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2 years ago

Date:

Mathematics

1 answer:

katrin2010 [14]2 years ago

5 0

The volume of any shape is the amount of space in it.

The volume of the cylinder is 1570 square units

<h3>How to determine the volume?</h3>

The question is incomplete. Assume the following parameters

Shape = Cylinder

Radius, r = 10

Height, h = 5.

The volume of a cylinder is:

V = πr^2h

So, we have:

V = 3.14 * 10^2 * 5

Evaluate the product

V = 1570

Using the assumed values, the volume of the cylinder is 1570 square units

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3 years ago

Find a polynomial function of degree 3 with 2, i, -i as zeros.

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Answer:

$p(x)= x^3-2x^2+x-2$

Step-by-step explanation:

Here we are given that a polynomial has zeros as 2 , i and -i . We need to find out the cubic polynomial . In general we know that if $\alpha , \ \beta \ \& \ \gamma$ are the zeros of the cubic polynomial , then ,

$\sf \longrightarrow p(x)= (x -\alpha )(x-\beta)(x-\gamma)$

Here in place of the Greek letters , substitute 2,i and -i , we get ,

$\sf\longrightarrow p(x)= (x -2 )(x-i)(x+i)$

Now multiply (x-i) and (x+i ) using the identity (a+b)(a-b)=a² - b² , we have ,

$\sf \longrightarrow p(x)= (x-2)\{ x^2 - (i)^2\}$

Simplify using i = √-1 ,

$\sf \longrightarrow p(x)= (x-2)( x^2 + 1 )$

Multiply by distribution ,

$\sf \longrightarrow p(x)= x(x^2+1) -2(x^2+1)$

Simplify by opening the brackets ,

$\sf\longrightarrow p(x)= x^3+x-2x^2-2$

Rearrange ,

$\sf\longrightarrow \underline{\boxed{\blue{\sf p(x)= x^3-2x^2+x-2}}}$

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2 years ago

PLEASE HELP!!! ASAP!!!!!!!!!!!!!!! 10 POINTS

I am Lyosha [343]

$1800|2\\.\ 900|2\\.\ 450|2\\.\ 225|5\\.\ \ 45|5\\.\ \ \ 9|3\\.\ \ \ 3|3\\.\ \ \ 1|\\\\1880=2\cdot2\cdot2\cdot5\cdot5\cdot3\cdot3=2^3\cdot5^2\cdot3^2\\\\Answer:\ \boxed{2^3\cdot3^2\cdot5^2}$

$\sqrt[3]{320}\\\\320|2\\160|2\\.\ 80|2\\.\ 40|2\\.\ 20|2\\.\ 10|2\\.\ \ 5|5\\.\ \ 1|\\\\320=2\cdot2\cdot2\cdot2\cdot2\cdo2\cdot5=2^3\cdot2^3\cdot5=2^3\cdot2^3\cdot\\\\\sqrt[3]{320}=\sqrt[3]{2^3\cdot2^3\cdot5}=\sqrt[3]{2^3}\cdot\sqrt[3]{2^3}\cdot\sqrt[3]{5}=2\cdot2\sqrt[3]{5}=4\sqrt[3]5\\\\Answer:\ \boxed{\sqrt[3]{320}=4\sqrt[3]{5}}$