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quester [9]
3 years ago
15

If x=5^a, find the value of 5x

Mathematics
1 answer:
Harrizon [31]3 years ago
8 0

Answer:

The given expression is written as 5^{1+a}

Step-by-step explanation:

Given as :

The expression is written as  x = 5^{a}

Now foe 5 x , the expression is written as

5^{1} × 5^{a}

Now <u>from base indices method </u>

here base is same so, power should be added

∴ 5^{1+a}

Hence The given expression is written as 5^{1+a} , Answer

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Find the area of the given triangle to the nearest square unit. Angle a= 30 degrees, b=10, angle B=45 degrees
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Answer:

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Step-by-step explanation:

Suppose we have a general triangle like the one shown in the figure.

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A = 30\°\\\\B = 45\°\\\\b = 10

By definition I know that the sum of the internal angles of a triangle is always equal to 180 °.

So

A + B + C = 180\\\\30 + 45 + C = 180

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C = 180 - 30-45\\\\C = 105

We already know the three triangle angles.

Now we use the sine theorem to calculate the sides c and a.

The  sine theorem says that:

\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}

Then

\frac{sin(30)}{a}=\frac{sin(45)}{10}

\frac{sin(30)}{\frac{sin(45)}{10}}=a

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Also

\frac{sin(105)}{c}=\frac{sin(45)}{10}

\frac{sin(105)}{\frac{sin(45)}{10}}=c

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Finally, we use the Heron formula to calculate the triangle area

A=\sqrt{s(s-a)(s-b)(s-c)}

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s=\frac{a+b+c}{2}

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s=\frac{7.071+10+13.660}{2}

s=15.37

A=\sqrt{15.37(15.37-7.071)(15.37-10)(15.37-13.66)}

A=34\ units^2

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