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3 years ago

Helpppp meeee please I can’t fail

Mathematics

1 answer:

Mazyrski [523]3 years ago

8 0

7/12 by 4/3

Step by step:

3 1/2 * 1/6 = 7/12

8*1/6 = 8/6 = 4/3

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Pleasee help meee it’s due at 6:00

kykrilka [37]

Answer:

P’ = (4, 5)

Q’ = (5, 3)

R’ = (1, 1)

Step-by-step explanation:

8 0

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

6 0

3 years ago

Which expression is equivalent to (sqrt3 + i)^3?

Anarel [89]

Express √3 + i in polar form:

|√3 + i| = √((√3)² + 1²) = √4 = 2

arg(√3 + i) = arctan(1/√3) = π/6

Then

√3 + i = 2 (cos(π/6) + i sin(π/6))

By DeMoivre's theorem,

(√3 + i)³ = (2 (cos(π/6) + i sin(π/6)))³

… = 2³ (cos(3 • π/6) + i sin(3 • π/6))

… = 8 (cos(π/2) + i sin(π/2))

… = 8i

4 0

2 years ago

Can one of y’all help me with this pls

jolli1 [7]

Answer: A 15

Step-by-step explanation:

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3 years ago

Is my answer choice correct??

kolezko [41]

Yes that would be right

6 0

3 years ago