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lorasvet [3.4K]
3 years ago
13

The pass mark for a test is 86%. Steve scores 52 out of 61 marks. Does he pass the test?

Mathematics
2 answers:
Marina86 [1]3 years ago
5 0

Answer:

nope

Step-by-step explanation:

52÷61=0.85

0.85x100=85%

he needs 86% so he does not pass

laiz [17]3 years ago
4 0

Answer:

He fails

Step-by-step explanation:

Marks = 52/61

Percentage =  52/61  x 100 ~ 85%

Pass amrk =86%

85% < 86%  

So , he fails

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A road has a 10% grade, meaning increasing 1 unit of rise to every 10 units of run.
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\tan \theta = \dfrac{1}{10}

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

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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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