Answer:
<u><em>Attachment is below</em></u>
Step-by-step explanation:
Refer to the diagram shown below.
The right vertex is at (14, -1), and the center is at (-1, -1).
Therefore the semi-major axis is
a = 14 - (-1) = 15
The right focus is at (8, -1).
Therefore
c = 8 - (-1) = 9.
The distance of the directrix from the center is
d = c²/a = 9²/15 = 81/15 = 27/5.
Therefore the equation for the left directrix is
x = -1 - 27/5 = -32/5
Answer: x = -27/5
Answer:
The first term is when n= 1
3(1)+2 = 3+2
= 5
The second term is when n= 2
3(2)+2 = 6+2
= 8
The third term is when n=3
3(3)+2 = 11
Answer: There are 3 strips that can be cut from the roll of ribbon.
Step-by-step explanation:
since we have given that
Length of a ribbon is given by
![7\frac{1}{2}\ ft\\\\=\frac{15}{2}\ ft](https://tex.z-dn.net/?f=7%5Cfrac%7B1%7D%7B2%7D%5C%20ft%5C%5C%5C%5C%3D%5Cfrac%7B15%7D%7B2%7D%5C%20ft)
Length of pieces of ribbon cut into strips is given by
![2\frac{1}{2}\ ft\\\\=\frac{5}{2}\ ft](https://tex.z-dn.net/?f=2%5Cfrac%7B1%7D%7B2%7D%5C%20ft%5C%5C%5C%5C%3D%5Cfrac%7B5%7D%7B2%7D%5C%20ft)
So, we need to find the number of strips that can be cut is given by
![\text{ Number of strips }=\frac{\text{Length of roll}}{\text{ Length of strip}}\\\\=\frac{\frac{15}{2}}{\frac{5}{2}}\\\\=\frac{15\times 2}{2\times 5}\\\\=\frac{15}{5}\\\\=3](https://tex.z-dn.net/?f=%5Ctext%7B%20Number%20of%20strips%20%7D%3D%5Cfrac%7B%5Ctext%7BLength%20of%20roll%7D%7D%7B%5Ctext%7B%20Length%20of%20strip%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7B%5Cfrac%7B15%7D%7B2%7D%7D%7B%5Cfrac%7B5%7D%7B2%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7B15%5Ctimes%202%7D%7B2%5Ctimes%205%7D%5C%5C%5C%5C%3D%5Cfrac%7B15%7D%7B5%7D%5C%5C%5C%5C%3D3)
Hence, there are 3 strips that can be cut from the roll of ribbon.
Answer: 315.3 min^-1
Step-by-step explanation:
Given the following :
Speed = 45miles per hour
Diameter of wheels = 48inches
Number of complete revolutions the wheel makes in one minute =?
Since wheel diameter is in inches, we convert speed (miles/hour) to inch per minute
1 mile = 63360 ; 60minutes = 1 hour
45 miles / hour = (45 × 63360) / 60
= 2851200 inch/60 min
= 47520inch/min
Distance covered per revolution:
Circumference of a circle (C) = 2πr
Where r = radius ; r = diameter / 2
r = 48/2 = 24 inches
C = 2 * 3.14 * 24 = 150.72inches
Number of revolutions per minute:
Speed per minute / distance covered per revolution
(47520inch/min)/ (150.72 inch)
= 315.286 min^-1