We have the following equation:
D = m / V
Where,
m: mass
V: volume
D: density.
The volume of the rectangular prism is:
V = (5) * (10) * (8)
V = 400 cm ^ 3
For Lead:
m = D * V
m = (11.36) * (400)
m = 4544 grams
For Iron:
m = D * V
m = (7.87) * (400)
m = 3148 grams
The difference of the masses is:
4544 - 3148 = 1396 grams
Answer:
The mass of the prism made of lead is 1396 grams than the one made of iron
Given that Eric knits 18 squares on monday, and knits seven more each day starting from Tuesday, this would mean that in tuesday, he knits a 25 squares, at wednesday, he knits 32 squares, at thursday, he knits 39 squares; therefore, on friday, the number of squares Eric knits is 46 squares. Hope this answers your question.
![\dfrac{2}{\sqrt{2+\sqrt2}}=\dfrac{2}{\sqrt{2+\sqrt2}}\cdot\dfrac{\sqrt{2-\sqrt2}}{\sqrt{2-\sqrt2}}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B%5Csqrt%7B2%2B%5Csqrt2%7D%7D%3D%5Cdfrac%7B2%7D%7B%5Csqrt%7B2%2B%5Csqrt2%7D%7D%5Ccdot%5Cdfrac%7B%5Csqrt%7B2-%5Csqrt2%7D%7D%7B%5Csqrt%7B2-%5Csqrt2%7D%7D)
<em>use √(ab) = √a · √b</em>
![=\dfrac{2\sqrt{2-\sqrt2}}{\sqrt{(2+\sqrt2)(2-\sqrt2)}}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B2%5Csqrt%7B2-%5Csqrt2%7D%7D%7B%5Csqrt%7B%282%2B%5Csqrt2%29%282-%5Csqrt2%29%7D%7D)
<em>use (a + b)(a - b) = a² - b²</em>
![=\dfrac{2\sqrt{2-\sqrt2}}{\sqrt{2^2-(\sqrt2)^2}}=\dfrac{2\sqrt{2-\sqrt2}}{\sqrt{4-2}}=\dfrac{2\sqrt{2-\sqrt2}}{\sqrt2}\cdot\dfrac{\sqrt2}{\sqrt2}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B2%5Csqrt%7B2-%5Csqrt2%7D%7D%7B%5Csqrt%7B2%5E2-%28%5Csqrt2%29%5E2%7D%7D%3D%5Cdfrac%7B2%5Csqrt%7B2-%5Csqrt2%7D%7D%7B%5Csqrt%7B4-2%7D%7D%3D%5Cdfrac%7B2%5Csqrt%7B2-%5Csqrt2%7D%7D%7B%5Csqrt2%7D%5Ccdot%5Cdfrac%7B%5Csqrt2%7D%7B%5Csqrt2%7D)
<em>use √a · √a = a and √(ab) = √a · √b</em>
![=\dfrac{2\sqrt{2\cdot2-\sqrt2\cdot2}}{2}=\sqrt{4-2\sqrt2}\\\\Answer:\ \boxed{\dfrac{2}{\sqrt{2+\sqrt2}}=\sqrt{4-2\sqrt2}}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B2%5Csqrt%7B2%5Ccdot2-%5Csqrt2%5Ccdot2%7D%7D%7B2%7D%3D%5Csqrt%7B4-2%5Csqrt2%7D%5C%5C%5C%5CAnswer%3A%5C%20%5Cboxed%7B%5Cdfrac%7B2%7D%7B%5Csqrt%7B2%2B%5Csqrt2%7D%7D%3D%5Csqrt%7B4-2%5Csqrt2%7D%7D)
-6+2 is -4. hope I helped!