Area of triangle = (base x height)/2
There are all together 4 triangles and 1 square.
Therefore, surface area = area of square + 4 x area of triangle
height = 5.8 in, base = 6 in. area of square = 6x6 = 36 in^2.
area of 1 triangle = (5.8x6)/2
area of 4 triangles = 2x5.8x6 = 69.6 in^2
surface area = 69.6 + 36 = 105.6 in^2
Answer:
x = 22
Step-by-step explanation:
same- side exterior angles are supplementary, thus
4x + 15 + 3x + 11 = 180, that is
7x + 26 = 180 ( subtract 26 from both sides )
7x = 154 ( divide both sides by 7 )
x = 22
Answer:
1/6 a gallon of paint is in each container
Step-by-step explanation:
2/3 * 1/4 = 2/12
2/12 = 1/6
A force of 182.6 lb should be applied to lift 700 lb object.
<h3>How to calculate the force?</h3>
Let the force required to lift be F
Total length = 29 in.
Distance of short end from pivot = in.
Distance from long end = 29-6 = 23 in.
Now Equating moments
F × 23 = 700x6
23F = 4200
F = 4200/23
= 182.6 lb
A force of 182.6 lb should be applied to lift 700 lb object.
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The question is:
Check whether the function:
y = [cos(2x)]/x
is a solution of
xy' + y = -2sin(2x)
with the initial condition y(π/4) = 0
Answer:
To check if the function y = [cos(2x)]/x is a solution of the differential equation xy' + y = -2sin(2x), we need to substitute the value of y and the value of the derivative of y on the left hand side of the differential equation and see if we obtain the right hand side of the equation.
Let us do that.
y = [cos(2x)]/x
y' = (-1/x²) [cos(2x)] - (2/x) [sin(2x)]
Now,
xy' + y = x{(-1/x²) [cos(2x)] - (2/x) [sin(2x)]} + ([cos(2x)]/x
= (-1/x)cos(2x) - 2sin(2x) + (1/x)cos(2x)
= -2sin(2x)
Which is the right hand side of the differential equation.
Hence, y is a solution to the differential equation.
