A piece of plexiglass is in the shape of a semicircle with radius 2m. determine the dimensions of the rectangle with the greatest area that can be cut from the piece of plexiglass
Answers
The dimensions of the rectangle having greatest area in the piece of plexiglass which is a semicircle is [tex]2\sqrt{2}[/tex] and [tex]\sqrt{2}[/tex].
Given radius of piece of plexiglass which is a semi circle equal to 2m.
We have to find the dimensions of the rectangle which is inscribed in the semi circle.
Draw a rectangle in a semicircle.
Suppose the length of rectangle be x and width be y.
Draw a line from the center to the vertex of the rectangle which forms a right angled triangle with sides x,y and 2.
[tex](x/2)^{2} +y^{2} =2^{2}[/tex]
y=[tex]\sqrt{16-x^{2} }/2[/tex]
Area of rectangle=2xy
=x[tex]\sqrt{16-x^{2} }[/tex]/2
Finding the derivative of area
d A/dx=1/2[x(-2x)/2[tex]\sqrt{16-x^{2} }[/tex]+[tex]\sqrt{16-x^{2} }[/tex]]
d A/dx=0
1/2[[tex]-2x^{2} /2\sqrt{16-x^{2} }+\sqrt{16-x^{2} } ][/tex]=0
Solving for x
[tex]\sqrt{16-x^{2}[/tex]=[tex]x^{2} /\sqrt{16-x^{2} }[/tex]
16-[tex]x^{2}[/tex]=[tex]x^{2}[/tex]
16=2[tex]x^{2}[/tex]
[tex]x^{2}[/tex]=8
x=2[tex]\sqrt{2}[/tex]
put the value of x in y=[tex]\sqrt{16-x^{2} }/2[/tex] to get the value of y
y=[tex]\sqrt{16-8} /2[/tex]
=[tex]\sqrt{8} /2[/tex]
= 2[tex]\sqrt{2} /2[/tex]
=[tex]\sqrt{2}[/tex]
Hence the dimensions of rectangle which is in a semi circle of radius 2 is [tex]\sqrt{2} and 2\sqrt{2}[/tex].
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Related Questions
Find the area of the triangle.
Answers
Answer:
[tex] 28\: ft^2[/tex]
Step-by-step explanation:
Area of the triangle
[tex] = \frac{1}{ \cancel2} \times 7 \times \cancel 8 \\ \\ = 7 \times 4 \\ \\ = 28 \: {ft}^{2} [/tex]
will give you brianlist
Answers
Answer:
-50x - 66
Step-by-step explanation:
Answer:
-50x - 66
Step-by-step explanation:
A rectangle has a length of √7 meters and a width of (2√5 - √15) meters. What is its area?
Answers
Mensuration
Given :-A rectangle has length of √7 meters and width of ( 2√5 - √15 ) meters.
To Find :-Area of rectangle.
Formula to be Used :-[tex]\boxed{Area\:of\:rectangle=Length \times Width}[/tex]
Solution :-It is given that,
Length = √7 meters
Width = ( 2√5 - √15 ) meters
Applying formula,
Area = Length × Width
Area = √7 × ( 2√5 - √15 ) sq. meters
Area = ( 2√5 × √7 - √15 × √7 ) sq. meters
Area = ( 2√( 5 × 7 ) - √( 15 × 7 ) ) sq. meters
Area = ( 2√35 - √105 ) sq. meters
Answer :-So, area of given rectangle is
( 2√35 - √105 ) sq. meters
√7 x (2√5 - √15)
= 2√35 - √105 m²
Hope it helps!
Find the number of terms and the degree of this polynomial. -9
[tex]9 {r}^{9} [/tex]
Number of terms: Degree:
Answers
Answers:
Number of terms: 1Degree: 9===============================================
Explanation:
This is consider a monomial since we only have one term. Terms are separated by a plus sign, so something like 5x^2+10x has two terms.
The degree of a polynomial is the largest exponent when dealing with single variables. In the case of 9r^9, the largest exponent is 9, so the degree is 9. Going back to an example like 5x^2+10x, the largest exponent is 2 so this is the degree of this example.
