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2 years ago

Find the Area of the figure below, composed of a rectangle and a semicircle. Round to

Mathematics

1 answer:

chubhunter [2.5K]2 years ago

3 0

Answer:

Area = 74.1 square units

Step-by-step explanation:

Area of the composite figure = Area of the rectangle + Area of the semicircle

Area o the rectangle = Length × Width

= 10 × 6

= 60 square units

Area of the semicircle = $\frac{1}{2}\pi r^{2}$

Here, r = radius of the semicircle

For the semicircle with radius = $\frac{6}{2}$ = 3 units

Area = $\frac{1}{2}\pi (3)^{2}$

= 4.5π

= 14.14 units²

Total area of the composite figure = 60 + 14.14

= 74.14 square units ≈ 74.1 square units

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2x^3 + x^2 – 7x – 6 divided by 2x +3

nevsk [136]

Answer:

x^2 -x -2

Step-by-step explanation:

Use polynomial long division.

0 + x^2 -x -2

___________________________________

(2x+3) | 2x^3 +x^2 -7x -6

-2x^3 -3x^2

_________

-2x^2 -7x

+2x^2 +3x

__________

-4x -6

+2x +6

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6 0

2 years ago

Solve for XX. Assume XX is a 2×22×2 matrix and II denotes the 2×22×2 identity matrix. Do not use decimal numbers in your answer.

sveticcg [70]

The question is incomplete. The complete question is as follows:

Solve for X. Assume X is a 2x2 matrix and I denotes the 2x2 identity matrix. Do not use decimal numbers in your answer. If there are fractions, leave them unevaluated.

$\left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]$ · X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ =I.

First, we have to identify the matrix I. As it was said, the matrix is the identiy matrix, which means

I = $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

So, $\left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]$ · X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ = $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

Isolating the X, we have

X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ = $\left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]$ - $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

Resolving:

X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ = $\left[\begin{array}{ccc}2-1&8-0\\-6-0&-9-1\end{array}\right]$

X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ = $\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]$

Now, we have a problem similar to A.X=B. To solve it and because we don't divide matrices, we do X=A⁻¹·B. In this case,

X= $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ ⁻¹· $\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]$

Now, a matrix with index -1 is called Inverse Matrix and is calculated as: A . A⁻¹ = I.

So,

$\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ · $\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]$ = $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

9a - 3b = 1

7a - 6b = 0

9c - 3d = 0

7c - 6d = 1

Resolving these equations, we have a= $\frac{2}{11}$ ; b= $\frac{7}{33}$ ; c= $\frac{-1}{11}$ and d= $\frac{-3}{11}$ . Substituting:

X= $\left[\begin{array}{ccc}\frac{2}{11} &\frac{-1}{11} \\\frac{7}{33}&\frac{-3}{11} \end{array}\right]$ · $\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]$

Multiplying the matrices, we have

X= $\left[\begin{array}{ccc}\frac{8}{11} &\frac{26}{11} \\\frac{39}{11}&\frac{198}{11} \end{array}\right]$

6 0

2 years ago

help,for,points and brainliest math easy math hi a b c d e f g h i j k l m n o p q r s t u v w s y and z

Marrrta [24]

The answers are
D. 21
E. 30

3 0

2 years ago

What is the awnser to −35+7+(−15)

Wewaii [24]

Answer:

-43

Step-by-step explanation:

-35 + 7 + (-15)

-35 + 7 - 15

-50 + 7

= -43

4 0

1 year ago

Read 2 more answers

Solve for the missing angles and side lengths A= 20 degrees, b=4 a = 4.5 Find the measure of C

Reil [10]

Answer:

Its 142

Step-by-step explanation:

Theres a website called triangle calculator and you put in three things wether its SSA or ASA or whatever and it gives you all the measurements. Good luck on your quizzes and tests :)

6 0

2 years ago