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4 years ago

F=G (m×M)/r^(2); solve for r

Mathematics

1 answer:

eimsori [14]4 years ago

4 0

Multiply by (r^2)/F and take the square root.

(r²/F)·F = G·(m×M)/r²·(r²/F)

r² = G·m·M/F

$r=\sqrt{\dfrac{GmM}{F}}$

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HURRYY

erastovalidia [21]

Answer:

4.9 estimated but 4.8 non estimated

Step-by-step explanation:

4 0

3 years ago

"Select the equation of the least squares line for the data: (34.0, 1.30), (32.5, 3.25), (35.0, .65), (31.0, 6.50), (30.0, 5.85)

yulyashka [42]

Answer:

$y=-1.055 x +37.643$

And the best option would be:

a. ŷ= 37.643-1.0543x

Step-by-step explanation:

We assume that the data is this one:

x: 34.0, 32.5, 35.0, 31.0, 30.0, 27.5, 29.0

y: 1.30, 3.25, 0.65, 6.50, 5.85, 8.45, 6.50

Find the least-squares line appropriate for this data.

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i = 34.0+ 32.5+ 35.0+ 31.0+ 30.0+ 27.5+ 29.0
=219$

$\sum_{i=1}^n y_i =1.3+3.25+0.65+6.5+5.85+8.45+6.5=32.5$

$\sum_{i=1}^n x^2_i = 34.0^2+ 32.5^2+ 35.0^2+ 31.0^2+ 30.0^2+ 27.5^2+ 29.0^2
=6895.5$

$\sum_{i=1}^n y^2_i =1.3^2+3.25^2+0.65^2+6.5^2+5.85^2+8.45^2+6.5^2=202.8$

$\sum_{i=1}^n x_i y_i =34*1.3 + 32.5*3.25+ 35*0.65+ 31*6.5+30*5.585 +27.5*8.45 +29*6.5=970.45$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=6895.5-\frac{219^2}{7}=43.929$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=970.45-\frac{219*32.5}{7}=-46.336$

And the slope would be:

$m=-\frac{46.336}{43.929}=-1.055$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{219}{7}=31.286$

$\bar y= \frac{\sum y_i}{n}=\frac{32.5}{7}=4.643$

And we can find the intercept using this:

$b=\bar y -m \bar x=4.643-(-1.055*31.286)=37.643$

So the line would be given by:

$y=-1.055 x +37.643$

And the best option would be:

a. ŷ= 37.643-1.0543x

5 0

4 years ago

in 2018 the average monthly rainfall in the Amazon rainforest was 9.50 inches. in 2020 the average monthly rainfall was decrease

FrozenT [24]

Answer:

8.17 Inches

Step-by-step explanation:

Original:9.50 inches

% decreased :14% from original =.14*9.50=1.33

In year 2020 it will be = Original - decreased=9.50-1.33=8.17 inches

4 0

2 years ago

When he exercises after work,Marcus runs an average mile in 8.3 minutes. At this average, how many miles will he run after 36 mi

KIM [24]

He will run 4.3 miles in 36 minutes.

Step-by-step explanation:

Given,

8.3 minutes running = 1 mile distance

In one minute;

1 minute running = $\frac{1}{8.3}\ miles$

After 36 minutes;

36 minutes running = 36*1 minute running distance

36 minutes = $36*\frac{1}{8.3}$

$36\ minutes=\frac{36}{8.3}\\36\ minutes= 4.3 miles$

He will run 4.3 miles in 36 minutes.

Keywords: distance, speed

Learn more about distance at:

#LearnwithBrainly

4 0

3 years ago

Read 2 more answers

What is the range of the function g (x) = |x-12| - 2?

user100 [1]

Answer:

B. {y | y ≥ - 2}

Step-by-step explanation:

The minimum value of |y - 12| is 0, so

The minimum value of the function is - 2

4 0

3 years ago