Answer:
y = 2/3
Step-by-step explanation:
14 = 6(2) + 3y
14 = 12 + 3y
2 = 3y
y = 2/3
Answer:
=1
Step-by-step explanation:
log3(x+2)-log3(x)=1
Subtraction sign means you can divide the values inside the parintheses
log3(x+2/x)=1
split up the fraction into x/x and 2/x; x/x = 1
log3(1+(2/x))=1
Change of base - three to the first power = value in parintheses
3to1st=1+(2/x)
subtract 1 from both sides
2=2/x
divide both sides by 2
x=1
;)
We'll put y in function of x:
![y^2=4-x\\\\ y=\pm\sqrt{4-x}](https://tex.z-dn.net/?f=%20y%5E2%3D4-x%5C%5C%5C%5C%20y%3D%5Cpm%5Csqrt%7B4-x%7D)
Look the graph of the function in the attached figure. The areas above and below the x-axis are equal. So, we can represent the area bounded by the graph as:
![A=2\displaystyle\int \sqrt{4-x}\,dx}](https://tex.z-dn.net/?f=A%3D2%5Cdisplaystyle%5Cint%20%5Csqrt%7B4-x%7D%5C%2Cdx%7D)
Using that to calculate the area bounded is equal to calculate the double of area above the x-axis.
The line x=z divides the region into two regions of equal area with 0 ≤ x ≤ 2, then:
![A_1=A_2\\\\ 2\displaystyle\int^z_0\sqrt{4-x}\,dx}=2\displaystyle\int^2_z\sqrt{4-x}\,dx}\\\\ \displaystyle\int^z_0\sqrt{4-x}\,dx}=\displaystyle\int^2_z\sqrt{4-x}\,dx}\\\\ \left[-\dfrac{2}{3}(4-x)^{\frac{3}{2}}\right]^z_0=\left[-\dfrac{2}{3}(4-x)^{\frac{3}{2}}\right]^2_z\\\\ \left[(4-x)^{\frac{3}{2}}\right]^z_0=\left[(4-x)^{\frac{3}{2}}\right]^2_z\\\\](https://tex.z-dn.net/?f=%20A_1%3DA_2%5C%5C%5C%5C%202%5Cdisplaystyle%5Cint%5Ez_0%5Csqrt%7B4-x%7D%5C%2Cdx%7D%3D2%5Cdisplaystyle%5Cint%5E2_z%5Csqrt%7B4-x%7D%5C%2Cdx%7D%5C%5C%5C%5C%20%5Cdisplaystyle%5Cint%5Ez_0%5Csqrt%7B4-x%7D%5C%2Cdx%7D%3D%5Cdisplaystyle%5Cint%5E2_z%5Csqrt%7B4-x%7D%5C%2Cdx%7D%5C%5C%5C%5C%20%5Cleft%5B-%5Cdfrac%7B2%7D%7B3%7D%284-x%29%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Cright%5D%5Ez_0%3D%5Cleft%5B-%5Cdfrac%7B2%7D%7B3%7D%284-x%29%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Cright%5D%5E2_z%5C%5C%5C%5C%20%5Cleft%5B%284-x%29%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Cright%5D%5Ez_0%3D%5Cleft%5B%284-x%29%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Cright%5D%5E2_z%5C%5C%5C%5C)
The value of x in the triangle with angles 80, 40 and (13x - 5) degrees is 5.
<h3>Sum of angle in a triangle</h3>
The sum of angle in a triangle is equals to 180 degrees. Recall a triangle have three sides. Therefore,
80 + 40 + 13x - 5 = 180
120 - 5 + 13x = 180
115 + 13x = 180
subtract 115 from both sides of the equation
115 - 115 + 13x = 180 - 115
13x = 65
divide both sides by 13
13x / 13 = 65 / 13
x = 5
learn more on triangle here: brainly.com/question/15268683