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3 years ago

Place the indicated product in the proper location on the grid. (4ya - 6xb)(4ya + 6xb)

Mathematics

2 answers:

miv72 [106K]3 years ago

7 0

Answer:

Simplify the expression.

16y^2a - 36x^2b

Step-by-step explanation: hope this helps!

k0ka [10]3 years ago

6 0

Product of $(4ya - 6xb)(4ya + 6xb)$ is $16y^2a^2-36x^2b^2$

Step-by-step explanation:

We need to find the product of $(4ya - 6xb)(4ya + 6xb)$

Finding product:

Multiplying both terms:

$(4ya - 6xb)(4ya + 6xb)\\=4ya(4ya+6xb)-6xb(4ya+6xb)\\=16y^2a^2+24yaxb-24xbya-36x^2b^2\\=16y^2a^2-36x^2b^2$

So, product of $(4ya - 6xb)(4ya + 6xb)$ is $16y^2a^2-36x^2b^2$

Keywords: Product of polynomials

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What is the answer for 5x-2x+8=2+6x+6?

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3 years ago

Find the center of mass of the wire that lies along the curve r and has density =4(1 sin4tcos4t)

dolphi86 [110]

The mass of the wire is found to be 40π√2 units.

To calculate the mass of the wire which runs along the curve r ( t ) with the density function δ=5.

The general formula is,

Mass = $\int_a^b \delta\left|r^{\prime}(t)\right| d t$

To find, we must differentiate this same given curve r ( t ) with respect to t to estimate |r'(t)|.

The given integration limits in this case are a = 0, b = 2π.

Now, as per the question;

The equation of the curve is given as;

r(t) = (4cost)i + (4sint)j + 4tk

Now, differentiate this same given curve r ( t ) with respect to t.

$\begin{aligned}\left|r^{\prime}(t)\right| &=\sqrt{(-4 \sin t)^2+(4 \cos t)^2+4^2} \\&=\sqrt{16 \sin ^2 t+16 \cos ^2 t+16} \\&=\sqrt{16\left(\sin t^2+\cos ^2 t\right)+16}\end{aligned}$

Further simplifying;

$\begin{aligned}&=\sqrt{16(1)+16} \\&=\sqrt{16+16} \\&=\sqrt{32} \\\left|r^{\prime}(t)\right| &=4 \sqrt{2}\end{aligned}$

Now, use integration to find the mass of the wire;

$\begin{aligned}&=\int_a^b \delta\left|r^{\prime}(t)\right| d t \\&=\int_0^{2 \pi} 54 \sqrt{2} d t \\&=20 \sqrt{2} \int_0^{2 \pi} d t \\&=20 \sqrt{2}[t]_0^{2 \pi} \\&=20 \sqrt{2}[2 \pi-0] \\&=40 \pi \sqrt{2}\end{aligned}$

Therefore, the mass of the wire is estimated as 40π√2 units.

To know more about density function, here

brainly.com/question/27846146

#SPJ4

The complete question is-

Find the mass of the wire that lies along the curve r and has density δ.

r(t) = (4cost)i + (4sint)j + 4tk, 0≤t≤2π; δ=5

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1 year ago