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3 years ago

Write an expression for the eighth partial sum of the series using summation notation

Mathematics

1 answer:

balandron [24]3 years ago

4 0

Answer:

option B

Step-by-step explanation:

9/10 + 6/5 + 3/2...........

We find the difference between the terms

$\frac{6}{5} - \frac{9}{10}$

$\frac{12}{10} - \frac{9}{10} = \frac{3}{10}$

We will get the same difference when we subtract consecutive terms.

so , d= 3/10, a= 9/10

we find the formula for nth term

a_n = a+(n-1) d

$a_n = \frac{9}{10} + (n-1)\frac{3}{10}$

$a_n = \frac{9}{10} +\frac{3}{10}n-\frac{3}{10}$

$a_n = \frac{6}{10} +\frac{3}{10}n$

$a_n = \frac{3}{5} +\frac{3}{10}n$

we need to find eighth partial sum so we take n=1 to 8

sum of 8 terms ( $\frac{3}{5} +\frac{3}{10}n$ )

So option B is correct

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Select all the names for a in the expression.

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Answer:

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Step-by-step explanation:

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3 years ago

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Myra saved $15 a month for 18 months. She bought a book for $46.50 and a tennis racquet for $129.95. How much does she have left

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Answer:

Step-by-step explanation:

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3 years ago

Which equation is y = –6x^2 + 3x + 2 rewritten in vertex form? y = negative 6 (x minus 1) squared + 8 y = negative 6 (x + one-fo

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Answer:

$y = -6(x - \frac{1}{2})^2 -\frac{7}{2}$

Step-by-step explanation:

Given:

$y = -6x^2 + 3x + 2$

Required

Rewrite in vertex form

The vertex form of an equation is in form of: $y = a(x - h)^2+ k$

Solving: $y = -6x^2 + 3x + 2$

Subtract 2 from both sides

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Factorize expression on the right hand side by dividing through by the coefficient of x²

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$y - 2 = -6(x^2 - \frac{x}{2})$

Get a perfect square of coefficient of x; then add to both sides

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Rough work

The coefficient of x is $\frac{-1}{2}$

It's square is $(\frac{-1}{2})^2 = \frac{1}{4}$

Adding inside the bracket of $-6(x^2 - \frac{x}{2})$ to give: $-6(x^2 - \frac{x}{2} + \frac{1}{4})$

To balance the equation, the same expression must be added to the other side of the equation;

Equivalent expression is: $-6(\frac{1}{4})$

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The expression becomes

$y - 2 -6(\frac{1}{4})= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

$y - 2 -\frac{6}{4}= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

$y - 2 -\frac{3}{2}= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

Factorize the expression on the right hand side

$y - 2 -\frac{3}{2}= -6(x - \frac{1}{2})^2$

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$y - (\frac{7}{2})= -6(x - \frac{1}{2})^2$

$y +\frac{7}{2} = -6(x - \frac{1}{2})^2$

Make y the subject of formula

$y = -6(x - \frac{1}{2})^2 -\frac{7}{2}$

Solved

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coldgirl [10]

1.
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means that if the monthly income of John is $ 5,000 ,he can spend at most

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Or for example

if Johns monthly income is $8,000, then he can spend at most

f(8,000)=15,000+1.5*8,000=15,000+ 12,000=27,000 (dollars)

2.
Now, assume that the maximum amount that John can spend is y.

Then, y=15,000+1.5x

we can express x, the monthly income, in terms of y by isolating x:

y=15,000+1.5x

1.5x = y-15,000
X=y-15,000/1.5

thus, in functional notation, x, the monthly income, is a function , say g, of variable y, the max amount:
X=g(y) y-15000/1.5
since we generally use the letter x for the variable of a function, we write g again as:

G (x) x-15000/1.5
tells us that if the maximum amount that John can spend is 50,000 $, then his monthly income is 23,333 $.

3.

If John's limit is $60,000, his monthly income is
G(600,000)=60,000-15,000/ 1.5=45,000/1.5 =30,000

dollars.

Answer: $ 30,000

Remark: g is called the inverse function of f, since it undoes what f does.

instead of g(x), we could use the notation

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3 years ago