Log8(2-5x)=log8(-4x+3)

Answers

Answer 1

Answer: 2 - 5x > 0 and -4x + 3> 0

log8(2-5x)=log8(-4x+3) <=> 2 - 5x = - 4x + 3 <=> -5x + 4x = 3 - 2 <=> -x = 1 <=> x = -1;

2 - 5(-1) = 7 > 0 and -4(-1) + 3 = 7 > 0 ;

the solution is -1;

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Which term of the AP:3,15,27, 39,.....will be 132 more than its 54th term

Answers

Answer:

n=65th term

Step-by-step explanation:

AP:3,15,27,39......

From the AP

a=3

a+d=15

a+2d=27

3+d=15 (1)

3+2d=27 (2)

Subtract (1) from (2)

We have,

2d-d=27-15

d=12

54th term=a+(n-1)d

=3+(54-1)12

=3+(53)12

=3+636

=639

The term is 132 more than the 54th term

132+54th term

=132+639

=771

Find the term

771=a+(n-1)d

771=3+(n-1)12

771-3=12n-12

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768+12=12n

780=12n

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n=12

The term which is 132 more than the 54th term is the 65th term

In a right triangle, angle C measures 40. the hypotenuse of the triangle is 10 inches long. what is the approximate length of the side adjacent to angle C

Answers

Since angle C is not 90 degrees, it's one of the acute angles
in the right triangle.

   (The side adjacent to angle C ) divided by (hypotenuse)

is the cosine of angle C .

(adjacent) / (10 inches) = cos(40 degrees)

Multiply each side by (10 inches):

      Adjacent side = (10 inches) x cos(40) =

(10 inches) x 0.766 =

7.66 inches (rounded)

The approximate length of the side adjacent to angle $C$ is $\boxed{{\mathbf{7}}.7{\mathbf{ inches}}}$ .

Further explanation:

The trigonometry ratio used in the right angle triangles.

The cosine ratio can be written as,

$\cos \theta = (length\ of\ the\ side\ adjacent\ to\ \theta )/(hypotenuse)$

Here, base is the length of the side adjacent to angle $\theta$ and hypotenuse is the longest side of the right angle triangle where the length of side opposite to angle $\theta$ is perpendicular that is used in the sine ratio.

Step by step explanation:

Step 1:

The attached right angle triangle can be observed from the given information.

First define the hypotenuse and the base of the triangle.

The side $BC$ is adjacent to angle $C$ and the side $AC$ is the hypotenuse of $\Delta ABC$ .

Therefore, the ${\text{length of the side adjacent to C}}=BC$ and ${\text{hypotenuse}}=10$ .

Step 2:

Since, the cosine ratio is $\cos \theta = (length\ of\ the\ side\ adjacent\ to\ \theta )/(hypotenuse)$

Now put the value ${\text{length of the side adjacent to C}}=BC$ and ${\text{hypotenuse}}=10$ in the cosine ratio.

$\begin{aligned}\cos C&=\frac{{BC}}{{10}}\n{\text{co}}s40&=\frac{{BC}}{{10}}\n0.766&=\frac{{BC}}{{10}}\nBC&=7.66\n\end{aligned}$

Therefore, the approximate length of the side adjacent to angle $C$ is $7.66{\text{ inches}}$ .

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Trigonometry

Keywords: Distance, Pythagoras theorem, base, perpendicular, hypotenuse, right angle triangle, units, squares, sum, cosine ratio, adjacent side to angle, opposite side to angle.

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Answers

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