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
pochemuha
3 years ago
13

Jack wants to use a circular rug on his rectangular office floor to cover two small circular stains, each less than π/100 square

feet in area and each more than 3 feet from the nearest wall. Can the rug be placed to cover both stains ?(1) Jack's rug covers an area of 9π square feet.(2) The centers of the stains are less than 4 feet apart.
Mathematics
1 answer:
stepladder [879]3 years ago
5 0

Answer: YES

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

  • Area of each stain=less than π/100 square feet  
  • Each one 3 feet from the nearest wall
  • Area of rug: 9π square feet
  • The centers of the stains are less than 4 feet apart.

First, we have to apply the formula AREA OF A CIRCLE(A)= π r², to obtain the radius of each stain:

π/100 = π r²  

π/100 (1/ π)= π r²  

1/100 = r²

√1/100 =r

r = 1/10 ⇒ radius of each stain

The centers of the stains are less than 4 feet apart, so:

Max diameter needed to cover is 4+ 1/10 + 1/10 = 21/5 = 4.2

Finally, we have to obtain the diameter of the rug to compare:

Area of rug: 9π

: 9π = π r2 ⇒ r= 3  

⇒ d (diameter)= 3 x2 = 6 ft

With statements (1) and (2), we know that the diameter of the rug (6ft) can completely cover both stains (max distance is 4 .2ft)

You might be interested in
Please help me i’ll give points
Umnica [9.8K]

Answer:

A,B,D

Step-by-step explanation:

8 0
3 years ago
If p is a polynomial show that lim x→ap(x)=p(a
Lostsunrise [7]

Let p(x) be a polynomial, and suppose that a is any real number. Prove that

lim x→a p(x) = p(a) .

 

Solution. Notice that

 

2(−1)4 − 3(−1)3 − 4(−1)2 − (−1) − 1 = 1 .

 

So x − (−1) must divide 2x^4 − 3x^3 − 4x^2 − x − 2. Do polynomial long division to get 2x^4 − 3x^3 − 4x^2 – x – 2 / (x − (−1)) = 2x^3 − 5x^2 + x – 2.

 

Let ε > 0. Set δ = min{ ε/40 , 1}. Let x be a real number such that 0 < |x−(−1)| < δ. Then |x + 1| < ε/40 . Also, |x + 1| < 1, so −2 < x < 0. In particular |x| < 2. So

 

|2x^3 − 5x^2 + x − 2| ≤ |2x^3 | + | − 5x^2 | + |x| + | − 2|

= 2|x|^3 + 5|x|^2 + |x| + 2

< 2(2)^3 + 5(2)^2 + (2) + 2

= 40

 

Thus, |2x^4 − 3x^3 − 4x^2 − x − 2| = |x + 1| · |2x^3 − 5x^2 + x − 2| < ε/40 · 40 = ε.

3 0
3 years ago
Qual o resultado da expressão 2m elevado a 2-5m+3,para m=3?
ipn [44]
The answer is m=4 because -3+2+5
7 0
3 years ago
Round both numbers to find the answer-WRITE OUT THE NEW PROBLEM<br> 89 x 32
ankoles [38]

Answer:

2848

Step-by-step explanation:

89 x 32 = 2848

5 0
3 years ago
Read 2 more answers
Draw polygon abcdef in this coordinate plane, given its vertices a=(-2,-3), b=(0,-3), c=(0,1), d=(3,1), e=(3,3), f=(-2,3)
tiny-mole [99]

The polygon abcdef in the coordinate plane shown with area of 18 square units.

<h3>What is a regular polygon?</h3>

A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.

We have vertices for the polygon:

a=(-2,-3), b=(0,-3), c=(0,1), d=(3,1), e=(3,3), f=(-2,3)

After marking the coordinates on the coordinate plane and connecting the lines, we will get a polygon.

We can find the area of the shape:

Area of the shape = 18 square units

Thus, the polygon abcdef in the coordinate plane shown with area of 18 square units.

Learn more about the regular polygon here:

brainly.com/question/11810316

#SPJ1

7 0
2 years ago
Other questions:
  • Whats 67000000000000 x 10 to the number of 12?
    13·1 answer
  • Q(x)=4-x over (x-4)(x+2)
    14·1 answer
  • sally is y years old mike is the difference between 20 and Sally's age Joe is four years less than triple Sally's age
    15·1 answer
  • Multiply<br> 7i(5-9i)<br> Please Help!
    14·1 answer
  • Given g (c)=9 (c )^2+7=?
    10·1 answer
  • Draw a tape diagram for 2(x+3)=10
    12·1 answer
  • Cómo se escribe el número 88,317​
    10·2 answers
  • What is the solution set of 6x2 - 24 = 0?<br> a. {2}<br> b. {-2)<br> c. {-2, 2}
    14·2 answers
  • NEED AN ANSWER BEFORE 2:40!!!
    13·2 answers
  • HELP FAST PLEASE I WILL TRY TO MARK BRAINLIEST
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!