A globe has a diameter of 12 inches. It fits inside a cube-shaped box that has a side length of 12 inches. What is the volume, rounded to the nearest hundredth of a cubic inch, of the space inside the box that is not taken up by
Volume of globe: V =
3
globe?
4
πη3
Since the diameter is 12, the radius is
4
Substitute r into the formula: V =
V=
lin²
Volume of box (square prism): V = Bh
B = s2 so B = (12)2 =
Substitute B and h into the formula: V = - (12)
V=
in3
Space not occupied by globe means the difference of the two volumes, so I
(circle correct operation) add/subtract/multiply divide.
Vbox - Vglobe
-904.32 =
in3

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50

175

step-by-step explanation:

2 inches x 10 miles = 200 miles - 3 inches = 175