Call the hypotenuse of the 60° triangle "y". Then the definition of the sine function tells you
... sin(60°) = (8√2)/y
or (multiplying by y/sin(60°))
... y = (8√2)/sin(60°) = (8√2)/(√3/2) = (16/3)√6
Similarly, the definition of the sine function applied to the larger triangle tells you
... sin(45°) = y/x
or
... x = y/sin(45°) = ((16/3)√6)/(1/√2) = (32/3)√3 . . . . matches selection C.
Fifty , 50 20+30=50, not sure if its asking much else
Answer:
4y^{2}+3y
Step-by-step explanation:
First you need to distribute the values.
(4y+3)(2y) Using the "Rainbow Method" to multiply the polynomials
You Should get
8y^{2}+6y
Since this is the area of the rectangle and we need to find the area of the shaded region you need to dived 8y^{2}+6y in half because the shaded region is half of the rectangle.
8y^{2}+6y/2
Doing this you will get
4y^{2}+3y
Answer:
Using either method, we obtain:
Step-by-step explanation:
a) By evaluating the integral:
The integral itself can be evaluated by writing the root and exponent of the variable u as:
Then, an antiderivative of this is:
which evaluated between the limits of integration gives:
and now the derivative of this expression with respect to "t" is:
b) by differentiating the integral directly: We use Part 1 of the Fundamental Theorem of Calculus which states:
"If f is continuous on [a,b] then
is continuous on [a,b], differentiable on (a,b) and
Since this this function is continuous starting at zero, and differentiable on values larger than zero, then we can apply the theorem. That means: