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scZoUnD [109]
3 years ago
15

I neeeee helppppppppp

Mathematics
1 answer:
kaheart [24]3 years ago
7 0

Answer:

The pin number is 1147

Step-by-step explanation:

We have given that:

Maritza remembers her PIN because it is the product of two consecutive prime numbers that is between 1000 and 1500.

Pin number is between 1000 and 1500

PIN is the product of two consecutive prime numbers.

Prime numbers are those numbers which are divisible by one or itself only.

So,

prime numbers are 1, 3, 5, 7,………29, 31,37, 41, …..

Multiply  29 x 31 = 899  which does not come in the range of 1000 and 1500.

Next,

31 x 37 = 1147 this is between 1000 and 1500

Next

37 x 41 = 1517, which is above 1500.

Thus the pin number is 1147....

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Answer: R=20.84\ lb\quad 22.57^{\circ},15.43^{\circ}

Step-by-step explanation:

Given

Two forces of 9 and 13 lbs acts 38^{\circ} angle to each other

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\Rightarrow R=\sqrt{a^2+b^2+2ab\cos \theta}

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\Rightarrow R=\sqrt{9^2+13^2+2(9)(13)\cos 38^{\circ}}\\\Rightarrow R=\sqrt{81+169+184.394}\\\Rightarrow R=\sqrt{434.394}\\\Rightarrow R=20.84\ lb

Resultant makes an angle of

\Rightarrow \alpha=\tan^{-1}\left( \dfrac{b\sin \theta}{a+b\cos \theta}\right)\\\\\text{Considering 9 lb force along the x-axis}\\\\\Rightarrow \alpha =\tan^{-1}\left( \dfrac{13\sin 38^{\circ}}{9+13\cos 38^{\circ}}\right)\\\\\Rightarrow \alpha =\tan^{-1}(\dfrac{8}{19.244})\\\\\Rightarrow \alpha=22.57^{\circ}

So, the resultant makes an angle of 22.57^{\circ} with 9 lb force

Angle made with 13 lb force is 38^{\circ}-22.57^{\circ}=15.43^{\circ}

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