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3 years ago

What is the standard form of Y=2/5x+2

Mathematics

1 answer:

Troyanec [42]3 years ago

7 0

bearing in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

$\bf y = \cfrac{2}{5}x+2\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5}}{5(y)=5\left( \cfrac{2}{5}x+2 \right)}\implies 5y=2x+10 \\\\\\ -2x+5y=10\implies 2x-5y=-10$

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3 years ago

Two cubes are tossed. Find P(only one shows a 2).

djverab [1.8K]

The probability that only one shows a 2.

There are 36 different outputs (6x6) = 36

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There are 6 combinations where the second cube shows a 2: 1,2;2,2;3,2;4,2;5,2; and 6,2.

Of those one combination on each set shows two 2.

Then the number of combinations with only one 2 are 6 - 1 + 6 -1 = 10

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3 years ago

A truck travels 52 1/2 miles and uses 2 1/2 gallons of gasoline. What is the fuel rate in miles per gallon?

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1 year ago

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The mistake Shawna made was in her answer the 54 repeats so the bar should be over the .54 not the .545

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3 years ago

Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that

juin [17]

Answer:

The Taylor series of f(x) around the point a, can be written as:

$f(x) = f(a) + \frac{df}{dx}(a)*(x -a) + (1/2!)\frac{d^2f}{dx^2}(a)*(x - a)^2 + .....$

Here we have:

f(x) = 4*cos(x)

a = 7*pi

then, let's calculate each part:

f(a) = 4*cos(7*pi) = -4

df/dx = -4*sin(x)

(df/dx)(a) = -4*sin(7*pi) = 0

(d^2f)/(dx^2) = -4*cos(x)

(d^2f)/(dx^2)(a) = -4*cos(7*pi) = 4

Here we already can see two things:

the odd derivatives will have a sin(x) function that is zero when evaluated in x = 7*pi, and we also can see that the sign will alternate between consecutive terms.

so we only will work with the even powers of the series:

f(x) = -4 + (1/2!)*4*(x - 7*pi)^2 - (1/4!)*4*(x - 7*pi)^4 + ....

So we can write it as:

f(x) = ∑fₙ

Such that the n-th term can written as:

$fn = (-1)^{2n + 1}*4*(x - 7*pi)^{2n}$

6 0

3 years ago