Answer:
See Below.
Step-by-step explanation:
We are given that ∠A = ∠D, and we want to prove that ΔACB ~ ΔDCE.
Statements: Reasons:



Answer:
Step-by-step explanation:
Find the sum of the first 42 terms of the following series, to the nearest integer.
2,7,12
Solution
The sum is given by
SUM_n=n/2*(a_1+a_n)
a_n=a_1+(n-1)d
a_1=2, n=42, d=5
The 42nd term is therefore given by
a_42=2+(42-1)5=207
SUM_42=42/2*(2+207)=21*209=4389
The sum of the first 42 terms of the series, therefore, is 4389
Domain is all X values, and range is the Y values.
Answer:
Step-by-step explanation:
I used calculus for this, as I'm not sure there's any other way to do it and to do it as easily. This is the volume of a solid found by using the disk method of rotation:
where R(x) is the outer shell of the solid and r(x) is the space inbetween the solid and the axis of rotation. There is no space between the solid and the axis of rotation, so r(x) = 0. R(x) is the height of the solid which is 3. Therefore, f(x) = 3 and that's the function we put into the formula with the lower bound of 3 and the upper bound of 5:
and
and integrating:
and using the First Fundamental Theorem of Calculus:
V = π(9(5) - 9(3)) and
V = π(45 - 27) so
V = 18π units cubed or in decimal format,
V = 56.549 units cubed
(3,-1) pls thank me lol it makes me put 20 characters