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svp [43]
2 years ago
5

Use the change of base formula to compute log5 9.

Mathematics
1 answer:
Mekhanik [1.2K]2 years ago
5 0
Let log₅9 = x
Then
5ˣ = 9 

Take log to base 10 of both sides.
log₁₀5ˣ = log₁₀9
x log₁₀5 = log₁₀9

Therefore
log₅9 = log₁₀9/log₁₀5
         = 0.9542/0.699
         = 1.3652

Answer: 1.365 (nearest thousandth)
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Need help finding the area of the shaded region. Round to the nearest tenth. Need help ASAP
Sergio [31]

Answer:   294.4 m²

<u>Step-by-step explanation:</u>

Separate the shaded region into two parts:

  1. The section containing the central angle of 230° (360° - 130°)
  2. The triangle with sides 11.1, 11.1 & 20.12 (use Law of Cosines)

1.\ Area(A)=\pi\ r^2\ \bigg(\dfrac{\theta}{360}\bigg)\\\\\\.\qquad \qquad =\pi(11.1)^2\bigg(\dfrac{230}{360}\bigg)\\\\\\.\qquad \qquad =247.3

2.\ \text{Use Law of cosines to find the length of the third side.}\\\text{ Then use Heron's formula to find the Area of the triangle.}\\\\s=\dfrac{11.1+11.1+20.12}{2}=21.16\\\\\\A=\sqrt{s(s-a)(s-b)(s-c)}\\\\.\ =\sqrt{21.16(21.16-11.1)(21.16-11.1)(21.16-20.12)}\\\\.\ =\sqrt{2227}\\\\.\ =47.1

Area of shaded region = Area of (1) + Area of (2)

                                      =    247.3     +      47.1

                                      =               294.4

8 0
3 years ago
Read 2 more answers
A 13 foot board is cut into 2 pieces, if one piece is x feet long express the other length in terms x
pychu [463]

Answer:

if they are equal then it would be 6.5

7 0
2 years ago
Measure (7x+1) (2x+1)
Gemiola [76]

Smaller angle = 41°

Larger angle = 139°

Step-by-step explanation:

(7x - 1) + (2x + 1) = 180

7x + 2x - 1 + 1 = 180

9x = 180

x = 20

  • The measure of the smaller angle is

2x + 1

= 2(20) + 1

= 40 + 1

<u>= 41°</u>

  • The measure of the larger angle is

7x - 1

= 7(20) - 1

= 140 - 1

<u>= 139°</u>

4 0
2 years ago
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Write a number in which the value of the 3 is ten times greater than the value of the 3 in 135, 864
Aleonysh [2.5K]

Answer:

345,456

Step-by-step explanation:

The value of 3 in 135,864 is 30,000.

We want to write a number that is ten times 30,000.

We could write any other number in which the value of 3 is 300,000.

There are infinitely many numbers that we can write.

Some examples are:

345,456

1,315,445

5,354,456

and so on and so forth.

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3 years ago
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Reika [66]

Answer:

x

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−

8

3

Step-by-step explanation:

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3 years ago
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