Answer:
x = - 
, x = 
Step-by-step explanation:
Given
x² - x - 
= 0
Multiply through by 4 to clear the fraction
4x² - 4x - 3 = 0
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 4 × - 3 = - 12 and sum = - 4
The factors are + 2 and - 6
Use these factors to split the x- term
4x² + 2x - 6x - 3 = 0 ( factor the first/second and third/fourth terms )
2x(2x + 1) - 3(2x + 1) = 0 ← factor out (2x + 1) from each term
(2x + 1)(2x - 3) = 0
Equate each factor to zero and solve for x
2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = -
2x - 3 = 0 ⇒ 2x = 3 ⇒ x =
Last one :) djsjsjdndnwjdjnd
Answer:
y=29*x
Step-by-step explanation:
This problem is a linear function problem. We need at least two points to solve it. After finding two points we will compute the slope and then us the point-slope formula.
If you put 11 gallons of gasoline in your car it will allow you to drive 319 miles, this means that when x= 11 then, y=319. So the first point is (11,319). For the second point you now that if you have no gallons of gasoline then you won't be able to drive so, the second point is (0,0).
Now that we have to points we are able to compute the slope. The formula for the slope is:
.
this way
.
.
Now that we have the slope, we can use the point-slope formula to get the equation. The point-slope formula is:
(here it doesn't matter which point you use, you will get the same result).
Substituting the point (11,319) and the slope:
And we finaly get the equation!
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)
1. add the 4 to both sides
2. divide both sides by 3
