1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
zaharov [31]
3 years ago
11

The diagram shows a circular pond, of radius r metres, surrounded by a circular path.The circular path has a constant width of 1

.5 metres.The area of the path is the area of the pond.(a) Show that 2r2 − 60r − 45 = 0
Mathematics
1 answer:
Alenkasestr [34]3 years ago
3 0

The formula for calculating the area of a circle is expressed as;

A = πr²

  • Area of the pond = πr²
  • Area of the path = Area of the path + pond - area of pond
  • Area of path = π(r+1.5)² - πr²

Since the  area of the path is equal to the area of the pond, hence;

π(r+1.5)² - πr² = πr²

Add πr² to both sides

π(r+1.5)² - πr² + πr² =  πr² + πr²

π(r+1.5)² = 2πr²

(r+1.5)² =   2r²

Expand the parenthesis

r²+3r + 2.25 = 2r²

r²+3r + 2.25 - 2r² = 0

-r² + 3r + 2.25 = 0

r² - 3r - 2.25 = 0

Multiply through by 2

2r² - 6.0r - 4.5 = 0

<em>This proves the required equation</em>

<em />

Learn more on area of composite figures here: brainly.com/question/15981553

You might be interested in
Order the set of numbers from least to greatest<br><br>3/5, 3/10, 2/7, 1/4
Mkey [24]
3/10 2/7 1/4 3/5 that is least to greatest
8 0
3 years ago
Monica spent 3/4 hours listening to tapes of Beethoven and Brahms. She spent 1/5 hours listening to Beethoven . How many hours w
ELEN [110]

Answer:

Monica spent 0.55 hours listening to Brahms.

Step-by-step explanation:

We are given the following in the question:

Amount of time spent  listening to tapes of Beethoven and Brahms =

=\dfrac{3}{4}

Amount of time spent  listening to Beethoven =

=\dfrac{1}{5}

Total time spent listening to Brahms =

Amount of time spent  listening to tapes of Beethoven and Brahms - Amount of time spent  listening to Beethoven

=\dfrac{3}{4}-\dfrac{1}{5}\\\\=\dfrac{15-4}{20}\\\\=\dfrac{11}{20}\text{ Hours}\\\\=0.55\text{ Hours}

Thus, Monica spent  \frac{11}{20}\text{ hours} listening to Brahms.

7 0
3 years ago
Read 2 more answers
1) A line with gradient 2 passes through (0, 4). Write down the equation of the line.
blondinia [14]

<em>For</em><em> </em><em>the</em><em> </em><em>attached</em><em> </em><em>image</em><em>,</em><em> </em><em>note</em><em> </em><em>that</em><em> </em><em>slope</em><em> </em><em>is</em><em> </em><em>the</em><em> </em><em>same</em><em> </em><em>thing</em><em> </em><em>as</em><em> </em><em>gradient</em><em>.</em>

1) y = 2x + 4

2) Substituting in x = 1 and y = 1,

1 = 4(1) + c

1 = 4 + c

c = -3

So, the equation is y = 4x - 3

7 0
2 years ago
A quantity with an initial value of 120 decays exponentially at a rate of 9.5% every 7
blondinia [14]

Answer:

39.46

Step-by-step explanation:

6 0
2 years ago
Find the geometric mean of the pair of numbers. Give your answer in simplest radical form.
NARA [144]

9514 1404 393

Answer:

  10√5

Step-by-step explanation:

The geometric mean of two numbers is the square root of their product.

  m = √(20×25) = √500 = √100 × √5

  m = 10√5

The geometric mean of 20 and 25 is 10√5.

6 0
2 years ago
Other questions:
  • If they purchase one computer and five games how much do they spend before sales tax
    12·1 answer
  • Renaldo catches the bus at 4:00 pm to ride 3.2 miles from his house to the dentists office. he arrives at 4:30 pm, for a one hou
    6·1 answer
  • Khloe has 28 coins in her collection. That is five more than kourntey has. How many does kourtney have?
    7·2 answers
  • Describe the end behavior of F(x) = x^2 + 4x +3
    10·1 answer
  • Help with integer solutions to inequalities
    7·1 answer
  • A missing fraction on a number line is located exactly halfway between 3/6 and 5/6. what is the missing fraction
    7·2 answers
  • I need help on my math
    15·1 answer
  • Please help me I need this done I need someone who will SHOW WORK and complete all the questions for 15 points please help me if
    8·2 answers
  • Can someone give me 500 pts and 5 brainliest
    13·2 answers
  • How do I solve 22-(-2c+4) =3(c+4) +c​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!