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3 years ago

1. Check the divisibility of the following numbers by 2, 3, 9 and 11 a) 76543 b) 98765436

Mathematics

1 answer:

Alla [95]3 years ago

6 0

Answer:

1. ( I didnt understand the question but I divided them using the calculator.)

A.) 76543

÷ 2= 38,271.5

÷ 3= 25,514.333...

÷ 9= 8,504.777...

÷ 11= 6,958.454545...

B.) 98765436

÷ 2= 49,382,718

÷ 3= 32,921,812

÷ 9= 10,973,937.333...

÷ 11= 8,978,676

2. B

A.) 67894

÷ 4= 16,973.5

÷ 8= 8,486.75

B.) 9685048

÷ 4= 2,421,262

÷ 8= 1,210,631

Explanation:

I used the calculator to divide.

I hope this helps! I'm sorry if it's wrong.

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Show with work please.

kolbaska11 [484]

Answer:

$\csc \left(\theta-\frac{\pi }{2}\right)=0.73$

Step-by-step explanation:

The identity you will use is:

$\csc \left(x\right)=\frac{1}{\sin \left(x\right)}$

So,

$\csc \left(\theta-\frac{\pi }{2}\right)$

$\csc \left(\theta-\frac{\pi }{2}\right)=\frac{1}{\sin \left(-\frac{\pi }{2}+\theta\right)}$

Now, using the difference of sin

Note: state that $\text{sin}(\alpha\pm \beta)=\text{sin}(\alpha) \text{cos}(\beta) \pm \text{cos}(\alpha) \text{sin}(\beta)$

$\csc \left(\theta-\frac{\pi }{2}\right)=\frac{1}{-\cos \left(\theta\right)\sin \left(\frac{\pi }{2}\right)+\cos \left(\frac{\pi }{2}\right)\sin \left(\theta\right)}$

Solving the difference of sin:

$-\cos \left(\theta\right)\sin \left(\frac{\pi }{2}\right)+\cos \left(\frac{\pi }{2}\right)\sin \left(\theta\right)$

$-\cos \left(\theta\right) \cdot 1+0\cdot \sin \left(\theta\right)$

$-\text{cos} \left(\theta\right)$

Then,

$\csc \left(\theta-\frac{\pi }{2}\right)=-\frac{1}{\cos \left(\theta\right)}$

Once

$\text{sec}(-\theta)=\text{sec}(\theta)$

And, $\text{sec}(\theta)=-0.73$

$-\frac{1}{\cos \left(\theta\right)}=-\text{sec}(\theta)$

$-\frac{1}{\cos \left(\theta\right)}=-(-0.73)$

$-\frac{1}{\cos \left(\theta\right)}=0.73$

Therefore,

$\csc \left(\theta-\frac{\pi }{2}\right)=0.73$

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Answer:

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Step-by-step explanation:

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