A migrating salmon heads in the direction N

$$45 ^ { \circ }$$

E. swimming at 5 mi/h relative to the water. The prevailing ocean currents flow due east at 3 mi/h. Find the true velocity of the fish as a vector.

Write each equation in standard form. $x+\frac{1}{3} y=\frac{2}{9}$

find a set of parametric equations of the line. (There are many correct answers.) Passes through (-4, 5, 2) and is parallel to the xy-plane and the yz-plane

A car drives 500 ft on a road that is inclined 12 degrees to the horizontal, as shown in the figure. The car weighs 2500 lb. Thus, gravity acts straight down on the car with a constant force $\mathbf{F}=-2500 \mathbf{j}$. Find the work done by the car in overcoming gravity.

A woman walks due west on the deck of an ocean liner at 2 mi/h. The ocean liner is moving due north at a speed of 25 mi/h. Find the speed and direction of the woman relative to the surface of the water.

Find the horizontal and vertical components of the vector with given length and direction, and write the vector in terms of the vectors i and j.

$$| \mathbf { v } | = 50 , \quad \theta = 120 ^ { \circ }$$

Design a circuit to amplify the difference between two inputs by 2.5. (a) Use only one op amp. (b) Use two op amps.

If $n(A)=30, n(B)=40$ and $n(A \cup B)=45$ find $n(A \cap B)$

A jet is flying through a wind that is blowing with a speed of 55 mi/h in the direction N 30 degrees E . The jet has a speed of 765 mi/h relative to the air, and the pilot heads the jet in the direction N 45 degrees E.

Express the velocity of the wind as a vector in component form.

A jet is flying in a direction $\mathrm{~N} ~ 20^{\circ} \mathrm{~E }$ with a speed of $500 \mathrm{~\frac{mi}{h}}$. Find the north and east components of the velocity.

Solve each system by the substitution method.

$$\left\{ \begin{array} { l } { x y = 4 } \\ { x ^ { 2 } + y ^ { 2 } = 8 } \end{array} \right.$$

Find the difference. 14.7 - (-2.3)

A man pushes a lawn mower with a force of 30 lb exerted at an angle of

$$30 ^ { \circ }$$

to the ground. Find the horizontal and vertical components of the force.

Consider the function h defined by h(x) := x + 1 for

$$x \in [0, 1]$$

rational, and h(x) := 0 for

$$x \in [0, 1]$$

irrational. Show that h is not Riemann integrable.