Write the point-slope form of the equation of the line through the given point with the given slope. through: (2, 2), slope = 3
Answers
Answer:
y-2=3(x-2)
Step-by-step explanation:
point slope form:
y-y₁=m(x-x₁)
y-2=3(x-2)
Which is the best estimate of the sum of 18.9 and 99.3?
A. 100
B. 110
C. 120
D. 130
Answers
Answer:
120
Step-by-step explanation:
99.3 + 18.9 = 118.2
plss help me il mark you brainly
Answers
Answer:
thisl give u extra credit: 2.29*20 = 45.80 and 3.49*35 = 122.15.
Step-by-step explanation:
Answer:
1. 78.54 (area)
2. 25.13 (circumference)
3. 4.5 (radius)
4. 13 (diameter)
Step-by-step explanation:
find the area of the figure
Answers
Answer:
24 sq units
Step-by-step explanation:
Answer:
24 square units
Step-by-step explanation:
The boxes that only have a half-shaded in can be counted as 0.5.
If you combine these half-shaded boxes, it will give you 1.
Since there are 8 half-shaded boxes, that equal to 0.5, you can multiply these together and get 4.
Add this to the 20 whole boxes, and you will get 24.
Please answer this as soon as you can I really need this done
Answers
2) yes I think
3)-x-6>-3.5 but -x-6>3.5 should also work
4) open
Left
Closed
Left
You are reading a new book. On Monday you read 3 pages. On each day after that, you read 3 times the number of pages you read on the previous day. How many pages do you read on Thursday?
pages plz answer me
Answers
81 pages.
Step-by-step explanation:
Tuesday: 3 x 3 = 9
Wednesday: 9 x 3 = 27
Thursday: 27 x 3 = 81
Answer:
81
Step-by-step explanation:
3x3x3x3
What is the circumference of a circle with a diameter of 15 inches
Answers
Answer:
C=47.1
Step-by-step explanation:
take the diameter(15) and multiply it by pi(3.14).
15 x 3.14 = 47.1
What is clustering?
A. a data point that does not fit the general pattern in the data
B. a group of data points around a value
C. a relationship between two variables
D. a graph showing the relationship between two sets of data
Answers
Answer:
B. a group of data points around a value
Step-by-step explanation:
A cluster in math is when data is clustered or assembled around one particular value.
2x – 5 > 3 or 11 – 3x > -2
Answers
Answer:
x > 4 and x <3
Step-by-step explanation:
Given the system of inequalities
2x – 5 > 3 or 11 – 3x > -2
for 2x – 5 > 3
2x > 3+5
2x>8
x>8/2
x> 4
For 11-3x > -2
-3x > 2-11
-3x > -9
x < -9/-3
x<3
hence the result will be x > 4 and x <3
Solve for w.
2w+8=13
Answers
Subtract 8 from both sides.
2w = 5
Divide both sides by 2.
w = 5/2
Answer:
w = 2.5
Step-by-step explanation:
do minus 8 on both sides making the formula
2w =5
then divide both sides by two so the 2w is now just w making it
w = 5÷2
w = 2.5
1440 tons of grain where brought to a silo over two days. On the second day 80 percent of the amount of the amount of the grain delivered during the first day where brought in. How many tons where delivered on the first day
Answers
Answer:
1152 tons of grains
Step-by-step explanation:
We are told in the above question:
Total number of grains = 1440 tons of grain
On the second day 80 percent of the amount of the amount of the grain delivered during the first day where brought in.
Hence,
The number of grains brought in during the first day = 80% × 1440 tons
= 80/100 × 1440 tons
= 1152 tons of grains
Which of the following interpretations for the given expression is correct?
A.
The sum of 2 and the quotient of 9 and 3.
B.
The product of 2 + 9 and 3.
C.
The quotient of 2 + 9 and 3.
D.
The sum of 2 and the product of 9 and 3.
