Solve the inequality. 6x + 10 + 10x < 4(4x + 3)
2 answers:
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Answer:
Total weight of the wheat placed on 45th square will be =
Step-by-step explanation:
King rewarded the inventor of chess by giving grain of wheat on every square of the chess board. He places one grain of wheat on first square, 2 on second, 4 on 3rd, 8 on 4th and so on.
In fact he places grains of wheat in a progression S = 1, 2, 4, 8, 16.........n terms where value of n is 64.
We can rewrite the progression as S = 2°, 2, 2², 2³,.........n terms (n = 64)
In a geometric progression we know the nth term =
where a = first term of the series, r = common ratio, n = number of terms
Now we have to calculate the weight of all wheat placed on 45th square.
So we will put the values in the given formula 45th term =
=
=
Then the weight of wheat will be = =
Complete question is;
A park has a 3 meter tall tether ball pole and a 6.8 m tall flagpole. The lengths of their shadows are proportional to their heights.
Which of the following could be the lengths of the shadows?
Choose 2 answers from the options attached.
Answer:
Options B & D
Step-by-step explanation:
From the question, the proportional relationship between the height and shadow length is a direct proportionality. This means that an increase in the height, leads to an increase in the length of shadow and vice versa. Thus, the height to shadow length ratio is a constant.
Now, if we use x and y to denote length of shadow of tether ball pole and length of flagpole receptively, we will have;
3/x = 6.8/y
Let's make y the subject.
y = 6.8x/3
Looking at the options;
Option A: When x = 1.35 m, we have;
y = (6.8 × 1.35)/3 = 3.06 m
For Option B:
When x = 1.8 m,
y= (6.8 × 1.8)/3 = 4.08 m
For Option C:
When x= 3.75 m,
y = (6.8 × 3.75)/3 = 8.5 m
For option D:
When x = 0.6
y = (6.8 × 0.6)/3 = 1.36 m
For option E;
When x = 2,
y = (6.8 × 2)/3 = 4.533 m
From our calculations, the only values of y that correspond with the given value of y in the options are Options B & D
