Let x = one of the side lengths of the base.
Then area of the base = x². So volume of the base = x²h.
That gives us x²h = 20. Solving for x, we get x = √(20/h²).
Glass is needed to cover the sides of the aquarium. There are 4 sides and 1 base. Area of a side = hx = h√(20/h²). Area of the base = x² = 20/h. Total area of glass = h√(20/h²) + 20/h. So the cost for glass = 8 * [h√(20/h²) + 20/h] = 8 h√(20/h²) + 160/h.
Metal frame is needed along the edges of the sides. There are 4 edges on the top, 4 edges in the bottom and 4 vertical edges. So the total length of metal frame = 4x + 4x + 4h = 8 √(20/h²) + 4h. Then the cost for metal frame = 7 * [8 √(20/h²) + 4h] = 56 √(20/h²) + 28h.
So the total cost = 8 h√(20/h²) + 160/h + 56 √(20/h²) + 28h
Answer:
D) 3.8 cm
Step-by-step explanation:
There are several ways this problem can be solved. Maybe the easiest is to use the Law of Cosines to find angle BAC. Then trig functions can be used to find the length of the chord.
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In triangle BAC, the Law of Cosines tells us ...
a² = b² +c² -2bc·cos(A)
A = arccos((b² +c² -a²)/(2bc)) = arccos((8² +6² -3²)/(2·8·6)) = arccos(91/96)
A ≈ 18.573°
The measure of half the chord is AB times the sine of this angle:
BD = 2(AB·sin(A)) ≈ 3.82222
The length of the common chord is about 3.8 cm.
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<em>Additional comment</em>
Another solution can be found using Heron's formula to find the area of triangle ABC. From that, its altitude can be found.
Area ABC = √(s(s-a)(s-b)(s-c)) . . . . where s=(a+b+c)/2
s=(3+8+6)/2 = 8.5
A = √(8.5(8.5 -3)(8.5 -8)(8.5 -6)) = √54.4375 ≈ 7.64444
The altitude of triangle ABC to segment AC is given by ...
A = 1/2bh
h = 2A/b = 2(7.64444)/8 = 1.911111
BD = 2h = 3.822222
Every line from the tangent to the centre is 90°. This is said in the circle theorems.
So angle OBC and ODC are 90°.
angle O is twice the size of angle F. This is another circle theorem.
Therefore angle O is 152°.
The quadrilateral of ODBC would equal to 360°. Which means 90° + 90° + 152° = 332°
360° - 332° = 28°.
The answer is 28°
Answer:
- A. fraction 1 and 1 over 2 cubic inches
Step-by-step explanation:
Unit cube side = 1/8 in
<u>Volume of prism:</u>
- V= lwh =
- 16*(1/8)*8*(1/8)*6*(1/8) =
- 2*1*3/4 =
- 3/2 = 1 1/2 cubic inches
Correct option is A
Answer:OK sure and hi my name is Chase!
so for this look for the number A and look at the bottom and side count how many squares up and sideways your number is. Hope this helps but i dont wanna give the answer because i want you to learn hope that makes sense and btw im in 5th grade and i did this last year!
Step-by-step explanation:
