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3 years ago

Find the y intercept!

Mathematics

1 answer:

Irina-Kira [14]3 years ago

6 0

Answer:

-23

Step-by-step explanation:

We note that as x increases by 36 from -72 to 36, y decreases by 24 from 25 to 1.

Increasing x from -36 by another 36 to zero will correspond to a decrease in y by another 24 from 1 to -23.

The y-intercept is -23.

_____

You could go to the trouble to use these observations to compute the slope as -24/36 = -2/3. Then you could pick one of the points and write the equation in point-slope form as ...

y = -2/3(x +36) +1 . . . point-slope form with m=-2/3, (h, k) = (-36, 1)

y = -2/3x -24 +1 . . . . . eliminate parentheses

y = -2/3x -23 . . . . . . . y-intercept is -23

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3 years ago

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3 years ago

In the diagram, TC represents a vertical building. The points, A and B, are on the same level as the foot C of the building such

Alenkinab [10]

Answer:

(a) The height of the building is 60.06 m

(b) The distance AB is 139.43 m

Step-by-step explanation:

The given parameters are

Given that segment BT = segment AT + 29

By trigonometric ratios, we have;

cos∠ATC = CT/AT

cos∠BTC = CT/BT

Therefore, we have;

cos(40°) = CT/AT.................................(1)

cos(56°) = CT/BT = CT/(AT + 29).....(2)

cos(56°) = CT/(AT + 29)......................(3)

From equation (1)

CT = AT×cos(40°)

From equation (3)

AT×cos(56°) + 29 × cos(56°) = CT

Therefore;

AT×cos(40°) = AT×cos(56°) + 29 × cos(56°)

AT×cos(40°) - AT×cos(56°) = 29 × cos(56°)

AT×(cos(40°) - cos(56°)) = 29 × cos(56°)

AT = 29 × cos(56°)/(cos(40°) - cos(56°)) = 78.4 m

TC = CT = AT×cos(40°) = 78.4×cos(40°) = 60.06 m

The height of the building = 60.06 m

(b) BT = AT + 29 = 78.4 m + 29 m= 107.4 m

AB = AT×sin(∠ATC ) + BT×sin(∠BTC) = 78.4×sin(40°) + 107.4×sin(56°) = 139.43 m

The distance AB = 139.43 m.

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3 years ago