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2 years ago

-67 = 6x - 1

1 answer:

5 0

-66=6x
x=-11

-4e=28
e=-7

-40=-5q
q=8

-96=12t
t=-8

10k=250
k=25

-x=-72
X=72

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Convert from rectangular to polar coordinates: note: choose rr and θθ such that rr is nonnegative and 0≤θ<2π0≤θ<2π (a)(9,0

DochEvi [55]

Answer:

Step-by-step explanation:

Convert rectangle (x , y) to polar coordinates ( r , θ)

$x=r \cos \theta, y= r \sin \theta$

$r=\sqrt{x^2+y^2} , \theta =tan^-^1 (\frac{y}{x} )$

a) converts (9, 0) to polar coordinates ( r , θ)

$r=\sqrt{x^2+y^2} \\\\=\sqrt{9^2+0} \\\\=9$

$\theta= \tan^-^1 (\frac{0}{9} )\\\\=0$

b) Convert $(18,\frac{18}{\sqrt{3} } )$ to polar coordinates ( r, θ)

$r = \sqrt{18^2+(\frac{18}{\sqrt{3} })^2 } \\\\=\sqrt{324+108} \\\\=\sqrt{432}$

$\frac{x}{y} \theta = \tan^-^1(\frac{\frac{18}{\sqrt{3} } }{18} )\\\\= \tan ^-^1(\frac{1}{\sqrt{3} } )\\\\= \frac{\pi}{6}$

c) converts (-5, 5) to polar coordinates ( r , θ)

$r =\sqrt{(-5)^2+(5)^2} \\\\=\sqrt{50} \\\\=5\sqrt{2}$

$\theta=\tan^-^1(\frac{5}{-5} )\\\\= \tan^-^1(-1)\\\\=\frac{3\pi}{4}$

d) converts (-1, √3) to polar coordinates ( r , θ)

$r=\sqrt{(-1)^2+(\sqrt{3})^2 } \\\\= \sqrt{4} \\\\=2$

$\theta=\tan^-^1(\frac{\sqrt{3} }{-1} )\\\=\tan^-^1(-\sqrt{3} )\\\\=\frac{2\pi}{3}$

$= \frac{2\pi}{\sqrt{3} }$

6 0

3 years ago

Jerome went on a hike. He climbed 3/4 of a mile in 2/3 of an hour. What was his hiking speed in miles per hour?

Anvisha [2.4K]

1 hour = 60 mins 1 mile = 60 mins 3/4 = 45 mins. 2/3 = 40 mins. So 45+ 40 = 1 hour and 25 mins.

6 0

2 years ago

A formula is given that states 6x-k=wk. Solve this formula for k in terms of the other variables in the equation.

nadya68 [22]

Answer:

k = 6x/(w + 1)

Step-by-step explanation:

6x - k = wk

6x = wk + k

k(w+1) = 6x

k = 6x/(w + 1)

3 0

3 years ago

What does the point (1,8) mean in this situation?

sesenic [268]

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▹ Answer

<em>There are 8 chocolate chips in one pancake.</em>

▹ Step-by-Step Explanation

The x is labeled as Number of Pancakes.

The y is labeled as Number of Chocolate Chips

Therefore, the 1 represents the pancakes and the 8 represents the amount of chocolate chips per pancake. This would be stated as:

There are 8 chocolate chips in one pancake.

Hope this helps!

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Brainliest is greatly appreciated!

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7 0

3 years ago

Read 2 more answers

Lazurus Steel Corporation produces iron rods that are supposed to be 36 inches long. The machine that makes these rods does not

Igoryamba

Answer:

Step-by-step explanation:

We would construct a confidence interval.

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Since the sample size is large and the population standard deviation is known, we would use the following formula and determine the z score from the normal distribution table.

Margin of error = z × σ/√n

Where

σ = population standard Deviation

n = number of samples

From the information given

x = 36.02 inches

σ = 0.1 inches

n = 40

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.99 = 0.01

α/2 = 0.01/2 = 0.005

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.005 = 0.995

The z score corresponding to the area on the z table is 2.58. Thus, confidence level of 99% is 2.58

Margin of error = 2.58 × 0.1/√40 = 0.041

Confidence interval = 36.02 ± 0.041

The lower end of the confidence interval is

36.02 - 0.041 = 35.979 inches

The upper end of the confidence interval is

36.02 - 0.041 = 36.061 inches

Since 36.061 > 36.05, then we would conclude that the machine needs an adjustment.

The formula used is

Confidence interval =

Sample mean ± z × σ/√n

7 0

3 years ago