Answer:
Total length of ribbon to line the long sides will be 22 in
Step-by-step explanation:
In the given figure of kite if we draw a line "h" vertically will form two right angle triangles.
Then by applying Pythagoras theorem in both the triangles.
h²= (3x + 5)² + (2x + 1)² ------(1)
h²= (5x + 1)² + 5² ------(2)
By equating both the equations
(3x + 5)² + (2x + 1)² = (5x + 1)² + 25
9x² + 25 + 30x + 4x² + 4x + 1 = 25x² + 10x + 1 + 25
13x² + 34x + 26 = 25x² + 10x + 26
13x² - 25x² + 34x - 10x + 26 - 26 = 0
- 12x² + 24x = 0
12x² - 24x = 0
x² - 2x = 0
x(x - 2) = 0
x = 2
Now we will put x = 2 in the measure of sides of the kite.
Side 1 = (3x + 5)
= 3×2 + 5
= 11
Side 2 = (5x + 1)
= 5×2 + 1
= 11
Side 3 = (2x + 1)
= 2×2 + 1
= 5
Therefore, Total length of ribbon to line the long sides will be = 11 + 11
= 22 in.

Here , the given data is :
- Principal = Rs 4400 . ( P )
- Time = 3 years . ( T )
- Rate of Internet = 8% . ( R )
We can calculate Simple Interest using ,

On substituting the respective values ,
⇒ SI = P × R × T / 100.
⇒ SI = Rs 4400 × 8 × 3 / 100 .
⇒ SI = Rs 44 × 8 × 3 .
⇒ SI = Rs 1,056 .
<u>Hence</u><u> </u><u>the</u><u> </u><u>requ</u><u>ired</u><u> </u><u>Interest</u><u> </u><u>is</u><u> </u><u>Rs</u><u> </u><u>1</u><u>,</u><u>0</u><u>5</u><u>6</u><u>.</u>
Answer:
volume of the solid generated when region R is revolved about the x-axis is π ₀∫^a (
x + b )² dx
Step-by-step explanation:
Given the data in the question and as illustrated in the image below;
R is in the region first quadrant with vertices; 0(0,0), A(a,0) and B(0,b)
from the image;
the equation of AB will be;
y-b / b-0 = x-0 / 0-a
(y-b)(0-a) = (b-0)(x-0)
0 - ay -0 + ba = bx - 0 - 0 + 0
-ay + ba = bx
ay = -bx + ba
divide through by a
y =
x + ba/a
y =
x + b
so R is bounded by y =
x + b and y =0, 0 ≤ x ≤ a
The volume of the solid revolving R about x axis is;
dv = Area × thickness
= π( Radius)² dx
= π (
x + b )² dx
V = π ₀∫^a (
x + b )² dx
Therefore, volume of the solid generated when region R is revolved about the x-axis is π ₀∫^a (
x + b )² dx