Answer:
z = -ln│5eᵗ + C│
Step-by-step explanation:
dz/dt + 5eᵗ⁺ᶻ = 0
dz/dt = -5eᵗ⁺ᶻ
dz/dt = -5eᵗeᶻ
-e⁻ᶻ dz = 5eᵗ dt
e⁻ᶻ = 5eᵗ + C
-z = ln│5eᵗ + C│
z = -ln│5eᵗ + C│
A = lw
l =
w = 50 mm
a = 250 sq. mm
l =
= 5 mm
Hence, the length is 5 mm.
Answer:
x = 1
y = 3
Step-by-step explanation:
<h2>
<em><u>Substitution Method</u></em><em><u>:</u></em></h2>
Step 1:
Name The Equation
4x + y = 7 ...(1)
3x + 2y = 9 ...(2)
Step 2:
From Equation (1) we get,
4x = 7 - y
i.e.,
x = 7 - y/4
Step 3:
Substitute the value of <em><u>x = 7 - y/4</u></em> in equation (2)
i.e.,
3(7 - y/4) + 2y = 9
21 - 3y/4 + 2y = 9
21 - 3y + 8y/4 = 9
21 - 3y + 8y = 9 * 4
21 + 5y = 36
5y = 36 - 21
5y = 15
y = 15/5
<em><u>y = 3</u></em>
Step 4:
Substitute the value of <em><u>y = 3</u></em> in equation (1)
4x + y = 7
i.e.,
4x + (3) = 7
4x + 3 = 7
4x = 7 - 4
4x = 4
x = 4/4
<em><u>x = 1</u></em>
<h2><em><u>Verification</u></em><em><u>:</u></em><em><u> </u></em></h2>
4x + y = 7 i.e., <em>4(1) + (3) = 7</em>
3x + 2y = 9 i.e., <em><u>3(1) + 2(3) = 9</u></em>
1.5 * 8/5 = 0.3*8 = 2.4
2.5 * 8/5 = 0.5*8 = 4.0
Answer:
B) a²-(2*4)
Step-by-step explanation:
Since we are looking for the gray area only, we need to find the total area of the figure, but subtract that from the area of the unshaded area.
The total area of the figure is a*a=a²
The area of the unshaded figure is 2*4=8 units^2
This means the gray area is a²-(2*4) units^2, making B correct