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2 years ago

Find all polar coordinates of point P where P = ordered pair 5 comma negative pi divided by 6 .

Mathematics

1 answer:

max2010maxim [7]2 years ago

6 0

Answer:

The correct option is B.

Step-by-step explanation:

If polar coordinates of point P are

$P=(r,\theta)$

Where, r is real number and θ is in radian, then all polar coordinates of point P are defined as

$P=(r,\theta+2n\pi)$

$P=(-r,\theta+(2n+1)\pi)$

The given coordinates are $P(5,-\frac{\pi}{6})$ . So, all polar coordinates of point P are

$P=(5,-\frac{\pi}{6}+2n\pi)$

$P=(-5,-\frac{\pi}{6}+(2n+1)\pi)$

Therefore correct option is B.

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Daniel deposited $500 into a savings account and after 8 years, his investment is worth $807.07. The equation A = d(1.005)12t mo

shtirl [24]

Answer:

Step-by-step explanation:

The equation A = d(1.005)^12t modelling the value of Daniel’s investment shows a monthly compounded interest. This means that the interest is compounded 12 times in a year.

We can confirm by inputting the given values

t = 8 years

d = 509

Therefore,

A = 500(1.005)12 × 8

A = 500(1.005)^96

A = $807.07

Therefore, the true statements are

Increases

Exponential

Never Decrease

5 0

2 years ago

Hailey is shopping at a department store during a 20% off everything sale. She also has a coupon for $5.00 off the sale amount.

Kipish [7]

Possible inequality:

= $x\leq 87.50$

4 0

2 years ago

Read 2 more answers

Two processes are used to produce forgings used in an aircraft wing assembly. Of 200 forgings selected from process 1, 10 do not

tangare [24]

Answer:

$\bar p_1=0.05\\\bar p_2=0.067$

b-Check illustration below

c.(-0.0517,0.0177

Step-by-step explanation:

a.let $p_1 \& p_2$ denote processes 1 & 2.

For $p_1$ : T1=10,n1=200

For $p_2$ :T2=20,n2=300

Therefore

$\bar p_1=\frac{t_1}{N_1}=\frac{10}{200}=0.05\\\bar p_2=\frac{t_2}{N_2}=\frac{20}{300}=0.067$

b. To test for hypothesis:-

$H_0:p_1=p_2\\H_A=p_1\neq p_2\\\alpha=0.05$

ii.For a two sample Proportion test

$Z=\frac{\bar p_1-\bar p_2}{\sqrt(\bar p(1-\bar p)(\frac{1}{n_1}+\frac{1}{n_2})}\\$

iii. for $\frac{\alpha}{2}=(-1.96,+1.96)$ (0.5 alpha IS 0.025),

reject $H_o$ if $|Z|>1.96$

iv. Do not reject $H_o$ . The noncomforting proportions are not significantly different as calculated below:

$z=\frac{0.050-0.067}{\sqrt {(0.06\times0.94)\times \frac{1}{500}}}$

z=-0.78

c. $(1-\alpha).100\%$ for the p1-p2 is given as:

$(\bar p_1-\bar p_2)\pm Z_0_._5_\alpha \times \sqrt \frac{ \bar p_1(1-\bar p_1)}{n_1}+\frac{\bar p_2(1-\bar p_2)}{n_2}\\\\=(0.05-0.067)\pm 1.645 \times \sqrt \ \frac{0.05+0.95}{200}+\frac{0.067+0.933}{300}\\$

=(-0.0517,+0.0177)

*CI contains o, which implies that proportions are NOT significantly different.

4 0

2 years ago

in the year 2010, the luxury bike industry had two bike manufactures splendor and passion with the market shares of 30% and 70%,

kari74 [83]

Answer: 50%

Step-by-step explanation:

In 2010, there were only 2 bike manufacturers and they had market shares of 30% and 70%.

A new manufacturer joins the market and captures 10% of the market share and Splendor increases to 40% of market share.

Market shares:

Yamaha = 10%

Splendor = 40%

Passion = 100% - 10% - 40%

= 50%

8 0

2 years ago

What is the horizontal asymptote for y(t) for the differential equation dy dt equals the product of 2 times y and the quantity 1

marta [7]

First, we need to solve the differential equation.
$\frac{d}{dt}\left(y\right)=2y\left(1-\frac{y}{8}\right)$
This a separable ODE. We can rewrite it like this:
$-\frac{4}{y^2-8y}{dy}=dt$
Now we integrate both sides.
$\int \:-\frac{4}{y^2-8y}dy=\int \:dt$
We get:
$\frac{1}{2}\ln \left|\frac{y-4}{4}+1\right|-\frac{1}{2}\ln \left|\frac{y-4}{4}-1\right|=t+c_1$
When we solve for y we get our solution:
$y=\frac{8e^{c_1+2t}}{e^{c_1+2t}-1}$
To find out if we have any horizontal asymptotes we must find the limits as x goes to infinity and minus infinity.
It is easy to see that when x goes to minus infinity our function goes to zero.
When x goes to plus infinity we have the following:
$$$\lim_{x\to\infty} f(x)$$=y=\frac{8e^{c_1+\infty}}{e^{c_1+\infty}-1} = 8$
When you are calculating limits like this you always look at the fastest growing function in denominator and numerator and then act like they are constants.
So our asymptote is at y=8.

3 0

2 years ago