The dimensions that give the maximum area is 5 cm by 5 cm.
Given:
The perimeter of this rectangle is 20 cm, and formula for perimeter is
P= 2(W+L)
P = 20 cm = 2W + 2L.
Then W + L = 10 cm,
or W = (10 cm) - L.
The area of the rectangle is A = L·W, and is to be maximized.
On substituting the values, we get A = L[ (10 cm) - L ], or A = 10L - L²
Note that this is the equation of a parabola that opens down. With coefficients a = -1, b = 10 and C = 0, we find that the x-coordinate of the vertex (which is the x-coordinate of the maximum as well) is
x = -b / (2a). Subbing 10 for b and -1 for a, we get:
x = -[10] / [2·(-1)] = 10/2, or 5.
This tells us that one dimension of the rectangle is 5 cm.
Since P = 20 cm = 2L + 2W, and if we let L = 5 cm, we get:
20 cm = 2(5 cm) + 2W, or
10 cm = W + 5 cm, or W = 5 cm.
Therefore, choosing L = 5 cm and W = 5 cm results in a square, which in turn leads to the rectangle having the maximum possible area.
Learn more:
Answer:
5 cm by 5 cm
Step-by-step explanation:
The perimeter of this rectangle is 20 cm, and the relevant formula is
P = 20 cm = 2W + 2L. Then W + L = 10 cm, or W = (10 cm) - L.
The area of the rectangle is A = L·W, and is to be maximized. Subbing (10 cm) - L for W, we get A = L[ (10 cm) - L ], or A = 10L - L²
Note that this is the equation of a parabola that opens down. With coefficients a = -1, b = 10 and C = 0, we find that the x-coordinate of the vertex (which is the x-coordinate of the maximum as well) is
x = -b / (2a). Subbing 10 for b and -1 for a, we get:
x = -[10] / [2·(-1)] = 10/2, or 5.
This tells us that one dimension of the rectangle is 5 cm.
Since P = 20 cm = 2L + 2W, and if we let L = 5 cm, we get:
20 cm = 2(5 cm) + 2W, or
10 cm = W + 5 cm, or W = 5 cm.
Thus, choosing L = 5 cm and W = 5 cm results in a square, which in turn leads to the rectangle having the maximum possible area.
Based on the right-angle triangle shown below, thesine of ∠A include the following: B.) 3/5.
In order to determine the magnitude of angle A, we would apply the basic sine trigonometric ratio because the given side lengths represent the opposite side (CB) and hypotenuse (AB) of a right-angled triangle;
sin(θ) = Opp/Hyp
Where:
Based on sine trigonometric ratio, the magnitude of angle A can be calculated as follows:
sin(θ) = Opp/Hyp
sin(A) = CB/AB
sin(A) = 3/5.
In conclusion, we can reasonably and logically deduce that thesine of angle A (m∠A) is 3/5.
Complete Question:
Find the sine of ∠A.
A.) 3/4
B.) 3/5
C.) 4/5
D.) 4/3
B: –24
C: –15
D: –6
Answer:
The correct answer is D. -6
Step-by-step explanation:
f(x) = 3x + 3
g(x) = 3x + 3
h(x) = x + 3
We need to find : [g o f o h](–5)
⇒ [g o f o h](–5)
⇒ [g o f]h(-5)
⇒ [g o f](-5 + 3)
⇒ [g o f](-2)
⇒ [g]f(-2)
⇒ [g](3 × -2 + 3)
⇒ [g](-6 + 3)
⇒ g(-3)
⇒ 3 × -3 + 3
⇒ -9 + 3
⇒ -6
Therefore, The correct answer is D. -6
Find the total number of acres Mrs. Chen owns, to the nearest hundredth of an acre and please explain how to do it.
The cost of 7 cakes will be equal to 5.6.
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the cost of 5 cakes is 4. The cost of 7 cakes will be calculated as,
5 cakes = 4
1 cake = 4 / 5
7 cakes = ( 4 x 7 ) / 5
7 cakes = 5.6
To know more about an expression follow
#SPJ2