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irina1246 [14]
3 years ago
8

8 is 40 show work divied

Mathematics
1 answer:
svetoff [14.1K]3 years ago
4 0

Answer: 5

0 Remainder

Step-by-step explanation:

Step 1:

Start by setting it up with the divisor 8 on the left side and the dividend 40 on the right side like this:

             

   8 ⟌ 4 0  

Step 2:

The divisor (8) goes into the first digit of the dividend (4), 0 time(s). Therefore, put 0 on top:

       0    

   8 ⟌ 4 0  

Step 3:

Multiply the divisor by the result in the previous step (8 x 0 = 0) and write that answer below the dividend.

       0    

   8 ⟌ 4 0  

       0    

Step 4:

Subtract the result in the previous step from the first digit of the dividend (4 - 0 = 4) and write the answer below.

       0    

   8 ⟌ 4 0  

     - 0    

       4    

Step 5:

Move down the 2nd digit of the dividend (0) like this:

       0    

   8 ⟌ 4 0  

     - 0    

       4 0  

Step 6:

The divisor (8) goes into the bottom number (40), 5 time(s). Therefore, put 5 on top:

       0 5  

   8 ⟌ 4 0  

     - 0    

       4 0  

Step 7:

Multiply the divisor by the result in the previous step (8 x 5 = 40) and write that answer at the bottom:

       0 5  

   8 ⟌ 4 0  

     - 0    

       4 0  

      4 0  

Step 8:

Subtract the result in the previous step from the number written above it. (40 - 40 = 0) and write the answer at the bottom.

       0 5  

   8 ⟌ 4 0  

     - 0    

       4 0  

     - 4 0  

         0  

You are done, because there are no more digits to move down from the dividend.

The answer is the top number and the remainder is the bottom number.

Therefore, the answer to 40 divided by 8 calculated using Long Division is:

5

0 Remainder

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Find sin(a)&amp;cos(B), tan(a)&amp;cot(B), and sec(a)&amp;csc(B).​
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Answer:

Part A) sin(\alpha)=\frac{4}{7},\ cos(\beta)=\frac{4}{7}

Part B) tan(\alpha)=\frac{4}{\sqrt{33}},\ tan(\beta)=\frac{4}{\sqrt{33}}

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Step-by-step explanation:

Part A) Find sin(\alpha)\ and\ cos(\beta)

we know that

If two angles are complementary, then the value of sine of one angle is equal to the cosine of the other angle

In this problem

\alpha+\beta=90^o ---> by complementary angles

so

sin(\alpha)=cos(\beta)

Find the value of sin(\alpha) in the right triangle of the figure

sin(\alpha)=\frac{8}{14} ---> opposite side divided by the hypotenuse

simplify

sin(\alpha)=\frac{4}{7}

therefore

sin(\alpha)=\frac{4}{7}

cos(\beta)=\frac{4}{7}

Part B) Find tan(\alpha)\ and\ cot(\beta)

we know that

If two angles are complementary, then the value of tangent of one angle is equal to the cotangent of the other angle

In this problem

\alpha+\beta=90^o ---> by complementary angles

so

tan(\alpha)=cot(\beta)

<em>Find the value of the length side adjacent to the angle alpha</em>

Applying the Pythagorean Theorem

Let

x ----> length side adjacent to angle alpha

14^2=x^2+8^2\\x^2=14^2-8^2\\x^2=132

x=\sqrt{132}\ units

simplify

x=2\sqrt{33}\ units

Find the value of tan(\alpha) in the right triangle of the figure

tan(\alpha)=\frac{8}{2\sqrt{33}} ---> opposite side divided by the adjacent side angle alpha

simplify

tan(\alpha)=\frac{4}{\sqrt{33}}

therefore

tan(\alpha)=\frac{4}{\sqrt{33}}

tan(\beta)=\frac{4}{\sqrt{33}}

Part C) Find sec(\alpha)\ and\ csc(\beta)

we know that

If two angles are complementary, then the value of secant of one angle is equal to the cosecant of the other angle

In this problem

\alpha+\beta=90^o ---> by complementary angles

so

sec(\alpha)=csc(\beta)

Find the value of sec(\alpha) in the right triangle of the figure

sec(\alpha)=\frac{1}{cos(\alpha)}

Find the value of cos(\alpha)

cos(\alpha)=\frac{2\sqrt{33}}{14} ---> adjacent side divided by the hypotenuse

simplify

cos(\alpha)=\frac{\sqrt{33}}{7}

therefore

sec(\alpha)=\frac{7}{\sqrt{33}}

csc(\beta)=\frac{7}{\sqrt{33}}

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