Rewrite 1/2 3/4 as a unit rate
1 answer:
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Answer:
8x - 5y = - 30
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 8x - 5y = 2 into this form
Subtract 8x from both sides
- 5y = - 8x + 2 ( divide all terms by - 5 )
y = x -
← in slope- intercept form
with slope m =
• Parallel lines have equal slopes, hence
y = x + c ← is the partial equation of the parallel line
To find c substitute (- 5, - 2) into the partial equation
- 2 = - 8 + c ⇒ c = - 2 + 8 = 6
y = x + 6 ← in slope- intercept form
Multiply through by 5
5y = 8x + 30 ( subtract 5y from both sides )
0 = 8x - 5y + 30 ( subtract 30 from both sides )
8x - 5y = - 30 ← in standard form
Answer:
Step-by-step explanation:
The shortest distance d, of a point (a, b, c) from a plane mx + ny + tz = r is given by:
--------------------(i)
From the question,
the point is (5, 0, -6)
the plane is x + y + z = 6
Therefore,
a = 5
b = 0
c = -6
m = 1
n = 1
t = 1
r = 6
Substitute these values into equation (i) as follows;
Therefore, the shortest distance from the point to the plane is
So we have a 6 at the bottom, and the root is 3, so hmm how to take it out, simple enough, just let's get something to make the 6 a 6³, so it comes out of the root
so
![\bf \cfrac{2+\sqrt[3]{3}}{\sqrt[3]{6}}\cdot \cfrac{\sqrt[3]{6^2}}{\sqrt[3]{6^2}}\implies \cfrac{(2+\sqrt[3]{3})(\sqrt[3]{6^2})}{(\sqrt[3]{6})(\sqrt[3]{6^2})}\implies \cfrac{2\sqrt[3]{36}+\sqrt[3]{3}\cdot \sqrt[3]{36}}{\sqrt[3]{6^3}} \\\\\\ \cfrac{2\sqrt[3]{36}+\sqrt[3]{3\cdot 36}}{6}\implies \cfrac{2\sqrt[3]{36}+\sqrt[3]{108}}{6}\implies \cfrac{2\sqrt[3]{36}+\sqrt[3]{3^3\cdot 4}}{6} \\\\\\ \cfrac{2\sqrt[3]{36}+3\sqrt[3]{ 4}}{6}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B2%2B%5Csqrt%5B3%5D%7B3%7D%7D%7B%5Csqrt%5B3%5D%7B6%7D%7D%5Ccdot%20%5Ccfrac%7B%5Csqrt%5B3%5D%7B6%5E2%7D%7D%7B%5Csqrt%5B3%5D%7B6%5E2%7D%7D%5Cimplies%20%5Ccfrac%7B%282%2B%5Csqrt%5B3%5D%7B3%7D%29%28%5Csqrt%5B3%5D%7B6%5E2%7D%29%7D%7B%28%5Csqrt%5B3%5D%7B6%7D%29%28%5Csqrt%5B3%5D%7B6%5E2%7D%29%7D%5Cimplies%20%5Ccfrac%7B2%5Csqrt%5B3%5D%7B36%7D%2B%5Csqrt%5B3%5D%7B3%7D%5Ccdot%20%5Csqrt%5B3%5D%7B36%7D%7D%7B%5Csqrt%5B3%5D%7B6%5E3%7D%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B2%5Csqrt%5B3%5D%7B36%7D%2B%5Csqrt%5B3%5D%7B3%5Ccdot%2036%7D%7D%7B6%7D%5Cimplies%20%5Ccfrac%7B2%5Csqrt%5B3%5D%7B36%7D%2B%5Csqrt%5B3%5D%7B108%7D%7D%7B6%7D%5Cimplies%20%5Ccfrac%7B2%5Csqrt%5B3%5D%7B36%7D%2B%5Csqrt%5B3%5D%7B3%5E3%5Ccdot%204%7D%7D%7B6%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B2%5Csqrt%5B3%5D%7B36%7D%2B3%5Csqrt%5B3%5D%7B%204%7D%7D%7B6%7D)
so