2x+4=7 subtract 4 from both sides
2x=3 divide both sides by 2
x=3/2
x=1.5
10x - 12 + 10 = 18 - 20
10x - 2 = -2
10x = 0
x = 0
For the derivative tests method, assume that the sphere is centered at the origin, and consider the
circular projection of the sphere onto the xy-plane. An inscribed rectangular box is uniquely determined
1
by the xy-coordinate of its corner in the first octant, so we can compute the z coordinate of this corner
by
x2+y2+z2=r2 =⇒z= r2−(x2+y2).
Then the volume of a box with this coordinate for the corner is given by
V = (2x)(2y)(2z) = 8xy r2 − (x2 + y2),
and we need only maximize this on the domain x2 + y2 ≤ r2. Notice that the volume is zero on the
boundary of this domain, so we need only consider critical points contained inside the domain in order
to carry this optimization out.
For the method of Lagrange multipliers, we optimize V(x,y,z) = 8xyz subject to the constraint
x2 + y2 + z2 = r2<span>. </span>
Answer: 100/25 and 4/1 and 60/15
Step-by-step explanation:
20/5=4, 100/25=4, 4/1=4, and 60/15=4
A] Given that the last years's sales was $144,600 and this years sales should increase by 1/3. Then:
i] Amount the sales should increased by will be:
(last year's sales)*(increase)
=144,600*(1/3)
=48,200
ii] The sales in the new year will be:
(last year's sales)+(increase)
=144600+48600
=$192, 800
2] Given that the sales of hifi which included 6% tax was 205,000. The actual sales was:
Actual percentage sales=100%
percentage sales after taxation=100-6=94%
thus the actual sales was:
(100)/(94)*205,000
=218, 085.1064
3]Given that the rate per $100 is $0.83, and the insurance was for 90000, the insurance premium will be:
(total insurance) *(unit rate)/(number of units)
plugging the values we obtain:
90000*0.83/100
$747
