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3 years ago

12. Venu and Tanuj are running along a circular track. They take 48 seconds and 56 seconds to

Mathematics

1 answer:

brilliants [131]3 years ago

8 0

Answer:

The meet at first time at starting point after 336 seconds,

Vanu have completed 7 laps while Tanuj has completed 6 laps.

Step-by-step explanation:

Given that Venu and Tanuj take 48 seconds and 56 seconds to

complete a lap respectively.

To meet them again at the startiong point, the time taken must be multiple of 56 and 48.

So, the minimum time required to meet them again at the startiong point is time taken for first time meet.

Time taken to first time meet is the smallest number which can be divided by 56 and 48, i.e the lowest common factor (LCM) of 56 and 48 which is 336 seconds or 5 minutes 36 seconds.

Number of laps by Venu

$=\frac{336}{48}=7$

Number of laps by Tanuj

$=\frac{336}{56}=6$

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3 years ago

A projectile is fired straight up from ground level. After t seconds, its height above the ground is s feet, where s= - 16t² + 1

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For the time period of the projectile at least 192 feet above the ground is between 2 second and 6 second

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1 year ago

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3 years ago

Find the angles of a rhombus if the ratio of the angles that the diagonals form with a side is 6:9.

fomenos

Answer:

The measures of the angles of the rhombus are 72° , 108° , 72° , 108°

Step-by-step explanation:

* Lets revise the properties of the rhombus

- It has 4 equal sides

- Each two opposite angles are equal

- Each two adjacent angles are supplementary (their sum = 180°)

- The diagonals are perpendicular to each other

- The diagonals bisect the vertices angles (divide each vertex into two

equal parts)

* Now lets solve the problem

- Let the name of the rhombus is ABCD

- The two diagonals are AC and BD

- Let the diagonals AC and BD make the angles BAC and ABD with

side AB

∵ The diagonals of the rhombus bisect the vertex angles

∴ m∠BAC is half m∠A

∴ m∠ABD is half m∠B

- There is a ratio between the measures of the angles BAC and ABD

∵ m∠BAC : m∠ABD = 6 : 9

∵ m∠A + m∠B = 180° ⇒ consecutive angles

∴ m∠BAC + m∠ABD = 1/2 × 180° = 90°

∵ m∠BAC : m∠ABD : their sum

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? : ? : 90° ⇒(the sum of the angles)

∴ m∠BAC = 6/15 × 90° = 36°

∴ m∠ABD = 9/15 × 90° = 54°

∵ m∠BAC is half m∠A

∴ m∠A = 36° × 2 = 72°

∵ m∠ABD is half m∠B

∴ m∠B = 54° × 2 = 108°

* The measures of the angles of the rhombus are 72° , 108° , 72° , 108°

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2 years ago