Answer:
The answer is below
Step-by-step explanation:
Mrs. Fielder decides to build a small snow shelter for her children to wait in before the school bus arrives in the morning. She has only enough wood for a total perimeter of 20 feet.
a. Make a table of all the whole number possibilities for the length and width of the shelter. Find the area of each shelter.
b. What dimensions should Mrs. Fielder choose to have the greatest area in her shelter?
c. What dimensions should Mrs. Fielder choose to have the least area in her shelter?
d. Township building codes require 3 square feet for each child in a snow shelter. Which shelter from part (a) will fit the most children? How many children is this? Explain your reasoning.
Solution:
a) Let W represent the width of the school shelter and let L represent the length of the school shelter. Therefore:
Perimeter of the school shelter = 2(length + breadth)
20 = 2(L + W)
L + W = 10
Also, the area of the school shelter = L * W
Length (ft) Width (ft) Area(ft²) = length * width
1 9 9
2 8 16
3 7 21
4 6 24
5 5 25
b) The shelter with a length of 5 ft and width of 5 ft has the largest area.
c) The shelter with a length of 1 ft and width of 9 ft has the least area.
d) The 4 by 6 ft shelter can hold 8 children (24 ft² / 3 ft² = 8) and the 5 by 5 ft shelter can hold 8 children with an extra space (25 ft² / 3 ft² = 8.33).
Answer:
The shadow is decreasing at the rate of 3.55 inch/min
Step-by-step explanation:
The height of the building = 60ft
The shadow of the building on the level ground is 25ft long
Ѳ is increasing at the rate of 0.24°/min
Using SOHCAHTOA,
Tan Ѳ = opposite/ adjacent
= height of the building / length of the shadow
Tan Ѳ = h/x
X= h/tan Ѳ
Recall that tan Ѳ = sin Ѳ/cos Ѳ
X= h/x (sin Ѳ/cos Ѳ)
Differentiate with respect to t
dx/dt = (-h/sin²Ѳ)dѲ/dt
When x= 25ft
tanѲ = h/x
= 60/25
Ѳ= tan^-1(60/25)
= 67.38°
dѲ/dt= 0.24°/min
Convert the height in ft to inches
1 ft = 12 inches
Therefore, 60ft = 60*12
= 720 inches
Convert degree/min to radian/min
1°= 0.0175radian
Therefore, 0.24° = 0.24 * 0.0175
= 0.0042 radian/min
Recall that
dx/dt = (-h/sin²Ѳ)dѲ/dt
= (-720/sin²(67.38))*0.0042
= (-720/0.8521)*0.0042
-3.55 inch/min
Therefore, the rate at which the length of the shadow of the building decreases is 3.55 inches/min
Answer:
A,D,E. Hope this helps!
Step-by-step explanation:
A. x=5
B. x=11
C. x=11/6
D. x=5
E. x=5
F. x=1/5
The Correct Answer Is...
<u><em>5/8!</em></u>
Any Questions? Comment Below!
<u><em>-AnonymousGiantsFan</em></u>
Solving inequalities is almost the same as solving equalities for basic cases. Only thing you've to watch out for is signs.
For example, in 2x + 3 > 5,
We may subtract 3 from both sides,
2x > 2
Hence, by dividing both sides by 2, we get x>1.
The inequality sign changes on multiplying with (-)
For example, 2 < 6
But, -2 > -6
And when you interchange a fraction
E.g. 3/4 > 2/3
But, 4/3 < 3/2
You can now solve these of your own
Try yourself