Answers
Answer:
the answer is the quotient of 2+9 and 3
Find the values of x and y if l // m.
Show all work.
Answers
Answer:
x = 7, y = 24
Step-by-step explanation:
23x -16 + 8x - 21 = 180 because they are supplementary angles
31x - 37 = 180
31x = 217
x = 7
23(7)-16 = 7y - 23 because they are vertical angles
168 = 7y
y = 24
if 49 = 7 and 7 = 3 + 4, then 49 = 3 + 4
Answers
Answer:
49 = (3 + 4)²
Step-by-step explanation:
note that 49 = 7² , then
49 = (3 + 4)²
The difference of x and 4 (Algebraic expression)
Answers
Answer:
x - 4
Step-by-step explanation:
The difference means subtraction
The algebraic expression of the phrase is x-4.
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.
Given phrase:
The difference of x and 4.
Here, we have the phrase difference.
So, we will use the subtraction operation.
So, the algebraic expression,
x - 4.
Therefore, x -4 is the algebraic expression.
To learn more about the expression;
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Find the surface area of the triangular prism
Answers
Answer:
168.43524
Step-by-step explanation:
A=ah+bh+ch+1
2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=7·6+7·6+7·6+1
2·﹣74+2·(7·7)2+2·(7·7)2﹣74+2·(7·7)2﹣74≈168.43524
Factor the expression.
(_q^2r+_s^2)(_q^4t^2-6q^2rs^2t+_s^4t^2)
Answers
Answer:
2
3
4
9
Step-by-step explanation:
Michael Had a birthday party. She bought a bag of candy with 96 starbursts, 72 Hershey's, and 68 Reese's. She wanted to use all the candy she bought to make goody bags with the same amount of starbursts, Hershey's and Reese's in each bag. What is the largest number of bags she can make
Answers
Answer: 68 bags.
Step-by-step explanation: She make 68 bags before the Reese's run out.
hope this helps :)
What is the quotient of the complex numbers below? (5-5i) - (3 - i) ©
A. 1 + i
B. 1 - i
C. 2 + i
D. 2 - i
Answers
Answer:
2-4i
Step-by-step explanation:
(5-5i)-(3-i)=5-3-5i-(-i)=2-5i+i=2-4i
Answer:
the answer is D.2-i
Step-by-step explanation:
5-5i-3+i
4-2i
2-i
Factor 60 - 36w to identify the equivalent
expressions.
Answers
Answer:
Step-by-step explanation:
−36w+60
=12(−3w+5)
12(−3w+5)
Please help me!!!!
3. Compute the product axb in each of the
following cases:
a) a = -7.5
and b=0.25 ;
b) a = -2.5
and b=-18;
c) a = -812
and b=-0.75;
d) a = 4.25 and b= -326.
Answers
Answer:
a). -7.5*0.25 = -1.875
b). -2.5*(-18) = 45
c). -812*(-0.75) =609
d). 4.25*(-326) = -1385.5
You want to have $10,000 in your account after five years. Find the amount your initial deposit should be if the account pays 3.5% annual interest compounded monthly.
Answers
Answer: 8396.71
Step-by-step explanation:
what is -6x - 8 < 4
on a number line
Answers
Answer:
x > -2
Step-by-step explanation:
-6x - 8 < 4
-6x < 12
x > -2
Hope this helps
Can someone help me please
I’ll mark as brainliest
Answers
Answer true
Step-by-step explanation:
Rewrite using the
distributive property.
14 + 35?
whats the answer plz
Answers
Answer 7+7+35
Step-by-step explanation:
Answer:
I think (10*1)+4+(10*3)+5??
Step-by-step explanation:
the * represents a multiplication sign btw
Shane took out a 5.5-year loan from the bank in order to purchase at $12,000 motorcycle. At the end of the loan, he had paid $3267 in interest. Find the interest rate. Help me please
Answers
Answer:
4.95%
Step-by-step explanation:
3,267 ÷ 5.5 = $594 interest per year
$594 ÷ $12,000 = 0.0495 aka 4.95%