X^2 x 8x -3x^2 +5 x 8x -5 x 3
8x^3 -3x^2 +40x -15
Answer:
x=6 y=12
Step-by-step explanation:
30-60-90 triangle
shorter leg is x
longer leg is
hypotenuse is 2x
since the longer leg is than makes x=6
and y=2(6)=12
complete question:
The sum of the digits of a two-digit numeral is 8. If the digits are reversed, the new number is 18 greater than the original number. How do you find the original numeral?
Answer:
The original number is 10a + b = 10 × 3 + 5 = 35
Step-by-step explanation:
Let
the number = ab
a occupies the tens place while b occupies the unit place. Therefore,
10a + b
The sum of the digits of two-digits numeral
a + b = 8..........(i)
If the digits are reversed. The reverse digit will be 10b + a. The new number is 18 greater than the original number.
Therefore,
10b + a = 18 + 10a + b
10b - b + a - 10a = 18
9b - 9a = 18
divide both sides by 9
b - a = 2...............(ii)
a + b = 8..........(i)
b - a = 2...............(ii)
b = 2 + a from equation (ii)
Insert the value of b in equation (i)
a + (2 + a) = 8
2a + 2 = 8
2a = 6
a = 6/2
a = 3
Insert the value of a in equation(ii)
b - 3 = 2
b = 2 + 3
b = 5
The original number is 10a + b = 10 × 3 + 5 = 35
Solution :
We observe that :
But BA is the perpendicular.
From the center B and WX is a chord.
Therefore, TW = TX (perpendicular from the centre of a circle to a chord bisects it)
Consider Δ BTX,
∠BTX = 90° (BA ⊥ WX)
BT = XT (Δ BTX is isosceles)
Since the angles opposite to equal sides are equal of a triangle arc are equal.
∠BTX = ∠BXT
But in the triangle,
∠TBX + ∠TXB + ∠BTX = 180°
∠TBX + ∠TBX + 90° = 180°
2 ∠TBX = 90°
∠TBX = 45°
From trigonometry, we get
...............(1)
WX = 10
i.e., TX + TW = 10
But TX = TW
2 TX = 10
Tx = 5
BX = radius of circle.
∴
= 7
Therefore, the radius of the circle is 7 units.