Find a single expression that represents the surface area of the rectangular prism

Mathematics

1 answer:

densk [106]3 years ago

7 0

2(L * W) + 2(L * H) + 2(W * H) = surface area

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What should be added to a²-2ab+b² to get a²-ab-2b²

dybincka [34]

SOLUTION:

what should be added to a²-2ab+b² to get a²-ab-2b²

let the added no is P

$\pmb{P+(a^2-2ab+b^2)=(a^2-ab-2b^2) }$

$\pmb{P=(a^2-ab-2b^2)-(a^2-2ab+b^2) }$

$\pmb{P=a^2-ab-2b^2-a^2+2ab-b^2 }$

$\pmb{P=ab-3b^2 }$

$\therefore{\pmb{ab-3b^2 }}$ should be added to a²-2ab+b² to get a²-ab-2b²

5 0

3 years ago

Find the formula for the area of the shaded region in the figure. x² = 4py ہے

Alexandra [31]

The formula for the area of the shaded region in the figure.

x² = 4py is mathematically given as

$A=\frac{8}{3} \sqrt{p h} \cdot h$

<h3>What is the formula for the area of the shaded region in the figure?</h3>

Parameters

$x^{2}=4 p y$

$y=h$

$\therefore x^{2}=4 p h \Rightarrow x=2 \sqrt{p h} \\$

Generally, the equation for the Area is mathematically given as

$& A=2 \int_{0}^{2 \sqrt{p h}}\left(h-\frac{x^{2}}{4 p}\right) d x \\\\& A=2\left(h x-\frac{x^{3}}{12 p}\right]_{0}^{2 \sqrt{p h}} \\\\& A=2\left[\left[h 2 \sqrt{p h}-\frac{1}{12 p} \cdot(2 \sqrt{p h})^{3}-0\right]\right. \\$

$&A=2\left[2 h^{3 / 2} \sqrt{p}-\frac{8(\sqrt{p})^{3}(\sqrt{h})^{3}}{12 p}-0\right] \\\\&A=2\left[2 h^{k / 2} \sqrt{p}-\frac{2}{3} \sqrt{p} \cdot h^{3 / 2}\right] \\\\&A=2 \times \frac{4 \sqrt{p} \cdot h^{3 / 2}}{3} \\\\&A=\frac{8}{3} \cdot \sqrt{p} \cdot \sqrt{h} \cdot h \\\\&A=\frac{8}{3} \sqrt{p h} \cdot h$