Answer:
<u>Volume</u>
For the rectangle, h = 3cm, l = 8cm, w = 6cm
V = length x width x height
V = 8cm x 6cm x 3cm
V = 144cm^3
For the semi circle, we need to find the radius. The radius is width/2, so 6cm/2 = 3cm. r = 3cm, 
= 3.14
V = radius^2 x height x
V = 3cm^2 x 3cm x 3.14
V = 84.8 cm^3/2 (because the cylinder needs to be divided to form a semi-circle)
V= 42.4cm^3 (there are two cylinders though so we will multiply this by 2 in the total volume)
Total volume:
V = 144cm^3 + 42.4cm^3(2)
V = 186.4cm^3
<u>Surface Area</u>
Rectangular prism:
A = 2[w(l) + h(l) + h(w)]
A = 2[6cm(8cm) + 3cm(8cm) + 3cm(6cm)]
A = 180cm^2
But there are two sides that are covered by the semi-circular prisms, so we will have to calculate those sides and remove them.
A = l x w
A = 6cm x 3cm
A = 18cm^2(2) (2 being the two faces)
A = 36cm^2
A = 180cm^2 - 36cm^2
A = 144cm^2 (the area of the rectangle)
Semi-circular prism:
A = 2rh + 2r^2
Earlier, we found out that the radius of the circle is 3cm, so we will plug that in.
A = 2(3.14)(3cm)(3cm) + 2(3.14)(3cm)^2
A = 113.09cm^2
Total surface area:
A = 144cm^2 + 133.09cm^2
A = 277.09cm^2
Therefore the total volume of the prism is 186.4cm^3 and the total surface area is 277.09cm^2.
Answer:
y = 1/6 x^2 + 8/3 x + 49/6
Step-by-step explanation:
This is a parabola which opens upwards.
The distance of a point (x, y) from the focus is
√[(x - -8)^2 + (y - -1)^2] and
the distance of the point from the line y = -4
= y - -4
These distances are equal for a parabola so:
√[(x - -8)^2 + (y - -1)^2] = y + 4
Squaring both sides:
(x + 8)^2 + (y + 1)^2 = (y + 4)^2
x^2 + 16x + 64 + y^2 + 2y + 1 = y^2 + 8y + 16
x^2 + 16x + 64 + 1 - 16 = 8y - 2y
6y = x^2 + 16x + 49
y = 1/6 x^2 + 8/3 x + 49/6 is the equation of the parabola.
Add the balance and allotment:
22.90 + 50.00 = 72.90
This is how much she can actually spend.
She spent 85.50.
Subtract the two:
85.50 - 72.90 = 12.60
Since she spent more than she actually could be balance would be a negative number.
The balance would be - $12.60
For proportionality constant problems, set up the equation as,
,
Where x and y are the two variables you are comparing and <em>K </em>is the proportionality constant. If we take <em>Caramel Corn </em>values as x and <em>Cheddar Corn </em>values as y, and then solve for <em>K </em>for each ratio lines, we will get the same answer. Let's check.
,
, and
.
Hence, the proportionality constant, in this case <em>K,</em> is equal to 
or 1.5. First answer choice is correct.
ANSWER: 1.5
Answer: 52,416,000 km
Step-by-step explanation:
If a comet travels 273,000 km/hr
1) Multiply 273,000 km by 24 hours to find how far the comet travels in one day
2) multiply the answer from 1 by 8 to determine how far it travels in 8 days
1) 
*
= 
(hours cancel out)
2)*8 day= 52,416,000 km in 8 days
The comet approximately travelled 52,416,000km from when it began to travel to when it reached Earth. Hope this helped :)
