As the equation is already given, we can just substitute the corresponding values in it!
Volume = 6 x 2 x 8
= 96 in3
So the answer is C. :)
<h3>
Answer: C. 3/10</h3>
A terminating decimal only happens when the fraction has a denominator with factors of 2 and/or 5. No other factors are allowed (other than 1).
Something like 1/12 has the denominator 12 with factors 2*2*3. That '3' means we won't have a terminating decimal. Similarly, the fractions 2/9 and 2/3 won't convert to a terminating decimal either.
3/10 on the other hand does convert to a terminating decimal and 3/10 = 0.3
Answer:
(a) x +5y = 22
(b) p = 11, q = 5
Step-by-step explanation:
<h3>(a)</h3>
The derivative of a function tells you the slope of its curve at every point. Then the slope of C at x=2 is ...
dy/dx = 2³ +2(2) -7 = 5
The normal to the curve at the point of interest will have a slope that is the opposite reciprocal of this: -1/5. Then the point-slope equation of the normal line can be written as ...
y -k = m(x -h) . . . . line with slope m through point (h, k)
y -4 = -1/5(x -2) . . . . line with slope -1/5 through point (2, 4)
5y -20 = -x +2 . . . . multiply by 5
x +5y = 22 . . . . . . add x+20 to put in standard form
The graph shows curve C and the desired normal line.
__
<h3>(b)</h3>
The power rule for derivatives tells you ...
(d/dx)(a·x^n) = a·n·x^(n-1)
This relation gives you two ways to find the values of p and q.
a) using the exponent of the term
b) using the coefficient of the term
Either way, the values are ...
p = 10 +1 = 11
q = 4 +1 = 10/2 = 5
The answer is b because Ashley and Camden are the only quadrilaterals