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3 years ago

What angle does the tangent to the curve y(x)=sin^2 (x/4)+12sin(x/4) at x=4_ make with the x-axis?

Mathematics

1 answer:

cluponka [151]3 years ago

8 0

y(x)=sin^2 (x/4)+12sin(x/4)

y(x) = sin^2(x/7) +16sin(x/7)

From the Chain Rule,

y'(x) = 2sin(x/4)*(1/4)cos(x/4) + 12(1/4)cos(x/4).

At x=4pi, the slope of the tangent line is

y'(4pi) = 2sin(4pi/4)*(1/4)cos(4pi/4) + 12(1/4)cos(4pi/4).

= 2sin(pi)*(1/4)cos(pi) + 12(1/4)cos(pi)

= 2(0)(1/4)(-1) + 12(1/4)(-1)

= -3

The angle (in radians) that the tangent line makes to the positive x-axis is

pi - arctan(3)= 1.249 rad =71.565 degree

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bonufazy [111]

Answer:

Birds $F_b=14.3\%$

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Step-by-step explanation:

From the question we are told that:

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Number of birds $n_b=2$

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Number of fish $n_f=3$

Number of hamsters $n_h=3$

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Generally the frequency for Gerbils $F_g$ is mathematically given b

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$F_g=42.9\%$

Generally the frequency for fish $F_f$ is mathematically given b

$F_f=\frac{n_f}{n}*100$

$F_f=\frac{3}{14}*100$

$F_f=21.4\%$

Generally the frequency for fish $F_h$ is mathematically given b

$F_h=\frac{n_h}{n}*100$

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3 years ago

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Lostsunrise [7]

Answer:

x = 3 (see below)

Step-by-step explanation:

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In this case, we have:

15 = 5x

5x is the same thing as 5 (x) or 5 times x. This means the reverse operation is division. So, we need to divide both sides of the equation by 5:

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3 years ago

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