Jean runs 6 mi and then rides 24 mi on her bicycle in a biathlon. she rides 7 mph faster than she rns. if the total time for her to complete the race is 2.25 hr, deterimine her average speed running and her average speed riding her bicycle

Average running speed: 8.52 mph

Average biking speed: 15.52 mph

Step-by-step explanation:

The formula for velocity is v= d/t where d is distance and t is time.

We know that Jean runs a distance of 6 miles and rides a distance of 24 miles.

We know that if she runs at a x mph, then she rides at x + 7 mph.

From the formula of distance, we get that t = d/v

Therefore, substituting these values in the formula for time we get:

If we apply the general formula to this quadratic equation we get:

x= -2.19

x=8.52

Jean cannot have an average negative running speed. Therefore our answer is x= 8.52

And her average running speed is 8.52 mph and her average speed riding her bicycle is 15.52 mph

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9

you estimate that the angle of elevation to the top of the 86th floor (the observatory) is 82 .the total height of the building is another 123 meters above the 86th floor.

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