Answer:
1. No solution
2. Infinite many solutions
3. One solution
4. No solution
5. No solution
6. One solution
7. No solution
8. One solution
9. Infinite many solutions
10. Infinite many solutions
Step-by-step explanation:
Dy/dx = (ycos(x))/(1 + y²)
(1 + y²)/y dy = cos(x) dx
(1/y + y) dy = cos(x) dx
Integrating:
ln(y) + y²/2 = sin(x) + c
ln(1) + 1/2 = sin(0) + c
c = 1/2
Thus,
ln(y) + y²/2 = sin(x) + 1/2
Answer:
The length of the longer base he 35 units
Step-by-step explanation:
Here, we want to find the length of the longer base of the trapezoid
Mathematically, we can find the area using the formula;
1/2( a + b) h
where a is the shorter base
b is the longer base
h is the height
Let the shorter base be x
The other base is 5 times this length and that makes 5 * x = 5x
Height is the average of both bases;
(x + 5x)/2 = 6x/2 = 3x
Substituting these in the formula, we have ;
1/2(x + 5x)3x = 441
3x(6x) = 882
18x^2 = 882
x^2 = 882/18
x^2 = 49
x^2 = 7^2
x = 7
But the longer base is 5x and that will be 5 * 7 = 35 units
Answer:
26
Step-by-step explanation:
Because DAC is a straight line we can equate that:
4x - 8 + 34 + 76 - x = 180
3x + 102 = 180
3x = 78
x = 26
C= 2 x r where r = 8
C = 2 x 8
C = 16.
Hope I helped:)
