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Hunter-Best [27]
3 years ago
12

=" \frac{ \sqrt{-4} }{(3+1)-(2+3i)} " alt=" \frac{ \sqrt{-4} }{(3+1)-(2+3i)} " align="absmiddle" class="latex-formula">  simplfy the expression
Mathematics
1 answer:
frozen [14]3 years ago
8 0
\sqrt{-4} can also be written as 2i 
where i = √-1

\frac{2i}{4-2-3i} =  \frac{2i}{2-3i}

Rationalizing denominator,

\frac{2i(2+3i)}{(2-3i)(2+3i)} =  \frac{4i-6}{4+9} =  \frac{4i-6}{13}
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on Saturday Leo and his brother drove into town to visit their mom Leo is trying to remember how much he spent on gas and tolls
Gwar [14]

Let t be the number of tolls they crossed.

Amount they spent at each toll = $1.75.

Amount they spent at gas station = $28.

Let C be the total amount they spent on gas and tolls.

If they crossed 1 toll, then

C = 28 + 1.75(1).

If they crossed 3 tolls, then,

C = 28 + 1.75(3)

If they crossed t tolls, then,

C = 28 + 1.75t

Here, the terms are 28 and 1.75t and the factors are 1.75 and t.

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2 years ago
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Bas_tet [7]
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4 0
2 years ago
5/9+1/9 in simplest form. Explain.
Lana71 [14]

Answer:

2/3

Step-by-step explanation:

5/9 + 1/9

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2 years ago
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Step-by-step explanation:

5 0
3 years ago
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find the equations of the tangents to the curve y= x(x-1)(x+2) at the points where the curve cuts the x axis
antoniya [11.8K]

First of all, we compute the points of interest, i.e. the points where the curve cuts the x axis: since the expression is already factored, we have

x(x-1)(x+2) = 0 \iff x=0\ \lor\ x-1=0\ \lor\ x+2=0

Which means that the roots are

x=0\ \lor\ x=1\ \lor\ x=-2

Next, we can expand the function definition:

y = x(x-1)(x+2) = x^3 + x^2 - 2x

In this form, it is much easier to compute the derivative:

y' = 3x^2+2x-2

If we evaluate the derivative in the points of interest, we have

y'(-2) = 6,\quad y'(0)=-2,\quad y'(1)=3

This means that we are looking for the equations of three lines, of which we know a point and the slope. The equation

y-y_0=m(x-x_0)

is what we need. The three lines are:

y-0=6(x+2) \iff y = 6x+12  This is the tangent at x = -2

y-0=-2(x-0) \iff y = -2x  This is the tangent at x = 0

y-0=3(x-1) \iff y = 3x-3  This is the tangent at x = 1

7 0
3 years ago
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