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3 years ago

A right cylinder has a radius of 4 and a height of 11 what’s the surface area

Mathematics

2 answers:

postnew [5]3 years ago

6 0

Answer:

$A=376.99\ units^2$

Step-by-step explanation:

By definition, the surface area of a cylinder is given by the following formula:

$A = 2\pi r h + 2\pi r ^ 2$

Where r is the radius and h is the height.

In this case, we have to:

$r = 4\\\\h = 11$

then the surface area is:

$A = 2\pi(4)(11) + 2\pi(4) ^ 2$

$A=120\pi$

$A=376.99\ units^2$

morpeh [17]3 years ago

5 0

120pi units^2

Step-by-step explanation:

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4 years ago

Prove that the value of the expression does not depend on the variable x:

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Answer:

See below

Step-by-step explanation:

If an expression is not dependent on x, it simplified form must not contain x. To show that this is the case for (a) and (b) we need to simplify them and assess:

(a)

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3 years ago

Find all zeros of f(x)=x^4-3x^3+6x^2+2x-60 given that 1+3i is a zero of f(x)

Triss [41]

Answer:

The roots of f(x) are: -2, 3, (1+3i) and (1-3i)

Step-by-step explanation:

We are given an expression:

$f(x)=x^4-3x^3+6x^2+2x-60$

(1+3i) is a root of f(x)

We have to find the remaining roots of f(x).

Since, (1+3i) is a root of f(x),

$x-(1+3i)$

is a factor of given expression.

Now, we check if (1 - 3i) is a root of given function.

$f(x)=x^4-3x^3+6x^2+2x-60\\f(1-3i)=(1-3i)^4-3(1-3i)^3+6(1-3i)^2+2(1-3i)-60\\= (28+96i)-3(-26+18i)+6(-8-6i)+2(1-3i)-60 = 0$

Thus, (1-3i) is also a root of given function.

Since, (1-3i) is a root of f(x),

$x-(1-3i)$

is a factor of given expression.

Thus, we can write:

$(x-(1+3i))(x-(1-3i))\text{ is a factor of f(x)}\\x^2-x(1-3i)+x(1+3i)+(1-3i)(1+3i)\text{ is a factor of f(x)}\\x^2-2x+10\text{ is a factor of f(x)}$

Dividing f(x) by above expression:

$\displaystyle\frac{x^4-3x^3+6x^2+2x-60}{x^2-2x+10} = x^2-x-6$

To find the root, we equate it to zero:

$x^2-x-6 = 0\\x^2 - 3x+2x-6=0\\x(x-3)+2(x-3)=0\\(x+2)(x-3) = 0\\x = -2, x = 3$

Thus, the roots of f(x) are: -2, 3, (1+3i) and (1-3i)

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4 years ago