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Anettt [7]
2 years ago
14

The sum of the 6th and seventh terms in a sequence of 12 numbers with a common difference is 16. What is the Sum of the number s

equence
Mathematics
1 answer:
patriot [66]2 years ago
6 0

Answer:

96

Step-by-step explanation:

commom difference = d

a₆ + a₇ = 16

a₅ + a₈ = (a₆ - d) + (a₇ + d) = a₆ + a₇ = 16

a₄ + a₉ = (a₆ - 2d) + (a₇ + 2d) = a₆ + a₇ = 16

Similarly,

a₃ + a₁₀ = 16, a₂ + a₁₁ = 16, a₁ + a₁₂ = 16

so

a₁ + a₂ + ... + a₁₁ + a₁₂ = 6 x 16 = 96

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Using trigonometric relations, we will see that:

sin(θ ) = -0.8

<h3>How to get the sine of the angle?</h3>

For any point (x, y), the angle between the positive x-axis and the ray that connects the origin with the point (x, y) is:

θ = Atan(y/x)

In this case, the point is (3, -4), then the angle is:

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If you want to learn more about trigonometric functions:

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2 years ago
A prop for a school play is a sphere that will be hung from the ceiling. The surface area of the sphere is 5 024 cm'. If the sur
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Answer:

The radius of the sphere, to the nearest cm:

r\approx 20 cm

Step-by-step explanation:

The surface area of a sphere is given by the formula

A = 4πr²

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Given

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The radius of the sphere can be determined such as

A\:=\:4\pi r^2

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Plug in Surface Area of sphere =  5024, π = 3.14 in the formula

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Therefore, the radius of the sphere, to the nearest cm:

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3 0
2 years ago
A kitchen sink has a volume of 1800 cubic inches.What is the volume of a similar sink that is larger by a scale factor of 2
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Answer:

14400 cubic inches.

Step-by-step explanation:

Let l, b and h are length, breadth and height of a cuboid respectively, then

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Substitute k=2 and V=1800 in equation (i).

V_1=2^3(1800)

V_1=14400

Therefore, the volume of required sink is 14400 cubic inches.

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