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2 years ago

PLEASE HELP ME ASAP Explain why this graph does NOT represent a linear function

Mathematics

2 answers:

user100 [1]2 years ago

8 0

Answer:

Because the x is hitting/touching more than one point.

Step-by-step explanation:

myrzilka [38]2 years ago

5 0

Answer:

x=3 maps to more than one y-value

Step-by-step explanation:

The graph is described by a linear equation:

x = 3

However, the relation it describes is not a function, because one x-value (x=3) is associated with more than one y-value.

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Graph the line x-y= -1

hammer [34]

Answer:

y = x + 1

Step-by-step explanation:

x - y = -1

-y = -x - 1

y = (-x - 1) ÷ -1

y = x + 1

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3 years ago

A road has a 10% grade, meaning increasing 1 unit of rise to every 10 units of run.

fenix001 [56]

The grade is the ratio of rise to run, i.e. the slope aka the tangent.

$\tan \theta = \dfrac{1}{10}$

$\theta = \arctan 0.1 \approx 5.711^\circ$

Answer: (a) 6 degrees

For part b, the road is the hypotenuse c of a right triangle whose tangent of the small angle is 1/10. The height h or rise is the side opposite the small angle.

$\sin\theta = \dfrac h c$

$h = c \sin \theta$

We could just take the sine of the angle we got but let's get it from the tangent exactly.

$\cos^2 \theta + \sin ^2 \theta = 1$

Dividing by squared cosine

$1 + \tan ^2 \theta = 1/\cos^2 \theta = 1/(1- \sin^2 \theta)$

$(1- \sin^2 \theta) = 1/(1 + \tan^2 \theta)$

$\sin^2 \theta = 1 - 1/(1 + \tan^2 \theta)$

$\sin^2 \theta = 1 - 1/(1 + (1/10)^2) = 1-1/(101/100) = 1/101$

$h = c \sin \theta = 2 \sqrt{1/101} \approx 0.199$

Answer: (b) Rise of 0.199 km

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2 years ago

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