<h3><u>given</u><u>:</u></h3>
base= 25mm
height= 28mm
<h3><u>to</u><u> </u><u>find</u><u>:</u></h3>
the volume of the pyramid.
<h3><u>solution</u><u>:</u></h3>
v= a^2 h/3
v= 25^2 28/3
v= 5833.33333
v= 5833.3mm^3
Simple it says you use 33 drops of yellow originally and 44 drops of blue it appears that each drops are 11 drops lesser (from blue to yellow). Therefore, add 11 to 1212 and you get your answer.
It’s a positive slope, constant slope, and increasing function. Because it’s a straight line going diagonally to the top right, you know the slope is positive, constant, and the function is positive.
Answer:
============================
<h2>Given expression:</h2>
![\dfrac{\sqrt{14} }{\sqrt{7}-2} -\dfrac{\sqrt{14} }{\sqrt{7}+2}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%7B14%7D%20%7D%7B%5Csqrt%7B7%7D-2%7D%20-%5Cdfrac%7B%5Csqrt%7B14%7D%20%7D%7B%5Csqrt%7B7%7D%2B2%7D)
<h2>Simplify it in steps:</h2>
<h3>Step 1</h3>
Bring both fractions into common denominator:
![\dfrac{\sqrt{14} (\sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)} - \dfrac{\sqrt{14} (\sqrt{7}-2)}{(\sqrt{7}-2)(\sqrt{7}+2)}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%7B14%7D%20%28%5Csqrt%7B7%7D%2B2%29%7D%7B%28%5Csqrt%7B7%7D-2%29%28%5Csqrt%7B7%7D%2B2%29%7D%20-%20%5Cdfrac%7B%5Csqrt%7B14%7D%20%28%5Csqrt%7B7%7D-2%29%7D%7B%28%5Csqrt%7B7%7D-2%29%28%5Csqrt%7B7%7D%2B2%29%7D)
<h3>Step 2</h3>
Simplify:
![\dfrac{\sqrt{14} ((\sqrt{7}+2) - (\sqrt{7}-2))}{(\sqrt{7}-2)(\sqrt{7}+2)} =](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%7B14%7D%20%28%28%5Csqrt%7B7%7D%2B2%29%20-%20%28%5Csqrt%7B7%7D-2%29%29%7D%7B%28%5Csqrt%7B7%7D-2%29%28%5Csqrt%7B7%7D%2B2%29%7D%20%3D)
![\dfrac{\sqrt{14} (\sqrt{7}+2 - \sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)} =](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%7B14%7D%20%28%5Csqrt%7B7%7D%2B2%20-%20%5Csqrt%7B7%7D%2B2%29%7D%7B%28%5Csqrt%7B7%7D-2%29%28%5Csqrt%7B7%7D%2B2%29%7D%20%3D)
![\dfrac{4\sqrt{14} }{(\sqrt{7}-2)(\sqrt{7}+2)} =](https://tex.z-dn.net/?f=%5Cdfrac%7B4%5Csqrt%7B14%7D%20%7D%7B%28%5Csqrt%7B7%7D-2%29%28%5Csqrt%7B7%7D%2B2%29%7D%20%3D)
![\dfrac{4\sqrt{14} }{(\sqrt{7})^2-2^2} =](https://tex.z-dn.net/?f=%5Cdfrac%7B4%5Csqrt%7B14%7D%20%7D%7B%28%5Csqrt%7B7%7D%29%5E2-2%5E2%7D%20%3D)
![\dfrac{4\sqrt{14} }{7-4} =](https://tex.z-dn.net/?f=%5Cdfrac%7B4%5Csqrt%7B14%7D%20%7D%7B7-4%7D%20%3D)
![\dfrac{4}{3} \sqrt{14} }](https://tex.z-dn.net/?f=%5Cdfrac%7B4%7D%7B3%7D%20%20%5Csqrt%7B14%7D%20%7D)
<h3>Step 3</h3>
Compare the result with given expression to get:
Here are a couple I found:
<u>Similarities</u>:
- They have the same y-intercept of (0,5).
- They are both in slope-intercept form.
<u>Differences</u>:
- The line of y = -13x + 5 "falls" from left to right. The line of y = 2x + 5 "rises" from left to right.
- They have different x-intercepts. (y = 2x + 5 intersects (-
, 0) while y = -13x + 5 intersects at (
, 0)
<u></u>
<u>Explanation</u>:
Slope-intercept form is y = mx + b, and by looking at the equations, they both already fit that format, with m as their slope and b as their y-intercept. Also, since they both have a 5 as that "b," their y-intercepts are the same: (0,5).
As for differences, we can see that the coefficient in place of that "m" is positive in y = <u>2x</u> + 5 and negative in y = <u>-13x</u> + 5. Therefore, one line would rise due to their slope being positive and one would fall due to their slope being negative. They also have two different x-intercepts, which we can calculate by substituting 0 in place of the y, then isolating x.