Mallory began the month $135 in debt.

I need help with this math question Ags 2

vlada-n [284]

Step-by-step explanation:

$m(d) = 40(d - 35)$

$m = 40d - 1400$

$d = 40m - 1400$

or

$d = 40(m - 35)$

4 0

2 years ago

Test for convergence

Elan Coil [88]

You've established that

$\displaystyle\sum_{n\ge1}\frac1{2^n}\le\int_1^\infty\frac{\mathrm dx}{2^x}$

so all you need to do is compute the integral. Rewrite the integrand as

$\dfrac1{2^x}=2^{-x}=e^{\ln2^{-x}}=e^{-x\ln2}$

and replace $y=-x\ln2$ , so that $\mathrm dy=-\ln2\,\mathrm dx$ . Then

$\displaystyle\int_{x=1}^{x\to\infty}\frac{\mathrm dx}{2^x}=\int_{y=-\ln2}^{y\to-\infty}e^y\,\frac{\mathrm dy}{-\ln 2}=\frac1{\ln2}\int_{-\infty}^{-\ln2}e^y\,\mathrm dy$

By the fundamental theorem of calculus, this evaluates to

$\dfrac1{\ln2}e^y\bigg|_{y\to-\infty}^{y=-\ln2}=\dfrac1{\ln2}\left(e^{-\ln2}-\lim_{y\to-\infty}e^y\right)=\dfrac{e^{-\ln2}}{\ln2}=\dfrac{\frac12}{\ln2}=-\dfrac1{2\ln2}=\dfrac1{\ln4}$

and so the series converges.

You also could have used the fact that the series is geometric with common ratio less than 1 to arrive at the same conclusion, with the added perk of being able to find the exact value of the sum to corroborate this.

4 0

3 years ago

A car is traveling up a steep ramp to a parking garage.the ramp is 445 feet long and rises a vertical distance of 80 feet. What

Alecsey [184]

With the information provided in the problem, we can create a right triangle with the ramp as its hypotenuse, and the vertical rise as its opposite side from its angle of elevation.
Let $E$ be the angle of elevation from the car to the end of the ramp. We now know that the hypotenuse of our triangle measures 445 feet, and the opposite side measures 80 feet, so we need a trig function that relates our angle of elevation with the hypotenuse and the opposite side. That function is sine:
$sine(E)= \frac{80}{445}$
$E=arcsine( \frac{80}{445} )$
$E=10.36$

We can conclude that the angle of elevation from the car to the end of the ramp is 10.36°.

3 0

3 years ago

Read 2 more answers

A store had 50 bottles of olive oil. Each week, 40% of the olive oil bottles were sold and 20 new bottles arrived in shipments.

Wittaler [7]

Answer:

f(n) = f(n − 1) ⋅ 0.6 + 20, n > 0

Step-by-step explanation:

Each week 40% of the olive oil bottles were sold. This means, each week 60% of the bottles were left. In addition to these, 20 new bottles arrived in shipments.

So, every week the number of shipments was:

60% of the shipments of previous week + 20

In equation form this can written as:

Shipments in a week = 60% of shipments of previous week + 20

For, nth week we can re-write this equation as:

f(n) = 60% of f(n - 1) + 20

or

f(n) = f(n - 1) ⋅ 0.60 + 20

For example for first week, replace n by 1 to find the number of shipments in week 1 and same goes for next weeks.

8 0

3 years ago

Read 2 more answers

PLS HELP ASAPPPp!!! I DONT HAVE TIME I ONLY GOT 5 MINUTES PLS HELP THERES TWO QUESTIONS AHHH IM FREAKING OUT!

Cerrena [4.2K]

Answer:

1) $500

Step-by-step explanation:

It literally says $500 on the table hope this helps :D

For #2, i cant see the full question.

Hope this helps :D Please hit the crown if you want me to help you on the last one then tell me and make a new question !!!!!!!!!!!!

3 0

3 years ago

Read 2 more answers