Find the following ratio $\triangle D E F$ where $m \angle E$ = $90^\circ$ DE = 4, EF= 3, DF = 5.

$$\cos D$$

In $\triangle \mathrm { DEF } ,$ find $\angle \mathrm { F }$ to the nearest degree, if $\mathrm { DE } = 15 \mathrm { cm } , \mathrm { DF } = 18 \mathrm { cm } , \text { and } \angle \mathrm { E } = 90 ^ { \circ }$

Find the following ratio $\triangle D E F$ where $m \angle E$ = $90^\circ$ DE = 4, EF= 3, DF = 5.

$$\sin D$$

Suppose that the differentiable function y=f(x) has an inverse and that the graph of f passes through the point (2,4) and has a slope of 1/3 there. Find the value of df^{-1} / dx at x=4.

If $F(x, y, z)=\left(5 x^2 y / z^3\right), x=t^{3 / 2}+2, y=\ln 4 t$, and $z=e^{3 t}$, find dF/dt in terms of x,y,z, and t.

Consider an F-curve with df=(2, 14). Find the F -value with area 0.05 to its right.

If a parallelepiped with sides $\overline{DE}, \overline{DF}$, and $\overline{DG}$ has "7ero volume." what can you say about points D, E,F and $G$ ?

$$\begin{array} { l } { \text { In } \triangle \mathrm { DEF } } \\ { \mathrm { DF } = 6.0 \mathrm { km } } \\ { \angle \mathrm { E } = 44 ^ { \circ } } \\ { \angle \mathrm { F } = 90 ^ { \circ } } \end{array}$$

a) Draw this triangle and label the given information. b) Solve $\triangle \mathrm { DEF }$

BC=EF and AC=DF. Are the triangles congruent?

The triangle given are triangles ABC and DEF. The vertices are at A(-3,2), B(-3,4), C(1,4), D(-7,-2), E(-7,0), and (-3,0).

A. Yes

B. No

Let f(x)=x^2-4x-5, x>2 . Find the value of df^{-1} / dx at the point x=0=f(5).

Solve the equation or formula for the variable indicated.

$$\frac{df + 10}{6} = g,\ for\ f$$

Given f(x) = 2x^2, $x\geq 0$, a = 5: (a) Find f^{-1}(x). (b) Graph f and f^{-1} together. (c) Evaluate df/dx at x = a and df^{-1}/dx at x = f(a) to show that at these points df^{-1}/dx = 1/(df/dx).

Perform the operation : $DF$, where matrices $A$ and $C$ are :

$$D= \begin{bmatrix} 3 & 0\\ 1 & -1 \\ 2 & 5 \end{bmatrix} \ \ \ \ F= \begin{bmatrix} 1 \\ 0 \\ -1 \end{bmatrix}$$

Find the following ratio $\triangle D E F$ where $m \angle E$ = $90^\circ$ DE = 4, EF= 3, DF = 5.

$$\sin F$$