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3 years ago

Different ways in which intersect that cylinder and the cross section that results

1 answer:

7 0

If it is perpendicular to the axis, then a circle. If it is at an angle, then an ellipse. If it is parallel to the axis, then two parallel lines. These aren't mine but I hope they help you

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What is the simplified version of 3\sqrt{135}

Aleonysh [2.5K]

Answer:

The simplified version of $\sqrt[3]{135}$ is $3\sqrt[3]{5}$ .

Step-by-step explanation:

The given expression is

$\sqrt[3]{135}$

According to the property of radical expression.

$\sqrt[n]{x}=(x)^{\frac{1}{n}}$

Using this property we get

$\sqrt[3]{135}=(135)^{\frac{1}{3}}$

$\sqrt[3]{135}=(27\times 5)^{\frac{1}{3}}$

$\sqrt[3]{135}=(3^3\times 5)^{\frac{1}{3}}$

$\sqrt[3]{135}=(3^3)^{\frac{1}{3}}\times (5)^{\frac{1}{3}}$ $[\because (ab)^x=a^xb^x]$

$\sqrt[3]{135}=3\times \sqrt[3]{5}$ $[\because \sqrt[n]{x}=(x)^{\frac{1}{n}}]$

$\sqrt[3]{135}=3\sqrt[3]{5}$

Therefore the simplified version of $\sqrt[3]{135}$ is $3\sqrt[3]{5}$ .

7 0

3 years ago

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How do extraneous solutions arise from radical equations?

Blababa [14]

In general, extraneous solutions arise when we perform non-invertible operations on both sides of an equation. (That is, they sometimes arise, but not always.) ... Solvingequations involving square roots involves squaring both sides of anequation. I hope that this helps you out, Have a wonderful day!!

5 0

3 years ago

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Identify vertex and y-intercept of graph of function y= -3(x+2)^2+5

Doss [256]

Hello,

Vertex=(-2,5)
x=0==>y=-3(0+2)²+5=-7

3 0

3 years ago

If f(1) = 10 and f(n) = f(n = 1) – 4 then find the value of f(5).

svetoff [14.1K]

Given:

$f(1)=10$ and $f(n)=f(n-1)-4$ .

To find:

The value of f(5).

Solution:

We have,

$f(n)=f(n-1)-4$

For $n=2$ ,

$f(2)=f(2-1)-4$

$f(2)=f(1)-4$

$f(2)=10-4$

$f(2)=6$

For $n=3$ ,

$f(3)=f(3-1)-4$

$f(3)=f(2)-4$

$f(3)=6-4$

$f(3)=2$

For $n=4$ ,

$f(4)=f(4-1)-4$

$f(4)=f(3)-4$

$f(4)=2-4$

$f(4)=-2$

For $n=5$ ,

$f(5)=f(5-1)-4$

$f(5)=f(4)-4$

$f(5)=-2-4$

$f(5)=-6$

Therefore, the value of $f(5)$ is $-6$ .

5 0

3 years ago

What are the factors of 2x + 3x - 54? Select two options

tiny-mole [99]

Answer:

The answer: The factors are (2x-9) and (x+6).

The Problem:

Factor $2x^2+3x-54$

Step-by-step explanation:

So I'm going to do trial factors using the choices to aid me.

Factored form for this problem if it exist will be in the form:

$(mx+n)(kx+p)$ .

In general this is what it would look like if we factored any quadratic in terms of $x$ (given the quadratic is not prime but technically you could factor even over the complex numbers).

Let's look at:

$(mx+n)(kx+p)$

We want to choose $k \text{ and } m$ such that when you multiply them you get 2. Well those would have to be 2 and 1.

$(2x+n)(x+p)$

we want to choose $n \text{ and } p$ such that when you multiply them you get -54. Based on the choices we want to get with -9 and 6, or 9 and -6. We don't know the order we want to choose it in either.

For example which of these would work:

$(2x-6)(x+9)$

$(2x+6)(x-9)$

$(2x-9)(x+6)$

$(2x+9)(x-6)$

We are going to consider only the outer and inner of FOIL since we already know the first times the first is $2x^2$ and the last times the last is $-54$ .

Let's test the first one:

$(2x-6)(x+9)$

Outer: 2x(9)=18x

Inner: -6(x)=-6x

------------------------ADD!

18x-6x=12x

The first choice did not give us the middle term 3x.

Trying the second one would give us the opposite since they are in the same form as previous just the + and - are switched.

Let's look at the third one:

$(2x-9)(x+6)$

Outer: 2x(6)=12x

Inner: -9(x)=-9x

--------------------------ADD!

12x-9x=3x

This is the winner.

The answer: The factors are (2x-9) and (x+6).

7 0

3 years ago

Read 2 more answers