The illustration below shows the graph of y as a function

2) Dada a equação x2 – 4x – 12, faça o que se pede.

alexandr1967 [171]

Answer:

a) x1 = 6 and x2 = -2

b) -2

Step-by-step explanation:

a)

To find the roots of the quadratic equation, we can use the Bhaskara's formula:

Delta = b^2 - 4ac

Delta = (-4)^2 - 4*1*(-12) = 64

sqrt(Delta) = 8

x1 = (-b + sqrt(Delta)) / 2a

x1 = (4 + 8) / 2

x1 = 6

x2 = (-b - sqrt(Delta)) / 2a

x2 = (4 - 8) / 2

x2 = -2

b)

The roots are 6 and -2, so the smaller root is -2

4 0

3 years ago

O, R and S are points in the same horizontal plane. /OR/ = 20m and /OS/= 32m.The bearing of R and S from O are 030° and 135° res

Viktor [21]

<h3>Answer: roughly 12.6274 meters</h3>

The more accurate value is 12.6274169979696, though it's not fully exact.

Round this however you need to.

The exact distance 32*sin(45) - 10 meters.

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Explanation:

Refer to the diagram below.

I'll use point A in place of point O since the letter 'oh' is very similar looking to the number zero.

Plot point A at the origin (0,0). While at point A, look directly north. Then turn 30 degrees eastward to look at the bearing 030°. Next, move 20 meters along that bearing direction to arrive at point R. Segment AR is 20 meters long.

In the diagram, note how angle RAB is 30 degrees. The side opposite this is BR = m.

We can use the sine ratio to say that

sin(angle) = opposite/hypotenuse

sin(A) = BR/AR

sin(30) = m/20

m = 20*sin(30)

m = 10

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While still at point A, look directly north and turn 135 degrees clockwise (ie toward the east) and move 32 meters along that bearing. You'll arrive at point S as the diagram shows.

Notice how

angle RAB + angle RAC + angle CAS = 30+60+45 = 135

The remaining angle DAS is 180-135 = 45 degrees.

When focusing on triangle DAS, we can say

sin(A) = DS/AS

sin(45) = n/32

n = 32*sin(45)

n = 22.6274169979696

This value is approximate.

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Subtract the values of m and n

n - m = 32*sin(45) - 10 = exact distance