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3 years ago

What is the explicit rule for the sequence?

Mathematics

2 answers:

Triss [41]3 years ago

6 0

Answer: D

Step-by-step explanation:

balandron [24]3 years ago

3 0

Answer:

Step-by-step explanation:

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True or false: the linear regression line of a data set must be perpendicular to the linear trend in the data.

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It is False

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3 years ago

The perimeter of the square is four times as great as the length of any of its side determine if the perimeter of the square is

IRISSAK [1]

Let, the side of square = a

perimeter = 4a

two sides would be: a+a = 2a

it's ratio would be 4a/2a = 2

as, the number is not in fraction, so they are proportional

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4 years ago

Which equation represents a direct variation?

lord [1]

The answer is c) y=1/2x because a direct variation is in the formula b=ka where k is a constant.

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4 years ago

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A silo is to be built by attaching a hemisphere roof onto a circular cylinder. The hemisphere part of the silo is constructed by

crimeas [40]

The radius and height, in two decimal places are mathematically given as

r=10.60

<h3>What is the radius and height, in two decimal places?</h3>

Generally, the equation for the volume is mathematically given as

$V=\pi r^{2} h+\frac{2}{3} \pi r^{3}$

Therefore

$5000 &=\pi 0^{2} h+\frac{2}{3} \pi r^{3}$

$V(r, h) &=\pi r^{2} h+\frac{2}{3} \pi r^{3}-5000 \\\nabla V &=\left\langle 2 \pi r h+2 \pi r^{2}, \pi r^{2}\right\rangle \\$

$\cos t &=100\left(2 \pi r^{2}\right)+75(2 \pi r h) \\\\\cos t &=200 \pi r^{2}+150 \pi r h \\\\\nabla C(r, h) &=\langle 400 \pi r+150 \pi h, 150 \pi r\rangle$

Using Lagrange method

$\langle 400 \pi \gamma+150 \pi \gamma h, 150 \pi \gamma\rangle=\lambda\left\langle 2 \pi \gamma h+2 \pi \gamma^{2}, \pi r^{2}\right\rangle$

$400 \pi r+150 \pi r=\left(2 \pi r h+2 \pi r^{2}\right) \lambda$

$$400 \pi \gamma+150 \pi h=300 \pi h+300 \pi r \\\\$

$400 \pi r-300 \pi r=150 \pi h$

$$160 \pi r=150 \pi h \quad \\\\\\$

with

$h=\frac{2}{3} r $$

$\pi r^{2} h+\frac{2}{3} \pi r^{3}=5000$

$\pi r}\left(\frac{2}{3} r \right)+\frac{2}{3} \pi^{3}=5000$$

$$\frac{4 \pi \gamma^{3}}{3}=5000 \quad$

$r^{3}=\left(\frac{5000 \times 3}{4 \pi}\right)$$

r=10.60

In conclusion, the radius and height, in two decimal places is

r=10.60