Answer:
5.1 cm
. . . . . .
All we have to do is convert our 51mm to centimeters.
We divide the length value by 10 to get our centimeters.
51 divided by 10 = 5.1
All we have to do is move our "invisible decimal"
In my way, every whole number has an invisible decimal at it's end.
For ex: '60.'
We can get into exponents. 10 is 10¹, any exponent is the number of zeros at the end of a number may have. Ex: '10² = 100'
We can move our decimal to the left since we are dividing. The amount of exponent numbers are the amount you move it, multiplying and dividing are different things with that.
Let's get back on topic.
Moving our decimal to the left with dividing is 5.1 since 10¹ has a "1" as it's exponent, making us move it "1" to the left.
Multiplying is going the right way.
I hope this helps.
Answer:
Associative Property
For multiplication, the rule is "a(bc) = (ab)c"; in numbers, this means 2(3×4) = (2×3)4.
Answer:
<h2>a) 0.5367feet</h2><h2>b) 0.5223feet</h2><h2>c) 0.7292feet</h2>
Step-by-step explanation:
Given the rate at which an eucalyptus tree will grow modelled by the equation 0.5+6/(t+4)³ feet per year, where t is the time (in years).
The amount of growth can be gotten by integrating the given rate equation as shown;
a) The number of feet that the tree will grow in the second year can be gotten by taking the limit of the integral from t =1 to t = 2
![\int\limits^2_1 {0.5 + \frac{6}{(t+4)^{3} } } \, dt = [0.5t-3(t+4)^{-2}]^2_1\\= [0.5(2)-3(2+4)^{-2}] - [0.5(1)-3(1+4)^{-2}]\\= [1-3(6)^{-2}] - [0.5-3(5)^{-2}]\\ = [1-\frac{1}{12}] - [0.5-\frac{3}{25} ]\\= \frac{11}{12}-\frac{1}{2}+\frac{3}{25}\\ = 0.9167 - 0.5 + 0.12\\= 0.5367feet](https://tex.z-dn.net/?f=%5Cint%5Climits%5E2_1%20%7B0.5%20%2B%20%5Cfrac%7B6%7D%7B%28t%2B4%29%5E%7B3%7D%20%7D%20%20%7D%20%5C%2C%20dt%20%3D%20%5B0.5t-3%28t%2B4%29%5E%7B-2%7D%5D%5E2_1%5C%5C%3D%20%5B0.5%282%29-3%282%2B4%29%5E%7B-2%7D%5D%20-%20%5B0.5%281%29-3%281%2B4%29%5E%7B-2%7D%5D%5C%5C%3D%20%5B1-3%286%29%5E%7B-2%7D%5D%20-%20%5B0.5-3%285%29%5E%7B-2%7D%5D%5C%5C%20%3D%20%5B1-%5Cfrac%7B1%7D%7B12%7D%5D%20-%20%5B0.5-%5Cfrac%7B3%7D%7B25%7D%20%5D%5C%5C%3D%20%5Cfrac%7B11%7D%7B12%7D-%5Cfrac%7B1%7D%7B2%7D%2B%5Cfrac%7B3%7D%7B25%7D%5C%5C%20%20%20%3D%200.9167%20-%200.5%20%2B%200.12%5C%5C%3D%200.5367feet)
b) The number of feet that the tree will grow in the third year can be gotten by taking the limit of the integral from t =2 to t = 3
![\int\limits^3_2 {0.5 + \frac{6}{(t+4)^{3} } } \, dt = [0.5t-3(t+4)^{-2}]^3_2\\= [0.5(3)-3(3+4)^{-2}] - [0.5(2)-3(2+4)^{-2}]\\= [1.5-3(7)^{-2}] - [1-3(6)^{-2}]\\ = [1.5-\frac{3}{49}] - [1-\frac{1}{12} ]\\ = 1.439 - 0.9167\\= 0.5223feet](https://tex.z-dn.net/?f=%5Cint%5Climits%5E3_2%20%7B0.5%20%2B%20%5Cfrac%7B6%7D%7B%28t%2B4%29%5E%7B3%7D%20%7D%20%20%7D%20%5C%2C%20dt%20%3D%20%5B0.5t-3%28t%2B4%29%5E%7B-2%7D%5D%5E3_2%5C%5C%3D%20%5B0.5%283%29-3%283%2B4%29%5E%7B-2%7D%5D%20-%20%5B0.5%282%29-3%282%2B4%29%5E%7B-2%7D%5D%5C%5C%3D%20%5B1.5-3%287%29%5E%7B-2%7D%5D%20-%20%5B1-3%286%29%5E%7B-2%7D%5D%5C%5C%20%3D%20%5B1.5-%5Cfrac%7B3%7D%7B49%7D%5D%20-%20%5B1-%5Cfrac%7B1%7D%7B12%7D%20%5D%5C%5C%20%20%3D%201.439%20-%200.9167%5C%5C%3D%200.5223feet)
c) The total number of feet grown during the second year can be gotten by substituting the value of limit from t = 0 to t = 2 into the equation as shown
![\int\limits^2_0 {0.5 + \frac{6}{(t+4)^{3} } } \, dt = [0.5t-3(t+4)^{-2}]^2_0\\= [0.5(2)-3(2+4)^{-2}] - [0.5(0)-3(0+4)^{-2}]\\= [1-3(6)^{-2}] - [0-3(4)^{-2}]\\ = [1-\frac{1}{12}] - [-\frac{3}{16} ]\\= \frac{11}{12}+\frac{3}{16}\\ = 0.9167 - 0.1875\\= 0.7292feet](https://tex.z-dn.net/?f=%5Cint%5Climits%5E2_0%20%7B0.5%20%2B%20%5Cfrac%7B6%7D%7B%28t%2B4%29%5E%7B3%7D%20%7D%20%20%7D%20%5C%2C%20dt%20%3D%20%5B0.5t-3%28t%2B4%29%5E%7B-2%7D%5D%5E2_0%5C%5C%3D%20%5B0.5%282%29-3%282%2B4%29%5E%7B-2%7D%5D%20-%20%5B0.5%280%29-3%280%2B4%29%5E%7B-2%7D%5D%5C%5C%3D%20%5B1-3%286%29%5E%7B-2%7D%5D%20-%20%5B0-3%284%29%5E%7B-2%7D%5D%5C%5C%20%3D%20%5B1-%5Cfrac%7B1%7D%7B12%7D%5D%20-%20%5B-%5Cfrac%7B3%7D%7B16%7D%20%5D%5C%5C%3D%20%5Cfrac%7B11%7D%7B12%7D%2B%5Cfrac%7B3%7D%7B16%7D%5C%5C%20%20%20%3D%200.9167%20-%200.1875%5C%5C%3D%200.7292feet)
Answer:
28+4v
Step-by-step explanation:
multiply each term in parenthesis by 4.
multiply the numbers <u>4×7</u>+4v
= the solution 28+4v
