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

$$\cos F$$

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

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

If $F(x, y)=x^3-x y^2-y^4, x=2 \cos 3 t$, and $y=3 \sin t$, find dF/dt at t=0.

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

$$\sin D$$

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

Consider an F-curve with df=(2, 14). Find the F -va1ue with area 0.01 to its right.

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

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

$$\sin F$$

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.

Solve the equation or formula for the variable indicated.

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

$\triangle A B C \sim \triangle F D E$. What is DE?

Given that the length of $\overline{AC}=12$, $\overline{BC}=8$, $\overline{EF}=18$, and $\overline{DF}=6$

If in $\triangle \mathrm{A B C}$ and $\triangle \mathrm{D E F}$, AB = DE, $\mathrm{m} \angle \mathrm{A B C=\mathrm{m} \angle E D F}$, BC = DF, $\mathrm{A C}=(20 x-10)$, and $\mathrm{E F}=(15 x+15)$, what is the value of x?

True/False. If $\mathbf{f}: \mathbf{R}^{3} \rightarrow \mathbf{R}^{4}$ is differentiable, then Df(x) is a $3 \times 4$ matrix.

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