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Masja [62]
3 years ago
15

I need to understand question 14 and 15 and the last one cut off for tens in one

Mathematics
1 answer:
sp2606 [1]3 years ago
6 0

                                                 Question # 14

Given the numbers

10     11     12     13     14     15     16     17     18     19     20

Let 'x' be the number

The condition breakdown:

I am less than 20.

  • So the number 'x' must be less than 20 i.e. x < 20

I am more than 13.

  • So the number 'x' must be greater than 13 i.e. x > 13

I am less than 17.

  • So the number 'x' must be less than 17 i.e. x < 17

Finally:

I am 4 more than 12

i.e. 12+4 = 16

Thus, the number is x = 16

                                               Question # 15

Part a)

Given the numbers

10     11     12     13     14     15     16     17     18     19     20

Let 'x' be the number

The condition breakdown:

I am more than 10.

  • x > 10

I am less than 20.

  • x < 20

I am more than 12.

  • x > 12

I am less than 15.

  • x < 15

As the numbers left after all the conditions are fulfilled are 13 and 14.

  • But the last condition is, of the numbers that left, the number is greater than all the remaining numbers.

So, from the remaining number 13 and 14;

14 > 13

Thus, the number x = 14

Part b)

Drawing the number 14 in the place value:

          Chart

Tens                Ones

1                         4

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If you are looking for the product, then:

Use foil to get: sec²(1) - sec²(-csc²) -1(1) -1(-csc²)

= sec² + sec²csc² - 1 + csc²

= sec²csc² + sec² + csc² - 1

= sec²csc² + 1 - 1 (NOTE: sec² + csc² = 1 is an identity)

= sec²csc²

Answer: sec²csc²

***************************************************

If you are looking for the zeroes, then:

Using the zero product property, set each factor equal to zero and solve.

<u>First factor:</u>

sec²Θ - 1 = 0

sec²Θ = 1

secΘ = 1, -1

remember that secΘ is \frac{1}{cos}

\frac{1}{cos} = 1 \frac{1}{cos} = -1

cross multiply to get:

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use the unit circle (or a calculator) to find that Θ = 0 and π

<u>Second factor:</u>

1 - csc²Θ = 0

1 = csc²Θ

1, -1 = cscΘ

remember that cscΘ is \frac{1}{sin}

\frac{1}{sin} = 1 \frac{1}{sin} = -1

cross multiply to get:

sinΘ = 1 sinΘ = -1

use the unit circle (or a calculator) to find that Θ = \frac{\pi}{2} and \frac{3\pi}{2}

Answer: 0, π, \frac{\pi}{2} , \frac{3\pi}{2}

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