Answer:
The Inequality describing the situation is
.
Step-by-step explanation:
Let the number of laps he runs be !['r'](https://tex.z-dn.net/?f=%27r%27)
Let the number of laps he swims be !['s'](https://tex.z-dn.net/?f=%27s%27)
Now Given:
Time required to run each lap = 3 min
Time required to swim each lap = 2 min
Total minutes he need to exercise more than 45
we need to write the Inequality representing the same.
Solution:
Now we can say that;
Time required to run each lap multiplied by the number of laps he runs plus Time required to swim each lap multiplied by the number of laps he swims should be greater than Total minutes he need to exercise.
framing in equation form we get;
![3r+2s>45](https://tex.z-dn.net/?f=3r%2B2s%3E45)
Hence The Inequality describing the situation is
.
Answer:
the answer is the 3rd choice: Pe=$14, Qe=31
Step-by-step explanation:
locate the price where S1 and D1 intersect= 14
locate the quantity where S1 and D1 intersect= 31
so, Pe=$14 and Qe=31
The complete question in the attached figure
we know that
Tower B ( lower left)
a) Square Pyramid
V = 1/3 lwh
V = (1/3)(3)(3)(3)
V = (1/3)(3)(9)
V = (1/3)(27)
V = 9 cubic units
b) Rectangular Prism
V = lwh
V = (3)(50)(3)
V = (3)(150)
V = 450 cubic units
tower B volume
Va + Vb
450 + 9
<span>
459 cubic units </span>
Tower E (lower right) a) Cone
V = 1/3 pi r^2 h
V = (1/3)(3.14)(3^2)(3)
V = (1/3)(3.14)(9)(3)
V = (1/3)(3.14)(27)
V = (1/3)(84.78)
V = 28.26 cubic units
b) Cylinder
V = pi r^2 h
V = (3.14)(3^2)(50)
V = (3.14)(9)(50)
V = (3.14)(450)
V = 1,413 cubic units
Tower E Volume
Va + Vb
28.26 + 1,413
1,441.26 cubic units
Tower A (upper left)
a) Hemisphere
Since it is a hemisphere, divide the formula of sphere by 2.
V = (4/3)pi r^3 all over by 2
V = (4/3)(3.14)(3^3) all over by 2
V = 113.04 / 2
V = 56.52 cubic units
b) Cylinder
V = pi r^2 h
V = (3.14)(3^2)(50)
V = (3.14)(9)(50)
V = (3.14)(450)
V = 1,413 cubic units
3rd Tower Volume
Va + Vb
56.52 + 1,413
1,469.52 cubic units Tower D (upper right)
a) Triangular pyramid
V = 1/3(1/2 bh)(H)
where b is base of the triangular base
h is the height of the triangular base
H is the altitude of the pyramid
Since H is unknown, bisect the triangular base then use Pythagorean theorem to find H.
a^2 + b^2 = c^2
let a be the base of the right triangle
b be the H or missing side of the right triangle
c be the hypotenuse of the triangle
(1.5^2) + (b^2) = 3^2
2.25 + b^2 = 9
b^2 = 9 - 2.25
b^2 = 6.75
b = 2.6 units
H = 2.6 units
Substitute:
V = (1/3)[(1/2)(3)(2.6)](3)
V = (1/3)[3.9](3)
V = (1/3)(11.7)
V = 3.9 cubic units
b) Triangular Prism
V = (bh/2) H
V = [(1.5)(2.6)/2](50)
V = (3.9/2)(50)
V = (1.95)(50)
V = 97.5 cubic units
4th Tower Volume
Va + Vb
3.9 + 97.5
101.4 cubic units
Main Castle V = lwh
V = (100)(50)(30)
V = (100)(1500)
V = 150,000 cubic units
<span>
Total Volume </span>
V1 + V2 + V3 + V4 + V5
459 + 1,441.26 + 1,469.52 + 101.4 + 150,000 ------> 153,471.18 cubic units
<span>Therefore,
the answer is the volume of the castle and the towers is </span>
153,471.18 cubic units