Write an equation in slope-intercept form for the line that has the given slope andcontains the point.

Pavlova-9 [17]

<h3>Exact area = 12pi - 9*sqrt(3) square inches</h3><h3>Approximate area = 22.1106545749577 square inches</h3>

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Work Shown:

Assuming the chord is horizontal along with the diameter, then this means the two smallest minor arcs are both 30 degrees each. This leaves the northern most arc to be 180-30-30 = 120 degrees in measure

A = area of northern sector (you can think of it as a pizza slize)

A = (angle/360)*pi*r^2

A = (120/360)*pi*6^2

A = 12pi

B = area of triangle

B = (1/2)*side1*side2*sin(included angle)

B = (1/2)*6*6*sin(120)

B = 18*sqrt(3)/2

B = 9*sqrt(3)

C = area of shaded region

C = A - B

C = 12pi - 9*sqrt(3) .... exact area

C = 22.1106545749577 ... use a calculator to get the approximate area

6 0

3 years ago

4> Solve by using Laplace transform: y'+5y'+4y=0; y(0)=3 y'(o)=o

harina [27]

Answer:

$y=3e^{-4t}$

Step-by-step explanation:

$y''+5y'+4y=0$

Applying the Laplace transform:

$\mathcal{L}[y'']+5\mathcal{L}[y']+4\mathcal{L}[y']=0$

With the formulas:

$\mathcal{L}[y'']=s^2\mathcal{L}[y]-y(0)s-y'(0)$

$\mathcal{L}[y']=s\mathcal{L}[y]-y(0)$

$\mathcal{L}[x]=L$

$s^2L-3s+5sL-3+4L=0$

Solving for $L$

$L(s^2+5s+4)=3s+3$

$L=\frac{3s+3}{s^2+5s+4}$

$L=\frac{3(s+1)}{(s+1)(s+4)}$

$L=\frac3{s+4}$

Apply the inverse Laplace transform with this formula:

$\mathcal{L}^{-1}[\frac1{s-a}]=e^{at}$

$y=3\mathcal{L}^{-1}[\frac1{s+4}]=3e^{-4t}$

7 0

3 years ago

4 Consider the triangle below.

Maurinko [17]

<h2>=>> <u>Solution (part A</u>) :</h2>

Given :

▪︎Triangle AMG is an isosceles triangle.

▪︎Measure of segment AM = (x+1.4) inches

▪︎Measure of segment MG = (2x+0.1) inches

▪︎Measure of segment AG = (3x-0.4) inches

▪︎segment AG is the base of triangle AMG.

Since AG is the base of the isosceles triangle AMG, segment AM and segment MG will be equal.

Which means :

$= \tt x + 1.4 = 2x + 0.1$

$= \tt x + 1.4 - 0.1 = 2x$

$= \tt \: x + 1.3 = 2x$

$= \tt 1.3 = 2x - x$

$\color{plum} \hookrightarrow \tt x = 1.3$

Thus, the value of x = 1.3

Therefore :

▪︎The value of x = 1.3

<h2>=>> <u>Solution (Part B)</u> :</h2>

We know that :

▪︎The value of x = 1.3

Which means :

The length of the leg AM :

$= \tt x + 1.4$

$= \tt 1.3 + 1.4$

$\color{plum} \tt leg \: AM= 2.7 \: inches$

Thus, the length of the leg AM = 2.7 inches

The length of leg MG :

$= \tt 2x + 0.1$

$= \tt2 \times 1.3 + 0.1$

$= \tt 2.6 + 0.1$

$\color{plum} \tt\: leg \:MG = 2.7 \: inches$

Thus, the length of the leg MG = 2.7 inches

Since the measure of the two legs are equal (2.7=2.7), we can conclude that we have found out the correct length of each leg.

Therefore :

▪︎Measure of leg AM = 2.7 inches

▪︎Measure of leg MG = 2.7 inches

<h2>=>> <u>Solution </u><u>(</u><u>part C</u><u>)</u> :</h2>

We know that :

Value of x = 1.3

Then, measure of the base AG :

$= \tt 3x - 0.4$

$= \tt 3 \times 1.3 - 0.4$

$= \tt 3.9 - 0.4$

$\color{plum}\tt \: Base \: AG = 3.5 \: inches$

Thus, the measure of the base = 3.5 inches

Therefore :

▪︎ the length of base AG = 3.5 inches.

6 0

3 years ago

Multiplying mixed numbers and whole numbers 1 1/2 x 2/1 =

Nezavi [6.7K]

Answer: 3

Step-by-step explanation:

1. Convert the mixed number to fraction:

- Multiply the denominator of the fraction by the whole number.

- Add the product obtained and the numerator of the fraction.

- Write the sum obtained as the numerator and rewrite the original denominator of the fraction.

Then:

$1\ 1/2=\frac{(1)(2)+1}{2}=\frac{3}{2}$

2. Multiply the numerators.

3. Multiply the denominator.

4. Reduce the fraction.

Then:

$(\frac{3}{2})(\frac{2}{1})=\frac{6}{2}=3$

5 0

3 years ago

How can you use the Distributive Property to solve multistep equations?

Ad libitum [116K]

Answer:

just distibute the propertys to other propertys

Step-by-step explanation

3 0

3 years ago