$A B C D$ is a parallelogram. Find the value of each ratio. $m \angle C : m \angle D$

$A B C D$ is a parallelogram. Find the value of each ratio. $m \angle B : m \angle C$

$A B C D$ is a parallelogram. Find the value of each ratio. $A D :$ perimeter of $A B C D$

In Exercises $6-14, x=12, y=10,$ and $z=24 .$ Write each ratio in simplest form. $x$ to $y$

In Exercises $6-14, x=12, y=10,$ and $z=24 .$ Write each ratio in simplest form. $=$ to $x$

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$A B C D$ is a parallelogram. Find the value of each ratio. $A B : C D$

$1 : 1$

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$A B C D$ is a parallelogram. Find the value of each ratio. $A B : B C$

$A B C D$ is a parallelogram. Find the values of $x$ and $y$

If two resistors with resistances $ R_1 $ and $ R_2 $ are connected in parallel, as in the figure, then the total resistance $ R, $ measured in ohms $ (\Omega), $ is given by$ \frac {1}{R} = \frac {1}{R_1} + \frac {1}{R_2} $If $ R_1 $ and $ R_2 $ are increasing at rates of $ 0.3 \Omega/s $ and $ 0.2 \Omega/s, $ respectively, how fast is $ R $ changing when $ R_1 = 80 \Omega $ and $ R_2 = 100 \Omega? $

The circuit of Fig. $27-75$ shows a capacitor, two ideal batteries, two resistors, and a switch S. Initially S has been open for a long time. If it is then closed for a long time, what is thechange in the charge on the capacitor?Assume $C=10 \mu \mathrm{F},$ $\mathscr{E}_{1}=1.0 \mathrm{V}, \mathscr{E}_{2}=3.0$$\mathrm{V}, R_{1}=0.20 \Omega,$ and $R_{2}=0.40 \Omega$

The perimeter of a rectangle is 24 feet.a. If $x$ is the measure of one side of the rectangle, represent the measure of an adjacent side in terms of $x .$b. If $y$ is the area of the rectangle, express the area in terms of $x$ .c. Draw the graph of the function written in b.d. What are the dimensions of the rectangle with the largest area?

Analyze the solution $ y=\phi(x) $ to the initial value problem$$ \frac{d y}{d x}=y^{2}-3 y+2, \quad y(0)=1.5 $$using approximation methods and then compare with its exact form as follows.(a) Sketch the direction field of the differential equation and use it to guess the value of $ \lim _{x \rightarrow \infty} \phi(x) $(b) Use Euler's method with a step size of 0.1 to find an approximation of $ \phi(1) $.(c) Find a formula for $ \phi(x) $ and graph $ \phi(x) $ on the direction field from part (a).(d) What is the exact value of $ \phi(1) ? $ Compare with your approximation in part (b).(e) Using the exact solution obtained in part (c), determine $ \lim _{x \rightarrow \infty} \phi(x) $ and compare with your guess in part (a).

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## Recommended Questions

$A B C D$ is a parallelogram. Find the value of each ratio.

$A B : B C$

$A B C D$ is a parallelogram. Find the value of each ratio.

$A D :$ perimeter of $A B C D$

$A B C D$ is a parallelogram. Find the value of each ratio.

$m \angle C : m \angle D$

$A B C D$ is a parallelogram. Find the values of $x$ and $y$

$A B C D$ is a parallelogram. Find the values of $x$ and $y$

If two resistors with resistances $ R_1 $ and $ R_2 $ are connected in parallel, as in the figure, then the total resistance $ R, $ measured in ohms $ (\Omega), $ is given by

$ \frac {1}{R} = \frac {1}{R_1} + \frac {1}{R_2} $

If $ R_1 $ and $ R_2 $ are increasing at rates of $ 0.3 \Omega/s $ and $ 0.2 \Omega/s, $ respectively, how fast is $ R $ changing when $ R_1 = 80 \Omega $ and $ R_2 = 100 \Omega? $

The circuit of Fig. $27-75$ shows a capacitor, two ideal batteries, two resistors, and a switch S. Initially S has been open for a long time. If it is then closed for a long time, what is the

change in the charge on the capacitor?

Assume $C=10 \mu \mathrm{F},$ $\mathscr{E}_{1}=1.0 \mathrm{V}, \mathscr{E}_{2}=3.0$

$\mathrm{V}, R_{1}=0.20 \Omega,$ and $R_{2}=0.40 \Omega$

The perimeter of a rectangle is 24 feet.

a. If $x$ is the measure of one side of the rectangle, represent the measure of an adjacent side in terms of $x .$

b. If $y$ is the area of the rectangle, express the area in terms of $x$ .

c. Draw the graph of the function written in b.

d. What are the dimensions of the rectangle with the largest area?

Analyze the solution $ y=\phi(x) $ to the initial value problem

$$ \frac{d y}{d x}=y^{2}-3 y+2, \quad y(0)=1.5 $$

using approximation methods and then compare with its exact form as follows.

(a) Sketch the direction field of the differential equation and use it to guess the value of $ \lim _{x \rightarrow \infty} \phi(x) $

(b) Use Euler's method with a step size of 0.1 to find an approximation of $ \phi(1) $.

(c) Find a formula for $ \phi(x) $ and graph $ \phi(x) $ on the direction field from part (a).

(d) What is the exact value of $ \phi(1) ? $ Compare with your approximation in part (b).

(e) Using the exact solution obtained in part (c), determine $ \lim _{x \rightarrow \infty} \phi(x) $ and compare with your guess in part (a).