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finlep [7]
3 years ago
7

Help for 1,2,3,4 please

Mathematics
1 answer:
ikadub [295]3 years ago
5 0

In every case, you're finding the surface area of a rectangular prism. That area is the sum of the areas of the 6 rectangular faces. Since opposite faces have the same area, the formula can be written

... S = 2(LW +WH +HL)

The number of multiplications can be reduced if you rearrange the formula to

... S = 2(LW +H(L +W))

where L, W, and H are the length, width, and height of the prism. (It does not matter which dimension gets what name, as long as you use the same number for the same variable in the formula.)

When you're evaluating this formula over and over for diffferent sets of numbers, it is convenient to let a calculator or spreadsheet program do it for you.

1. S = 2((5 cm)(5 cm) +(5 cm)(5 cm +5 cm)) = 2(25 cm² +(5 cm)(10 cm))

... = 2(25 cm² + 50 cm²) = 150 cm²

2. S = 2(12·6 + 2(12+6)) mm² = 2(72 +36) mm² = 216 mm²

3. S = 2(11·6 + 4(11 +6)) ft² = 2·134 ft² = 264 ft²

4. S = 2(10·4 +3(10 +4)) in² = 164 in²

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Step-by-step explanation:

I believe this is right please correct me if I'm wrong.

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\displaystyle\int_Cx^2y\,\mathrm dS=\int_{t=0}^{t=\pi}x(t)^2y(t)\left\|\frac{\mathrm d\mathbf r(t)}{\mathrm dt}\right\|\,\mathrm dt
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Take u=\cos t, then

=\displaystyle-3^4\int_{u=1}^{u=-1}u^2\,\mathrm du
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For how many real values of x is <img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B120-%5Csqrt%7Bx%7D%7D%20" id="TexFormula1" title
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A good place to start is to set \sqrt{x} to y. That would mean we are looking for \sqrt{120-y} to be an integer. Clearly, y\leq 120, because if y were greater the part under the radical would be a negative, making the radical an imaginary number, not an integer. Also note that since \sqrt{x} is a radical, it only outputs values from [0,\infty], which means y is on the closed interval: [0,120].

With that, we don't really have to consider y anymore, since we know the interval that \sqrt{x} is on.

Now, we don't even have to find the x values. Note that only 11 perfect squares lie on the interval [0,120], which means there are at most 11 numbers that x can be which make the radical an integer. All of the perfect squares are easily constructed. We can say that if k is an arbitrary integer between 0 and 11 then:

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