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1 year ago

Which function represents the amount of money Melanie and Denzel have left, f(x), after buying x pounds of strawberries?

Mathematics

1 answer:

Sedbober [7]1 year ago

8 0

Answer:

A(the first one)

Step-by-step explanation:

I do mental math but if you need an example or the way I solved to copy down then just say so.

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Nikolay [14]

Replace x with π/2 - x to get the equivalent integral

$\displaystyle \int_{-\frac\pi2}^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx$

but the integrand is even, so this is really just

$\displaystyle 2 \int_0^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx$

Substitute x = 1/2 arccot(u/2), which transforms the integral to

$\displaystyle 2 \int_{-\infty}^\infty \frac{\cos(u)}{u^2+4} \, du$

There are lots of ways to compute this. What I did was to consider the complex contour integral

$\displaystyle \int_\gamma \frac{e^{iz}}{z^2+4} \, dz$

where γ is a semicircle in the complex plane with its diameter joining (-R, 0) and (R, 0) on the real axis. A bound for the integral over the arc of the circle is estimated to be

$\displaystyle \left|\int_{z=Re^{i0}}^{z=Re^{i\pi}} f(z) \, dz\right| \le \frac{\pi R}{|R^2-4|}$

which vanishes as R goes to ∞. Then by the residue theorem, we have in the limit

$\displaystyle \int_{-\infty}^\infty \frac{\cos(x)}{x^2+4} \, dx = 2\pi i {} \mathrm{Res}\left(\frac{e^{iz}}{z^2+4},z=2i\right) = \frac\pi{2e^2}$

and it follows that

$\displaystyle \int_0^\pi \cos(\cot(x)-\tan(x)) \, dx = \boxed{\frac\pi{e^2}}$

7 0

1 year ago

A _[blank 1]_ is a number whose only factors are 1 and itself. If a number has other factors besides 1 and itself, it is called

kykrilka [37]

Numbers whose only factors are 1 and itself is known as prime numbers , numbers whose factors besides 1 and itself are composite numbers, we can use the sieve of Eratosthenes to determine whether the number is prime or composite.

Given a paragraph in which there are blanks:

A _____ is a number whose only factors are 1 and itself. If a number has factors besides 1 and itself, it is called a _____. You can use divisibility rules or _______ to help you determine whether a number is prime or composite.

We are required to fill the blank with appropriate options.

We have to fill "prime numbers" in the first blank.

We have to fill "composite numbers" in the second blank.

We have to fill "the sieve of Eratosthenes" in the third blank.

Hence numbers whose only factors are 1 and itself is known as prime numbers , numbers whose factors besides 1 and itself are composite numbers, we can use the sieve of Eratosthenes to determine whether the number is prime or composite.

Learn more about prime numbers at brainly.com/question/145452

#SPJ1

3 0

11 months ago

In meters what is the value of x? Pls i really dont know how to do this

Hitman42 [59]

Answer:

x = 75 m

Step-by-step explanation:

This is a problem of similar triangles solved using proportions.

In similar triangles, corresponding side lengths are proportional.

Here the small and large triangles are similar because the have all three angles congruent.

By proportions, identifying corresponding sides,

x/45 = 50/30

solve for x

x = 45*(50/30) = 75 m

6 0

2 years ago

PLEASE HELPPP!!!! Will give brainiest!!!!

Lady_Fox [76]

Answer:

0.008 °C

Explanation:

1) Write the changes in the temperature of the city over the 4 days in an easy way to read.

1.34 °C

- 5 / 7 °C

- 0.75 °C

4/9 ° C

2) Write the expression to show the average daily change in temperature.

The average of a set of data is calculated with the expression:

Average = (sum of the data) / amount of data

Hence, you need to add the four change of temperature data and divide by 4.

The expression is:

Average = [ 1.34 °C + (- 5 / 7 °C) + ( - 0.75 °C) + 4/9 ° C ] / 4

3) Write the steps to solve the expression:

You can choose between adding fractions or adding the decimal forms of the numbers.

If you choose adding decimals, keep the complete decimals in your calculator, to avoid the accumulation of errors due to rounding. Round only the final result.

These are the steps.

a. Find the decimal forms of the fractions:

- 5/7 ≈ 0.71428

4 /9 ≈ 0.44444

b. Add the four data:

1.34°C + (- 0.71428 °C) + (-0.75 °C) + 0.44444 °C ≈ 0.32019 °C

c. Divide the sum by the number of data (4)

0.32019 °C / 4 ≈ 0.080004 °C

4. Round to the nearest hundredth

The place of the hundreth is the second after the decimal point, which is 8 in this case:

0.080004 °C ≈ 0.08 °C

7 0

2 years ago

You own a rectangular home lot that is 46,200 square feet in size. You get a quote of $10 per foot. If your lot is 220ft long an

olya-2409 [2.1K]

Answer:

Step-by-step explanation:

width=46200÷220=210 ft

what you mean by quote? i don't know.

3 0

2 years ago