One number is 3 less than a second number. Twice the second number is 9 more than 5 times the first
1 answer:
You might be interested in
Answer:
10. 285
11.
16.a. Stiles Family
<u>Reason</u>-The Styles family uses twice as much as the other two, because the electric consumption per person (which is =745 KWh) is much higher than the other two.
16.b. Mendelez family
Reason-The Mendelez family uses the least amount of water, because the water usage per person (which is =875 gallons) is much lower than the other two.
Step-by-step explanation:
10. In 6 mins, no. of machine parts produced = 114
in 1 min, no. of machine parts produced = 114/6
in 15 min, no. of machine parts produces
---------------------------------------------------------------------------------------------------------
11. To make 8 jumbo muffins take, amount of baking powder used =
To make 1 jumbo muffin, amount of baking powder used = =3/16
To make 3 dozens = (3 * 12 )= 36 muffins, amount of baking powder used = 36 *3/16
=
-------------------------------------------------------------------------------------------------------------
16. a. Electricity consumed by 1 person in the Mendelez family :
=1560/4
=390 KWh
Electricity consumed by 1 person in the Barton family:
=2130/6
=355 KWh
Electricity consumed by 1 person in the Styles Family:
=1490/2
=745 KWh
The Styles family uses twice as much as the other two, because the electric consumption by 1 person is much higher than the other two.
------------------------------------------------------------------------------------------------------------
16.b. Water consumed by 1 person in the Mendelez family = 3500/4=875 gallons
Water consumed by 1 person in the Barton family = 6400/6=1050 gallons
Water consumed by 1 person in the Styles family =2500/2=1250 gallons
Answer:
12pi(8-pi), or
183.158 to third decimal place
Step-by-step explanation:
The geometry is indicated in the attached figure.
A. by integration
We will find the volume of the solid by the method of shells, i.e. we will integrate strips parallel to the axis of rotation to form many thin shells, then integrate to get the sum of all these shells.
For each shell, of thickness dy, we integrate strips of length located at y
L(x) = y(x)
and area
L(x)dy
Each strip is at a distance of (4-y) from
for which the volume of each shell equals
dV = 2*pi*(4-y)*L(x)dy = 2*pi*(4-y)*y(x) dy
The total volume of the solid can be obtained by integrating y from 0 to pi
integral( dV ) from 0 to pi
= integral (2*pi*(4-y)*y(x) dy) for y from 0 to pi
= 12*pi(-sin(y)+y*cos(y)-4*cos(y)) for y from 0 to pi
=12(8-pi)*pi
= 183.158
B. Using Pappus theorem
Pappus theorem simplifies the calculation of volume of revolution by multiplying the area of the rotating region by 2pi times the distance between the centroid and the rotation axis.
Here the area of the figure is A=2*6=12, (2 is the area under the sine curve from 0 to pi), or
A = integral (6sin(x))dx, x from 0 to pi
= 6 cos(x), x from 0 to pi
= 6(1- (-1))
= 12
Distance from centroid to axis of rotation = (4-pi/2)
Volume = 2*pi*A*(4-pi/2) = 2*pi*12*(4-pi/2)
= 12pi(8-pi)
=183.158 as before
