\(\displaystyle{A}_{{{5}}}={266.4},\)

\({A}_{{{10}}}={266.66},\)

\({A}_{{{30}}}={266.67},\)

\(\lim_{{{n}\rightarrow\infty}}{A}_{{{n}}}={266.67}\)

asked 2021-08-14

Suppose you take a dose of m mg of a particular medication once per day. Assume f equals the fraction of the medication that remains in your blood one day later. Just after taking another dose of medication on the second day, the amount of medication in your blood equals the sum of the second dose and the fraction of the first dose remaining in your blood, which is m+mf. Continuing in this fashion, the amount of medication in your blood just after your nth does is \(\displaystyle{A}_{{{n}}}={m}+{m}{f}+\ldots+{m}{f}^{{{n}-{1}}}\). For the given values off and m, calculate \(\displaystyle{A}_{{{5}}},{A}_{{{10}}},{A}_{{{30}}}\), and \(\displaystyle\lim_{{{n}\rightarrow\infty}}{A}_{{{n}}}\). Interpret the meaning of the limit \(\displaystyle\lim_{{{n}\rightarrow\infty}}{A}_{{{n}}}\). f=0.25,m=200mg.

asked 2021-03-05

The daily cost c to manufacture e electric scooters is given by the function \(\displaystyle{c}{\left({e}\right)}={0.05}{e}^{{2}}+{65}{e}+{1000}.\)

(a) Find \(\displaystyle{\left({c}\cdot{e}\right)}{\left({h}\right)}.\)

(b) Evaluate \(\displaystyle{\left({c}\cdot{e}\right)}{\left({13}\right)}.\)

asked 2021-02-14

Mg reacts with H+ (aq) according to

\(\displaystyle{M}{g{{\left({s}\right)}}}+{2}{H}+{\left({a}{q}\right)}\to{M}{g}_{{2}}+{\left({a}{q}\right)}+{H}_{{2}}{\left({g}\right)}\)

Suppose that 0.524 g of Mg is reacted with 60.o ml of 1.0 M H+(aq). Assume that the density of the H+ (aq) solution os 1.00 g/ml,and that its specific heat capacity equals that of water. Theinitial and final temperatures are 22.0 degree celsius and 65.8degree celsius.

a) Is the reaction endothermic or exothermic?

b) Calculate \(\displaystyle\triangle{H}\) of of th reaction. Use correct sigs andgive units.

c) Calculate the \(\displaystyle\triangle{H}\) of the reaction per mole of magnesium.

\(\displaystyle{M}{g{{\left({s}\right)}}}+{2}{H}+{\left({a}{q}\right)}\to{M}{g}_{{2}}+{\left({a}{q}\right)}+{H}_{{2}}{\left({g}\right)}\)

Suppose that 0.524 g of Mg is reacted with 60.o ml of 1.0 M H+(aq). Assume that the density of the H+ (aq) solution os 1.00 g/ml,and that its specific heat capacity equals that of water. Theinitial and final temperatures are 22.0 degree celsius and 65.8degree celsius.

a) Is the reaction endothermic or exothermic?

b) Calculate \(\displaystyle\triangle{H}\) of of th reaction. Use correct sigs andgive units.

c) Calculate the \(\displaystyle\triangle{H}\) of the reaction per mole of magnesium.

asked 2021-01-05

\(\displaystyle{q}{\left({x}\right)}={x}^{{2}}+{7}\)

\(r(x)=\sqrt{x+8}\)

Find the following.

\(\displaystyle{q}\cdot{r}{\left({1}\right)}=?\)

\(\displaystyle{\left({r}\cdot{q}\right)}{\left({1}\right)}=?\)

asked 2021-02-26

\(\displaystyle{g{{\left({x}\right)}}}=\sqrt{{{5}{x}^{{2}}}}\)

\(\displaystyle{x}{\left({w}\right)}={2}{e}^{{w}}\)

\(g(x(ww))=?\)

Evalute the composite function at 1.

\(g(x(1))=?\)

asked 2020-11-08

a. Describe what the functions f and g model in terms of the price of the computer.

b. Find \(\displaystyle{\left({f}\circ{g}\right)}{\left({x}\right)}\) and describe what this models in terms of the price of the computer.

c. Repeat part (b) for \(\displaystyle{\left({g}\circ{f}\right)}{\left({x}\right)}\).

d. Which composite function models the greater discount on the computer, \(\displaystyle{f}\circ{g}\) or \(\displaystyle{g}\circ{f}\)?

asked 2021-06-13