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4 years ago

I need the answers ASAP!!

Mathematics

1 answer:

VLD [36.1K]4 years ago

4 0

Answer:

i’m pretty sure the first one is none of the above, the second is whole i’m pretty sure

Step-by-step explanation:

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Standard form of 89000

puteri [66]

Answer:

To write a linear expression in standard form, rearrange the terms in alphabetical order.

89000

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Find the volume of the cylinder in terms of pi.

Allushta [10]

Answer:

$\large\boxed{V=81\pi\ in^3}$

Step-by-step explanation:

The formula of a volume of a cylinder:

$V=\pi r^2H$

r - radius

H - height

We have r = 3in and H = 9in. Substitue:

$V=\pi(3^2)(9)=\pi(9)(9)=81\pi\ in^3$

5 0

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;

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