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2 years ago

EXTRA POINTS

Mathematics

1 answer:

anyanavicka [17]2 years ago

4 0

Answer:

This is a geometric sequence and the common ratio is equal to ⅛.

Step-by-step explanation:

The sequence is a geometric sequence because if we multiply a term with ⅛, we will get the consecutive term in the sequence.

The common ratio = 8/64 = 1/8

Thus, it has a common ratio of ⅛.

If we multiply 64 by ⅛, we would have the next term in the sequence. Thus:

64 × ⅛ = 64/8 = 8

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Clare is painting some doors that are all the same size. She used 2 liters of paint to cover 1 3/5 doors. How many liters of pai

barxatty [35]

Answer:

$1\frac{1}{4}\ liters$

Step-by-step explanation:

step 1

Convert mixed number to an improper fraction

$1\frac{3}{5}=\frac{1*5+3}{5}=\frac{8}{5}$

step 2

Using proportion

$\frac{2}{(8/5)}\frac{liters}{doors} =\frac{x}{1}\frac{liters}{door}\\ \\x=2/(8/5)\\ \\x=10/8\ liters$

step 3

Convert to mixed number

$\frac{10}{8}\ liters=\frac{8}{8}+\frac{2}{8}=1\frac{1}{4}\ liters$

8 0

3 years ago

PLZ HELP!!! Use limits to evaluate the integral.

Marrrta [24]

Split up the interval [0, 2] into n equally spaced subintervals:

$\left[0,\dfrac2n\right],\left[\dfrac2n,\dfrac4n\right],\left[\dfrac4n,\dfrac6n\right],\ldots,\left[\dfrac{2(n-1)}n,2\right]$

Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,

$r_i=\dfrac{2i}n$

where $1\le i\le n$ . Each interval has length $\Delta x_i=\frac{2-0}n=\frac2n$ .

At these sampling points, the function takes on values of

$f(r_i)=7{r_i}^3=7\left(\dfrac{2i}n\right)^3=\dfrac{56i^3}{n^3}$

We approximate the integral with the Riemann sum:

$\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{112}n\sum_{i=1}^ni^3$

Recall that

$\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4$

so that the sum reduces to

$\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{28n^2(n+1)^2}{n^4}$

Take the limit as n approaches infinity, and the Riemann sum converges to the value of the integral:

$\displaystyle\int_0^27x^3\,\mathrm dx=\lim_{n\to\infty}\frac{28n^2(n+1)^2}{n^4}=\boxed{28}$

Just to check:

$\displaystyle\int_0^27x^3\,\mathrm dx=\frac{7x^4}4\bigg|_0^2=\frac{7\cdot2^4}4=28$

4 0

2 years ago

Why does -2(x + 3y) = 18 equal y=-3-x/3? Please helppp

Citrus2011 [14]

Step-by-step explanation:

You're asking why

${- 2(x + 3y) = 18} = y = - 3 - \frac{x}{3}$

let's transpose the first equation for y

-2x-6y=18

-6y=18+2x

6y=-18-2x

y=-18/6-2x/6

y=-3-⅓x as required

8 0

3 years ago

Read 2 more answers

PLEAS EHEKP ILL GIVE BRAINLIEST SHOW WORK SO I CAN UNDERSTAND PLEASE

Mandarinka [93]

Answer:

$49.72

Step-by-step explanation:

The tip is 11% of the price of the pizza.

The price of the pizza is $452.

The tip is 11% of $452.

To find a percent of a number, change the percent to a decimal and multiply by the number. To change a percent to a decimal, divide the percent by 100 which is the same as moving the decimal point two places to the left.

11% of $452 =

= 0.11 * $452

= $49.72

Answer: $49.72

8 0

3 years ago

Rewrite in simplest rational exponent form x^1/2*X^1/4

jasenka [17]

Answer:

$\sqrt[4]{x^3}$

Step-by-step explanation:

First, let's examine our original statement.

$x^{\frac{1}{2} }\cdot x^{\frac{1}{4}}$

Using exponent rules, we know that if we have $x^a \cdot x^b$ , then simplified, the answer will be equivalent to $x^{a+b}$ .

So we can simplify this by adding the exponents $\frac{1}{2}$ and $\frac{1}{4}$ .

Converting $\frac{1}{2}$ into fourths gets us $\frac{2}{4}$ .

$\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$ .

So we now have $x^{\frac{3}{4}}$ .

When we have a number to a fraction power, it's the same thing as taking the denominator root of the base to the numerator power.

Basically, this becomes

$\sqrt[4]{x^3}$ . (The numerator is what we raise x to the power of, the denominator is the root we take of that).

Hope this helped!

4 0

3 years ago

Read 2 more answers

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