Nemo's aquarium is filled with 240024002400 cubic centimeters of water. The base of the aquarium is 20\text{ cm}20 cm20, space,
2 answers:
Answer:
10 cm
Step-by-step explanation:
Since, the volume of a cuboid is,
V = l × w × h,
Where,
l = length,
w = width,
h = height,
∵ The shape of the aquarium must be cuboid,
We have, l = 20 cm, w = 12 cm, V = 2400 cm³,
By substituting the values,
2400 = 20 × 12 × h
2400 = 240h
Hence, the height of the water in Nemo's aquarium would be 10 cm.
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Answers:
A = 120
b = 45.0
c = 33.2
Side Note: only one triangle is possible
See attached for a visual. I used GeoGebra to draw the triangle.
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Explanation:
We are given the following information
B = 35
C = 25
a = 68
We need to find the following
A, b, c
where the lower case letters represent the side lengths; the upper case letters are the angles. The angles are opposite their corresponding sides. For instance, side lowercase b is opposite angle uppercase B. The other letters are positioned the same way.
-----------------------
First use the idea that for any triangle, the three angles (A,B,C) must add to 180 degrees
A+B+C = 180
Replace B and C with 35 and 25. Solve for angle A
A+35+25 = 180
A+60 = 180
A+60-60 = 180-60
A = 120
Now that we know the three angles A = 120, B = 35, C = 25, we can find the missing sides 'b' and 'c'
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We will use the law of sines to find side b
sin(A)/a = sin(B)/b
sin(120)/68 = sin(35)/b
b*sin(120) = 68*sin(35) <<--- cross multiply
b = 68*sin(35)/sin(120)
b = 45.037013350222 <<--- use a calculator; this value is approximate
b = 45.0 <<--- round to the nearest tenth
-----------------------
Do the same for side c
sin(A)/a = sin(C)/c
sin(120)/68 = sin(25)/c
c*sin(120) = 68*sin(25) <<--- cross multiply
c = 68*sin(25)/sin(120)
c = 33.1838323365404 <<--- use a calculator; this value is approximate
c = 33.2 <<--- round to the nearest tenth
A = 120
b = 45.0
c = 33.2
Side Note: only one triangle is possible
See attached for a visual. I used GeoGebra to draw the triangle.
-------------------------------------------------------------
-------------------------------------------------------------
Explanation:
We are given the following information
B = 35
C = 25
a = 68
We need to find the following
A, b, c
where the lower case letters represent the side lengths; the upper case letters are the angles. The angles are opposite their corresponding sides. For instance, side lowercase b is opposite angle uppercase B. The other letters are positioned the same way.
-----------------------
First use the idea that for any triangle, the three angles (A,B,C) must add to 180 degrees
A+B+C = 180
Replace B and C with 35 and 25. Solve for angle A
A+35+25 = 180
A+60 = 180
A+60-60 = 180-60
A = 120
Now that we know the three angles A = 120, B = 35, C = 25, we can find the missing sides 'b' and 'c'
-----------------------
We will use the law of sines to find side b
sin(A)/a = sin(B)/b
sin(120)/68 = sin(35)/b
b*sin(120) = 68*sin(35) <<--- cross multiply
b = 68*sin(35)/sin(120)
b = 45.037013350222 <<--- use a calculator; this value is approximate
b = 45.0 <<--- round to the nearest tenth
-----------------------
Do the same for side c
sin(A)/a = sin(C)/c
sin(120)/68 = sin(25)/c
c*sin(120) = 68*sin(25) <<--- cross multiply
c = 68*sin(25)/sin(120)
c = 33.1838323365404 <<--- use a calculator; this value is approximate
c = 33.2 <<--- round to the nearest tenth
Answer:
B
Step-by-step explanation:
Note the common difference between consecutive terms of the sequence.
d = 16 - 12 = 20 - 16 = 4
This indicates the sequence is arithmetic with sum to n terms
=
[2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = 12 and d = 4, thus
=
[ (2 × 12) + (41 × 4) ]
= 21( 24 + 164) = 21 × 188 = 3948 → B