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3 years ago

If a textbook has a mass of 2.2kg and weighs 19.6 newtons on Venus what is the strength of gravity on Venus?

Mathematics

1 answer:

Neporo4naja [7]3 years ago

7 0

G=mg=>g=G/m=8,9m/s^2

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F(x)=2x-1 and g(x)=-3x

Ksenya-84 [330]

You should use youtube and learn how to do it, that's how i learned. you'll get frustrated but just pay attention.

6 0

2 years ago

Determine whether the geometric series is convergent or divergent. 6 + 5 + 25/6 + 125/36 + ...

Elina [12.6K]

The $n$ -th term in the series is 6 multiplied by the $(n-1)$ -th power of 5/6:

$a_1=6=6\left(\dfrac56\right)^{1-1}$

$a_2=5=6\left(\dfrac56\right)^{2-1}$

$a_3=\dfrac{25}6=6\left(\dfrac56\right)^{3-1}$

and so on.

$\displaystyle\sum_{n=1}^\infty6\left(\frac56\right)^{n-1}$

Consider the $N$ -th partial sum,

$S_N=\displaystyle\sum_{n=1}^N6\left(\frac56\right)^{n-1}$

$S_N=6\left(1+\dfrac56+\cdots+\dfrac{5^{N-2}}{6^{N-2}}+\dfrac{5^{N-1}}{6^{N-1}}\right)$

Multiplying both sides by 5/6 gives

$\dfrac56S_N=6\left(\dfrac56+\dfrac{5^2}{6^2}+\cdots+\dfrac{5^{N-1}}{6^{N-1}}+\dfrac{5^N}{6^N}\right)$

and substracting this from $S_N$ gives

$\dfrac16S_N=6\left(1-\dfrac{5^N}{6^N}\right)$

$S_N=36\left(1-\left(\dfrac56\right)^N}\right)$

As $N\to\infty$ , it's clear that the sum converges to 36.

5 0

3 years ago

B)convert 24 kilometres into miles - 1

Goryan [66]

Answer:14.9129

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Omaha’s factory has yet another type of cost structure. Its cost function is provided graphically. Its maximum capacity is 38,00

zlopas [31]

1. To find the rate of the cost per unit's decrease we need to find the slope of the graph for production levels above 12,000. We find the slope by dividing the change in y over the change in x. The two points that we will utilize for calculating the slope are the given points (12000, 0.85) and (38000, 0.59).

$\frac{0.59-0.85}{38000-12000} = \frac{-0.26}{26000}=-0.00001$

ANSWER: The rate of decrease is 0.00001 dollars per unit.

2. The function for the domain [12000, 38000] is just a linear equation that follows the form y = mx + b where m is the slope and b is the y-intercept. Since we have already calculated for the slope in the previous item, we will just compute the y-intercept. We will do this by using the point (38000,0.59) as our test point.

$y=mx+b$
$0.59=(-0.00001)(38000)+b$
$0.59=-0.38+b$
$b=0.97$

ANSWER: The function will then be $y=-0.00001x+0.97$

3. To know what the cost per unit when the company has produced 19,000 units already, we just use the function that we have built in the previous item. For this scenario, the value of x would be 19,000 and we are tasked to solve for y.

$y=-0.00001(19000)+0.97=-0.19+0.97=0.78$

ANSWER: The cost per unit at the production level of 19,000 is 0.78 dollars.

4. This special growth incentive can be seen on the graph thru the decreasing cost per unit after the production level of 12,000. We can only assume that last year's average were 12,000 units therefore exceeding that production level decreases the cost per unit since the company's tax burden is decreased.

5. For questions 5 and 6 I have found the graph/function for the Seattle and Wichita Factory. They are attached here, respectively.

Knowing the cost per unit for every factory, we just compare the cost and pick the lowest one.

Wichita: $1
Seattle: $0.75
Omaha: $y=-0.00001(15000)+0.97=-0.15+0.97=0.82$

ANSWER: We will send the order to the Seattle factory since they have the lowest cost per unit.

6a. For this subitem we are tasked to compare the cost per unit if we were to send two orders to a combination of any two factories. We will just find the cost per unit for every combination and show the average weighted cost by following the given formula.

Combination 1
Wichita: 7,000 units = $1
Seattle: 30,000 units = $0.68
Average Cost: $0.74

Combination 2
Wichita: 7,000 units = $1
Omaha: 30,000 units = $0.67
Average Cost: $0.73

Combination 3
Seattle: 7,000 units = $0.35
Omaha: 30,000 units = $0.67
Average Cost: $0.61

Combination 4
Omaha: 7,000 units = $0.85
Seattle: 30,000 units = $0.68
Average Cost: $0.71

Combination 5
Omaha: 7,000 units = $0.85
Wichita: 30,000 units = $0.80
Average Cost: $0.81

Combination 6
Seattle: 7,000 units = $0.35
Wichita: 30,000 units = $0.80
Average Cost: $0.71

6b. For this subitem we need to give all 37,000 units to one factory. We just need to calculate the cost per unit for every function. The calculation for the three factories is shown below (except when no calculation is needed, only inspection of the graph or function):

Wichita: not defined
Seattle: $C(x)=0.83- \frac{37,000}{200,000}=0.83-0.185=0.645$
Omaha: $y=-0.00001(37000)+0.97=-0.37+0.97=0.60$

6c. For this item, we will review our answers for the two previous subitems and select the one with the lowest cost per unit. Upon examining, we can see that letting Omaha produce all 37,000 units will yield the lowest cost.

ANSWER: Orders B and C should be produced by Omaha's factory.
Total # of units produced for the company today: 37,000
Average cost per unit for all production today: $0.60

3 0

3 years ago

Read 2 more answers

Hello, can somebody help me out with this problem? <br> (x)/(x-2)+(x-1)/(x+1)=1

IgorC [24]

$\dfrac x{x-2}+\dfrac{x-1}{x+1}=1$

$\dfrac x{x-2}\cdot\dfrac{x+1}{x+1}+\dfrac{x-1}{x+1}\cdot\dfrac{x-2}{x-2}=1$

So long as $x\neq-1$ and $x\neq2$ , we can carry out the manipulation above. Then

$\dfrac{x(x+1)}{(x-2)(x+1)}+\dfrac{(x-1)(x-2)}{(x+1)(x-2)}=1$

$\dfrac{x(x+1)+(x-1)(x-2)}{(x-2)(x+1)}=1$

$\dfrac{x^2+x+x^2-3x+2}{x^2-x-2}=1$

$\dfrac{2x^2-2x+2}{x^2-x-2}=1$

$\dfrac{2x^2-2x+2}{x^2-x-2}\cdot(x^2-x-2)=1\cdot(x^2-x-2)$

$2x^2-2x+2=x^2-x-2$

$x^2-x+4=0$

We can complete the square to solve:

$x^2-x+\dfrac14+\dfrac{15}4=0$

$\left(x-\dfrac12\right)^2=-\dfrac{15}4$

However, $y^2\ge0$ for all (real) values of $y$ , which means there is no real solution to this equation.

If you're solving over the complex numbers, we can take the square root of both sides to get

$x-\dfrac12=\pm i\dfrac{\sqrt{15}}2$

$\implies x=\dfrac{1\pm i\sqrt{15}}2$

3 0

3 years ago