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4 years ago

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A traffic helicopter descends 114 meters to be 454 meters above ground, as illustrated in the diagram to the right. Write an equ

ation to describe the situation using h as the original height of the helicopter. What was the original height of the helicopter?

1 answer:

loris [4]4 years ago

3 0

Answer:

H = h + x

h = 568 meters

Step-by-step explanation:

The helicopter descends 114 meters to be 454 meters above the ground.

Therefore, the equation which describes this situation using h as the original height will be given by

H = h + x ....... (1)

Where H is the final height from the ground and x is the height that the helicopter ascends(Positive sign) or descends(Negative sign). (Answer)

Here, in our case, H = 454 meters and x = -114 meters.

Therefore, the original height of the helicopter from ground will be

h = H - x = 454 - (-114) = 568 meters. (Answer)

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VladimirAG [237]

Answer:

Part 1) $c=\sqrt{146}\ cm$

Part 2) $c=8\sqrt{2}\ in$

Part 3) The diagonal of rectangle is $d=3\sqrt{29}\ cm$

Part 4) The length of the diagonal of computer monitor is $d=15\ in$

Part 5) The ramp is $10.59\ ft$ long

Part 6) The distance between their houses is $=4\sqrt{2}\ mi$

Part 7) $234.31\ mi$

Part 8) 120 feet of wire is required

Step-by-step explanation:

Part 1) we know that

To find the length of the hypotenuse in a right triangle apply the Pythagorean Theorem

$c^2=a^2+b^2$

where

c is the hypotenuse (the greater side)

a and b are the legs

we have

$a=11\ cm\\b=5\ cm$

substitute

$c^2=11^2+5^2$

$c^2=146$

$c=\sqrt{146}\ cm$

Part 2) we know that

To find the length of the hypotenuse in a right triangle apply the Pythagorean Theorem

$c^2=a^2+b^2$

where

c is the hypotenuse (the greater side)

a and b are the legs

we have

$a=8\ in\\b=8\ in$

substitute

$c^2=8^2+8^2$

$c^2=128$

$c=\sqrt{128}\ in$

simplify

$c=8\sqrt{2}\ in$

Part 3) we know that

To find the length of the diagonal in a rectangle apply the Pythagorean Theorem

$d^2=b^2+h^2$

where

d is the diagonal of rectangle

b and h are the base and the height of rectangle

we have

$b=15\ cm\\hb=6\ cm$

substitute

$d^2=15^2+6^2$

$d^2=261$

$d=\sqrt{261}\ cm$

simplify

$d=3\sqrt{29}\ cm$

Part 4) we know that

To find the length of the diagonal of a computer monitor apply the Pythagorean Theorem

$d^2=w^2+h^2$

where

d is the diagonal of computer monitor

w and h are the wide and the high of computer monitor

we have

$w=12\ in\\h=9\ in$

substitute

$d^2=12^2+9^2$

$d^2=225$

$d=\sqrt{225}\ in$

simplify

$d=15\ in$

Part 5) we know that

To find out the length of the ramp apply the Pythagorean Theorem

$L^2=x^2+y^2$

where

L is the length of the ramp

x is the horizontal distance of the ramp

y is the vertical distance of the ramp

we have

$x=10\ ft\\y=3.5\ ft$

substitute

$L^2=10^2+3.5y^2$

$L^2=112.25$

$L=10.59\ ft$

Part 6) we know that

To find the distance between their houses apply the Pythagorean Theorem

$c^2=a^2+b^2$

where

c is the hypotenuse (distance between their houses)

a and b are the legs

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substitute

$c^2=4^2+4^2$

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$c=4\sqrt{2}\ mi$

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The speed is equal to divide the distance by the time

$speed=distance/time$

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the distance is equal to multiply the speed by the time

$distance=speed*time$

<em>First train</em>

speed=60 mph

time=3 hours

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speed=50 mph

time=3 hours

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$c^2=a^2+b^2$

where

c is the hypotenuse (distance between the trains)

a and b are the legs

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To find out the length of one wire apply the Pythagorean Theorem

$c^2=a^2+b^2$

where

c is the hypotenuse (length of one wire)

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we have

$a=3\ ft\\b=4\ ft$

substitute

$c^2=3^2+4^2$

$c^2=25$

$c=5\ ft$

so

For one tree is required ----> (5)3=15 ft

therefore

For 8 trees is required

Multiply by 8

15(8)=120 ft

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