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erastova [34]
2 years ago
12

Approximate the area under the

Mathematics
1 answer:
taurus [48]2 years ago
4 0

Split up the interval [0, 3] into 3 equally spaced subintervals of length \Delta x = \frac{3-0}3 = 1. So we have the partition

[0, 1] U [1, 2] U [2, 3]

The left endpoint of the i-th subinterval is

\ell_i = i - 1

where i\in\{1,2,3\}.

Then the area is given by the definite integral and approximated by the left-hand Riemann sum

\displaystyle \int_0^3 f(x) \, dx \approx \sum_{i=1}^3 f(\ell_i) \Delta x \\\\ ~~~~~~~~~~ = \sum_{i=1}^3 (i-1)^3 \\\\ ~~~~~~~~~~ = \sum_{i=0}^2 i^3 \\\\ ~~~~~~~~~~ = 0^3 + 1^3 + 2^3 = \boxed{9}

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lianna [129]
Area of parallelogram = bh

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3 years ago
Pls helpppppppppppppppppppp
kotykmax [81]

Answer:

In 4 years, you will have $2,635.38

Step-by-step explanation:

The formula for annual compound interest, including principal sum, is:

A = P (1 + r/n) ^ (nt)

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A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per year

t = the number of years the money is invested or borrowed for

Note that this formula gives you the future value of an investment or loan, which is compound interest plus the principal. Should you wish to calculate the compound interest only, you need this:

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3 0
3 years ago
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From 1990 to 2000, the population of Florida increased by 2.13% per year. The population (in millions) in the year 1990 was 16 E
belka [17]

Answer:

19 million

Step-by-step explanation:

So generally whenever we express a exponential function, it's in the form: y=a(b)^x

where a=initial value aka when x=0

in this case, b can be expressed as: 1+r, where r is the growth rate, which in this case is 2.13%, and expressing that as a decimal (divide by 100), r=0.0213, thus b=1.0213

This gives us the following equation: y=16(1.0213)^x

To kind of give you a intuitive reason as to why this makes sense, think of that 1.0213 wrapping around the previous value.

So when x=0, it's actually just 16, since any number (besides 0) to the power of 0, equals 1.

When x=1, we get: 1.0213(16), which can be expressed as a 2.13% increase from year 0

When x=2, we get: 1.0213(1.0213(16)), which can be expressed as a 2.13% increase from year 1

when x=3, we get: 1.0213(1.0213(1.0213(16))), which can be expressed as a 2.13% increase from year 2.

In other words, each year we're getting another 1.0213 to multiply by (very definition of an exponent).

So to calculate the population in 1997, we put in x=7, since it's 7 years after 1990

We get the following equation: y=16(1.0213)^7

Using a calculator this simplifies to approximately: 18.5436

Rounding this to the nearest integer would yield 19, and since the values are expressed in millions, the answer would be 19 million

4 0
1 year ago
What is 2/3d -8=1/2d
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Answer:

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Step-by-step explanation:

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Multiplication: 2 + 5 - 18=
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