Which expression is equivalent to 8-(6r+2) a -6r+6 b 2r+2 c 6r+10 d -6=10
1 answer:
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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
Answer:
<em>x=-7</em>
<em>y=11</em>
Step-by-step explanation:
<u>Perpendicular Vectors</u>
Two vectors defined as their endpoints and
are perpendicular if their dot product a.b is zero. The dot product is
In other words
ac+bd=0
Let's treat all the points as the extremes of vectors, so we can easily find the missing coordinates
B (3,5) and C (7,15) define a segment, the vector
The point A is A (x,9), we need to form a vector with B
this vector must be perpendicular to BC, so, applying the dot product we have
The point D is D(17,y), we need to form a vector with C
this vector must be perpendicular to BC, so, applying the dot product we have
The points are