\(150= 65(2) + 4.75(s)\) where \(s=\) the number of socks you can buy \(20= 4.75(s)\)

\(\displaystyle\frac{{20}}{{4.75}}={4.2105}\ldots..\)

So you can buy 4 pairs of socks. (Round down because you cant buy 0.2 pairs of socks).

asked 2021-06-01

The regular price for a pair of shoes is $48. The store is having a buy one get one 1/2 off sale. If you buy 2 pairs of shoes for that price, what percent discount is that?

asked 2020-12-31

Use logarithmic differentiation to find

\(\frac{dy}{dx} y=x \sqrt{x^2+48}\)

asked 2021-05-23

asked 2021-05-12

asked 2021-06-16

asked 2021-06-02

If \(xy+8e^y=8e\) , find the value of y" at the point where \(x=0\)

\(y"=?\)

asked 2021-05-18

At a clothing store, 3 shirts and 8 hats cost $65. The cost for 2 shirts and 2 hats is $30. How much does each shirt and hat cost?

asked 2021-06-06

\(tf"(t)+f'(t)-f((t))^2=0\)

a) What is the order of this differential equation?

b) Show that \(f(t)=\frac{1}{t}\) is a particular solution to this differential equation.

c) Find a particular solution with \(f(0)=0\)

2. Find the particular solutions to the differential equations with initial conditions:

a)\(\frac{dy}{dx}=\frac{\ln(x)}{y}\) with \(y(1)=2\)

b)\(\frac{dy}{dx}=e^{4x-y}\) with \(y(0)=0\)

asked 2021-07-05

True or False? Justify your answer with a proof or a counterexample. You can determine the behavior of all first-order differential equations using directional fields or Euler's method.

asked 2021-05-28

True or False? Justify your answer with a proof or a counterexample. You can explicitly solve all first-order differential equations by separation or by the method of integrating factors.