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Anit [1.1K]
3 years ago
14

Write the verbal sentence as an equation:

Mathematics
1 answer:
asambeis [7]3 years ago
8 0
20 - (4xn) = 4 is the equation
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Use the definition to find an expression for the area under the curve y = x3 from 0 to 1 as a limit. lim n→∞ n i = 1 R (b) The f
Harlamova29_29 [7]

The summand (R?) is missing, but we can always come up with another one.

Divide the interval [0, 1] into n subintervals of equal length \dfrac{1-0}n=\dfrac1n:

[0,1]=\left[0,\dfrac1n\right]\cup\left[\dfrac1n,\dfrac2n\right]\cup\cdots\cup\left[1-\dfrac1n,1\right]

Let's consider a left-endpoint sum, so that we take values of f(\ell_i)={\ell_i}^3 where \ell_i is given by the sequence

\ell_i=\dfrac{i-1}n

with 1\le i\le n. Then the definite integral is equal to the Riemann sum

\displaystyle\int_0^1x^3\,\mathrm dx=\lim_{n\to\infty}\sum_{i=1}^n\left(\frac{i-1}n\right)^3\frac{1-0}n

=\displaystyle\lim_{n\to\infty}\frac1{n^4}\sum_{i=1}^n(i-1)^3

=\displaystyle\lim_{n\to\infty}\frac1{n^4}\sum_{i=0}^{n-1}i^3

=\displaystyle\lim_{n\to\infty}\frac{n^2(n-1)^2}{4n^4}=\boxed{\frac14}

8 0
3 years ago
You have 4/6 of a cup of lemonade concentrate. If you mix 1/3 of a cup of the concentrate with a quart of water you make a small
Vadim26 [7]

Answer:

Numbers of pitchers of lemonade = 8

Step-by-step explanation:

Given as

Amount of lemonade concentration = \frac{4}{6} of a cup

Now,  \frac{1}{3} of a cup of concentration mix with  \frac{1}{4} of water

So,  \frac{1}{3} -  \frac{1}{4} =  \frac{1}{12} of cup of lemonade,

∴ The number of small pitcher of lemonade =  (\frac{4}{6} /\frac{1}{12} )

                                                                         =  4 × 2 = 8    Answer            

8 0
3 years ago
Help math beats me up in dark alleys
andriy [413]

Replace x with 3:

f(x) = 20(0.5)^x

f(3) = 20(0.5)^3

First do 0.5^3 = 0.125

Now multiply that by 20:

20 x 0.125 = 2.5


f(3) = 2.5

3 0
3 years ago
-8w + 3z when w = 2.2 and z = 9.1.
amm1812
The answer would be 9.7
4 0
3 years ago
Write the equation of the line shown in the graph. Please help.
jeka57 [31]

Answer:

y = 3

Step-by-step explanation:

The y-coordinate of all points on the graph is 3.

The equation is y = 3

3 0
3 years ago
Read 2 more answers
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