm\frac{\sqrt{2} }{2} \hspace{3}n\in Z

As you can see it can be positive or negative, it depends on the quadrant. You maynotice that the cosine function is positive in the first quadrant and the fourth quadrant, and negative in the second quadrant and the third quadrant. 225 is a multiple of 45, (45+2*90=45+180=225) also 225 is in the third quadrant. So:

cos(45+180)=cos(225)=-\frac{\sqrt{2} }{2} \approx -0.707

Sedaia [141]3 years ago
3 0
Exact form: -square root 2/2 (I don't have a square root symbol)
Decimal form: -0.70710678

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Problem 10-01 NPV A project has an initial cost of $66,950, expected net cash inflows of $14,000 per year for 9 years, and a cos
svlad2 [7]

Answer:

NPV = $13,676.33

Step-by-step explanation:

First, find the present value of the cash inflows. You can solve this question using a Financial calculator;

14,000 per year is a recurring cashflow hence the PMT

PMT = 14,000

I/Y = 10%

N= 9

FV =0

then CPT PV = 80,626.33

NPV = -Initial investment + PV of future cash inflows

NPV = -66,950 + 80,626.33

NPV = $13,676.33

"NPV" button, then , then "CPT".

The answer to the NPV = $13,676.33

5 0
2 years ago
Please help, very confused
miss Akunina [59]

Answer:

1.

-3x + 8y = -5

6x + 2y = -8

Set the equations to a common variable.

-3x + 8y = -5 → 8y = 3x - 5 → y = 3/8x - 5/8

6x + 2y = -8 → 2y = -6x - 8 → y = -3x - 4

Set the equations equal to each other.

3/8x - 5/8 = -3x - 4

Combine like terms.

3x + 3/8x = -4 + 5/8

3.375x = -3.375

Divide by 3.375

x = -1

Plug x back in to find y.

-3x + 8y = -5

-3(-1) + 8y = -5

3 + 8y = -5

8y = -8

y = -1

answer: (-1, -1)

2.

3x + 2y = -16

-3x - 8y = 46

Set the equations to a common variable.

3x + 2y = -16 → 2y = -3x - 16 → y = -3/2x - 8

-3x - 8y = 46 → -8y = 3x + 46 → y = -3/8x - 23/4

Set the equations equal to each other.

-3/2x - 8 = -3/8x - 23/4

Combine like terms.

-9/8x = 9/4

or

-1.125x = 2.25

Divide by -1.125

x = -2

Plug x back in to find y.

3(-2) + 2y = -16

-6 + 2y = -16

2y = -10

y = -5

answer: (-2, -5)

6 0
3 years ago
Read 2 more answers
You play a game on your phone. For every correct move you make, you receive 50 points. For every second that it takes you to com
Vladimir79 [104]

Answer:

2005 points

Step-by-step explanation:

1. 35x50=750

2. 2 min. 45 sec.=(-165 sec.)

3. 500x5=2500

4. 2500-495=2005

Hope this helped!!:)

6 0
3 years ago
X-1.6=2.4+0.8x solve for x. <br><br>What did I do wrong?
trapecia [35]

\bf x-1.6=2.4+0.8x\implies \stackrel{\textit{subtracting 2.4}}{x-4=0.8x}\implies \stackrel{\textit{subtracting x}}{-4=0.8x-x} \\\\\\ -4=-0.2x\implies \cfrac{-4}{-0.2}=x\implies 20=x

3 0
3 years ago
Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for t
rjkz [21]

Answer:

COV (all stocks) = 0.55

COV (stocks and bonds) = 0.82

Step-by-step explanation:

Coefficient of Variation is used to measure variability.

It is defined as the ration of standard deviation and the mean.

It can be used to compare variability of two population or two samples.

Formula:

\text{Coefficient of Variation} = \displaystyle\frac{\text{Standard Deviation}}{\text{Mean}}

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}

where x_i are data points, \bar{x} is the mean and n is the number of observations.

Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}

x: 14, 0, 39, 25, 32, 27, 28, 14, 14, 15

Mean = \frac{208}{10} = 20.8

Standard~Deviation = \sqrt{\frac{1169.6}{9} } = 11.39

Coefficient~of~Variation = \frac{11.39}{20.8} = 0.55

y = 6, 2, 29, 17, 26, 17, 17, 2, 3, 5

Mean = \frac{124}{10} = 12.4

Standard~Deviation = \sqrt{\frac{924.4}{9} } = 10.13

Coefficient~of~Variation = \frac{10.13}{12.4} = 0.82%

Since coefficient of variation of x is less compared to y, thus it could be said bonds does not reduce overall risk of an investment portfolio.

6 0
3 years ago
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