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3 years ago

Calcula el valor de la serie: S = 12 + 22 + 32 +42 + ... 172

Mathematics

1 answer:

Doss [256]3 years ago

6 0

Answer:

S = 1564

Step-by-step explanation:

S = 12 + 22 + 32 + .. + 172

= 12 + (12+10) + (12+20) + .. + (12+160)

= 10(1 + 2 + .. + 16) + 12×17

= 10×16×17/2 + 12×17

= 1360 + 204

= 1564

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Answer:

c = 0.5 cm

Step-by-step explanation:

Using the Sine rule in the triangle, then

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c = ≈ 0.5 cm ( to the nearest tenth )

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2 years ago

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2 years ago

Y=2x-4 What is the five ordered pairs and completing the input/output table

kati45 [8]

Answer:

{(0, -4), (1, -2), (2, 0), (3, 2), (4, 4)}

Input values (x) = {0, 1, 2, 3, 4}

Output values (y) = {-4, -2, 0, 2, 4}

Step-by-step explanation:

Given the linear equation, y = 2x - 4, you could practically choose any input value (for x), to have an output value (for y).

If x = 0:

y = 2(0) - 4

y = 0 - 4

y = -4

First ordered pair: y-intercept = (0, -4)

If x = 1:

y = 2(1) - 4

y= 2 - 4

y = -2

Second ordered pair: (1, -2).

If x = 2:

y = 2(2) - 4

y= 4 - 4

y = 0

Third ordered pair: x-intercept = (2, 0).

If x = 3:

y = 2(3) - 4

y = 6 - 4

y = 2

Fourth ordered pair: (3, 2).

If x = 4:

y = 2(4) - 4

y = 8 - 4

y = 4

Fifth ordered pair: (4, 4).

Your input values (x) = {0, 1, 2, 3, 4}

Your output values (y) = {-4, -2, 0, 2, 4}

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2 years ago

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just olya [345]

Answer:

2 is the answer I did this once in class

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2 years ago

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 31 ft/s. (a) A

julsineya [31]

Answer:

a) -13.9 ft/s

b) 13.9 ft/s

Step-by-step explanation:

a) The rate of his distance from the second base when he is halfway to first base can be found by differentiating the following Pythagorean theorem equation respect t:

$D^{2} = (90 - x)^{2} + 90^{2}$ (1)

$\frac{d(D^{2})}{dt} = \frac{d(90 - x)^{2} + 90^{2})}{dt}$

$2D\frac{d(D)}{dt} = \frac{d((90 - x)^{2})}{dt}$

$D\frac{d(D)}{dt} = -(90 - x) \frac{dx}{dt}$ (2)

Since:

$D = \sqrt{(90 -x)^{2} + 90^{2}}$

When x = 45 (the batter is halfway to first base), D is:

$D = \sqrt{(90 - 45)^{2} + 90^{2}} = 100. 62$

Now, by introducing D = 100.62, x = 45 and dx/dt = 31 into equation (2) we have:

$100.62 \frac{d(D)}{dt} = -(90 - 45)*31$

$\frac{d(D)}{dt} = -\frac{(90 - 45)*31}{100.62} = -13.9 ft/s$

Hence, the rate of his distance from second base decreasing when he is halfway to first base is -13.9 ft/s.

b) The rate of his distance from third base increasing at the same moment is given by differentiating the folowing Pythagorean theorem equation respect t:

$D^{2} = 90^{2} + x^{2}$