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inna [77]
3 years ago
10

Prove that:

Mathematics
1 answer:
Monica [59]3 years ago
3 0

Recall that

sin²(<em>x</em>) = (1 - cos(2<em>x</em>))/2

so that

sin²(7<em>π</em>/8) = (1 - cos(7<em>π</em>/4))/2

sin²(5<em>π</em>/8) = (1 - cos(5<em>π</em>/4))/2

Then

sin²(7<em>π</em>/8) + sin²(5<em>π</em>/8) = (1 - cos(7<em>π</em>/4) + 1 - cos(5<em>π</em>/4))/2

… = 1 - 1/2 (cos(7<em>π</em>/4) + cos(5<em>π</em>/4))

… = 1 - 1/2 (1/√2 - 1/√2)

… = 1

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look at the cups shown below (images are not drawn to scale). how many more cubic inches of juice will cup B hold than cup A whe
Nimfa-mama [501]

Answer:

18.8 cubic inches

Step-by-step explanation:

✔️Amount of juice Cup B will hold than Cup A = Volume of cup B - volume of cup A

✔️Volume of Cup B = Volume of cylinder = πr²h

radius (r) = ½ of 2 = 1 in.

height (h) = 7 in.

Volume of cup B = π*1²*7 = 21.99 in.³

✔️Volume of Cup A = Volume of cone = ⅓πr²h

radius (r) = ½ of 2 = 1 in.

height (h) = 3 in.

Volume of cup B = ⅓*π*1²*3 = 3.14 in.³

✔️Amount of juice Cup B will hold than Cup A = 21.99 in.³ - 3.14 in.³ = 18.8 in.³ (nearest tenth)

7 0
3 years ago
What does it mean to say that two variables are positively​ associated?
stealth61 [152]

Answer:

Option A is correct.

Step-by-step explanation:

Correlation coefficients tell us how strongly the two variables are associated.

A positive correlation is a relation when both the variables move together in the same direction. Like if value of first increases the other also increases.

When the correlation coefficient is greater than 0, this means that both variables are correlated.

So, the answer here will be :

A. There is a linear relationship between the​ variables, and whenever the value of one variable​ increases, the value of the other variable increases.

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3 years ago
Help me im dying and i
inessss [21]

Answer:

The better bar to buy is the Nutty Crunch

Step-by-step explanation:

4.74 / 6 = 0.79 per bar

7.80 / 10 = 0.78 per bar

:)

6 0
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PLEASE HELP! 2 Images below! Have a great day!
Rus_ich [418]

Answer:

b

Step-by-step explanation:

so 0.5x is a slope of 1/2, which is rise 1 | run 2, and b matches that!

7 0
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Which conditional statement has a false converse?
exis [7]

Consider the converses:

a) If two planes have no points in common, then they are parallel. (true)

b) If a point lies on the y-axis, then it has x-coordinate 0. (true)

c) If two angles have the same measure, then they are congruent. (true)

d) If a figure has four sides, then it is a square. (FALSE) (A figure with 4 sides may not even be a plane figure.)

8 0
3 years ago
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