Answer:
Step-by-step explanation:
Water is being pumped into an inflated rubber sphere at a constant rate of 0.03 cubic meters per second.
So, dV/dt = 0.03.
We want to show that dS/dt is directly proportional to 1/r.
In other words, we want to establish the relationship that dS/dt = k(1/r), where k is some constant.
First, the volume of a sphere V is given by:
Therefore:
Next, the surface area of a sphere S is given by:
Therefore:
We can divide both sides by 2:
We can substitute this into dV/dt. Rewriting:
So:
Since dV/dt = 0.03 or 3/100:
Therefore:
Where k = 3/50.
And we have shown that dS/dt is directly proportional to 1/r.
The formula for volume is
... V = Bh . . . . . where B is the area of the base, and h is the height
You have
... 18/35 = 2/5·h
... 18/35·5/2 = h = 9/7
The height is 9/7 units.
Answer: 3
Step-by-step explanation: 2+1=3
By using scientific notation we calculated (2.3
10⁵)(1.5 10⁴) we got 345 10⁷.
Given that,
(2.310⁵)(1.5 10⁴)
By using scientific notation
The scientific notation allows us to express extremely large or extremely small numbers by multiplying them by single-digit integers and by 10 raised to the power of the corresponding exponent. The exponent is either positive or negative depending on how big or little the number is.
Now, we calculate
(2.310⁵)=2.5100000=230000
(1.5 10⁴)=1.510000=15000
Now,
=23000015000
=3450000000
=345 10⁷
Therefore, By using scientific notation we calculated (2.310⁵)(1.5 10⁴) we got 345 10⁷.
To learn more about scientific notation visit: brainly.com/question/18073768
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Hi there! So the the new price is $93, and went up from $55. Let's subtract the numbers. 93 - 55 is 38. The change is 38. To find the percent markup, we can write and solve a proportion. Set it up like this:
38/55 = x/100
This is because the amount of change goes above the original (55), and x represents the percent out of 100. We are looking for the markup. Let's cross multiply the values. 100 * 38 is 3,800. 55 * x is 55x. 3,800 = 55x. Now, divide each side by 55 to isolate the x. 55x/55 cancels out. 3,800/55 is 69.0909 or 69 when rounded to the nearest whole number. There. The percent of markup is approx. 69%.
