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3 years ago

Select the correct answer from the drop-down menu.

Mathematics

1 answer:

saul85 [17]3 years ago

3 0

For this case we have the following factorized expression:

$(2y-9) (2y-9)$

Applying distributive property we have:

$(2y) (2y) - (2y) (9) - (9) (2y) + (9) (9) =\\4y ^ 2-18y-18y + 81 =$

We add similar terms taking into account that: Equal signs are added and the same sign is placed.

$4y ^ 2-36y + 81$

ANswer:

$4y ^ 2-36y + 81$

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Find the volume of the solid whose base is the circle x2+y2=25 and the cross sections perpendicular to the x-axis are triangles

ivanzaharov [21]

Triangles with height $h$ and base $b$ , with $b=h$ have area $\dfrac{b^2}2$ .

Such cross sections with the base of the triangle in the disk $x^2+y^2\le25$ (a disk with radius 5) have base with length

$b(x)=\sqrt{25-x^2}-\left(-\sqrt{25-x^2}\right)=2\sqrt{25-x^2}$

i.e. the vertical (in the $x,y$ plane) distance between the top and bottom curves describing the circle $x^2+y^2=25$ .

So when $x=4$ , the cross section at that point has base

$2\sqrt{25-16}=6$

so that the area of the cross section would be 6^2/2 = 18.

In case it's relevant, the entire solid would have volume given by the integral

$\displaystyle\int_{-5}^5\frac{b(x)^2}2\,\mathrm dx=4\int_0^5(25-x^2)\,\mathrm dx=\frac{1000}3$

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3 years ago

How many length-6 strings over Σ = {0, 1, 2} have exactly two 2’s?

kogti [31]

Since the string has already two 2, then we will compute the whole number of strings whose length is 4, over the alphabet {0,1}: $2^4=16.$
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3 years ago

How would I be able to answer this?

Ilya [14]

Radius = Diameter ÷ 2 = 10 ÷ 2 = 5mm

Find Volume: 

Volume= πr²h

Volume = π (5)² (6) = 471.24mm³ (Nearest hundredth)

Find Surface Area:

Surface area = 2πr² + 2πrh

Surface area = 2π(5)² + 2π(5)(6) = 345.58 mm²

Answer: Volume = 471.24mm³ , Surface area = 345.58 mm²

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