Find the dimensions of a rectangle with area 343 m2 whose perimeter is as small as possible.
Answers
is always a square.
343 = 7³
If the area is 343 m², then the rectangle with the smallest perimeter
is the square with sides of
√343 = (7)^ ¹·⁵ = 7 √7 meters
Final answer:
To find the dimensions of a rectangle with the smallest possible perimeter given an area of 343 m², we must determine the dimensions that will minimize the sum of the lengths of the four sides. The dimensions of the rectangle are 7 m by 49 m.
Explanation:
To find the dimensions of a rectangle with the smallest possible perimeter given an area of 343 m², we must determine the dimensions that will minimize the sum of the lengths of the four sides. Since the perimeter is the sum of the lengths of the opposite sides of a rectangle, we can rewrite the perimeter formula as P = 2l + 2w, where l represents the length and w represents the width.
Now, let's solve for the dimensions:
1. Start with the formula for the area of a rectangle: A = lw.
2. Substitute the given area: 343 = lw.
3. Rewrite the perimeter formula: P = 2l + 2w.
4. Express one variable in terms of the other using the area formula: l = 343/w.
5. Substitute the expression for l in the perimeter formula: P = 2(343/w) + 2w.
6. Simplify the equation: P = (686/w) + 2w.
7. To find the minimum perimeter, differentiate the equation with respect to w and set it equal to zero: 0 = (686/w²) + 2.
8. Solve the equation for w: (686/w²) + 2 = 0. Subtract 2 from both sides: 686/w² = -2. Multiply both sides by w²: 686 = -2w².
9. Divide both sides by -2: -343 = w². Take the square root of both sides (ignoring the positive value since the width cannot be negative): w = -√343 = -7.
10. Substitute the value of w back into the area formula: 343 = l(-7). Solve for l: 343 = -7l. Divide both sides by -7: l = 343/-7 = -49.
Since both dimensions cannot be negative, we ignore the negative values and take the absolute values of w and l: w = 7 and l = 49.
Therefore, the dimensions of the rectangle with an area of 343 m² and the smallest possible perimeter are 7 m by 49 m.
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If f(x)=2x^2+5 square root (x-2) complete the following statement f(3)=___
2x²+10x=0 by using any method
Answers
The imagepoint of (3, -3) after a translation of is
.
Determination of the coordinates of resulting point after translation
Geometrically speaking, a translation is determined by following formula:
(1)
Where:
- Original point
- Translation vector
- Resulting point
If we know that and
, then the coordinates of the resulting point are, respectively:
The imagepoint of (3, -3) after a translation of is
.
To learn more on translations, we kindly invite to check this verified question: brainly.com/question/17485121
Answer:
(0, 1)
Step-by-step explanation:
(x, y)
Left and Right movement deals with the x value
Up and Down movement deals with the y value
3 units left = -3
4 units up = +4
(x - 3, y + 4)
(3 - 3, -3 + 4)
(0, 1)
Solve problems a,b,c,d,e,and f. With the graph
Answers
Answers:
a. f(-4)=2
b. f(0)=0
d. f(-5)=0
e. x when f(x)=-2 answer: 2
f. x when f(x)=0 answer: 0
Sorry, I can’t answer c. f(3)= because when x is three from the x-axis on the graph, the line that meets 3 from the x-axis doesn’t show a whole number y-coordinate on the graph :(
But I hope this helps and answers your question :)
Answers
No. of pieces he wants to cut=3
then each piece length=total length\no.pieces
=1.2\3
=0.4metres
hope this helps u!!!!!!!!
Answers
use 2 number 3,4,5,6
I will do all of them
so consecutive number
to find them this is the equation
x is a number
x+1= next consecutive number so
the group of 2 numbers is
x+x+1=154
2x+1=154
subtract 1
2x=153
divie by 2
we want counting numbers and 153 is odd so odd divided by 2 is not a conting number so there are no 2 consecutive countin g numbers that satisfy these conditions
so there is no such number
the smallest number is x
group of 3 numbers is
x+x+1+x+2=154
3x+3=154
subtract 3
3x=151
divide by 3
the result is a non-counting number so there are no 3 consecutive counting numbers that satisfy these conditons
the smallest number is x
group of 4 numbers is
x+x+1+x+2+x+3=154
4x+6=154
subtract 6 from both sdies
4x=152
divide both sides by 4
x=38
the first number is 38
the set is
38,39,40,41
the smallest number is 38
group of 5 numbers is x+x+1+x+2+x+3+x+4=154
5x+10=154
subtract 10
5x=144
divide by 5
this will result in a non counting number so there is not 5 consecutive conungint numbers that satisfy these conditions
so the smallest number is x
group of 6 numbers is
x+x+1+x+2+x+3+x+4+x+5=154
6x+15=154
subtract 15
6x=139
divide by 6
this will result in a non counting nubmers that do knowt satisfy the condtions so the smalles tnumber is x
2 numbers:x
3 numbers:x
4 numbers:38,39,40,41
5 numbers:x
6 numbers:x
Answers
x + y = 10 and 6/x = 9/y; You need y!
=> x = 10 -y and 9x = 6y => 9(10-y) = 6y => 90 - 9y = 6y => 15y = 90 => y = 6.
Answers
Answer:
= 3 3/4 m^2
or 15/4 m^2
Step-by-step explanation:
The base is the triangle.
A =1/2 bh
A = 1/2 (3 1/3 * 9/4)
Change 3 1/3 to an improper fraction (3*3+1)/3 = 10/3
A = 1/2 * 10/3 *9/4
Re arranging
= 1/2* 9/3 * 10/4
= 1/2 (3) 5/2
=15/4
Now writing as a mixed number
= 3 3/4 m^2