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3 years ago

Please help..........

Mathematics

1 answer:

wel3 years ago

3 0

C = sin⁻¹ (sin(B) * c / b) = sin⁻¹ (sin [90degrees] * 6 / 12.00) = 30 degrees

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Find the 9th term of the geometric sequence 6, 24, 96, ...

Lyrx [107]

Answer:

1,572,864

Step-by-step explanation:

1. 6 x 4 = 24

2. 24 x 4 = 96

3. 96 x 4 = 384

4. 384 x 4 = 1,536

5. 1,536 x 4 = 6,144

6. 6,144 x 4 = 24,576

7. 24,576 x 4 = 98,304

8. 98,304 x 4 = 393,216

9. 393,216 x 4 = 1,572,864

4 0

3 years ago

A lighthouse is located on a small island 2 km away from the nearest point P on a straight shoreline and its light makes four re

ddd [48]

Answer:

62.8 km per min

Step-by-step explanation:

Let the diagram of this situation is shown below,

In which $\theta$ is the angle made by light to the straight line joining the lighthouse and P,

∵ Light makes 4 revolutions per minute.

Also, 1 revolution = $2\pi$ radians

So, the change in angle with respect to t ( time ),

$\frac{d\theta}{dt}=8\pi\text{ radians per min}$

Let x be the distance of beam from P,

$\implies \tan \theta = \frac{x}{2}$

Differentiating with respect to x,

$\sec^2 \theta \frac{d\theta}{dt}=\frac{1}{2}\frac{dx}{dt}$

$(1+\tan^2 \theta) (8\pi) = \frac{1}{2}\frac{dx}{dt}$

$(1+\frac{x^2}{2^2})(8\pi) = \frac{1}{2}\frac{dx}{dt}$

If x = 1 km,

$(1+\frac{1}{4})8\pi =\frac{1}{2}\frac{dx}{dt}$

$\frac{5}{4}8\pi = \frac{1}{2}\frac{dx}{dt}$

$\implies \frac{dx}{dt}=\frac{80\pi}{4}= 20\pi\approx 62.8\text{ km per min}$

Hence, the beam of light moving along the shoreline with the speed of 62.8 km per min

7 0

4 years ago

Help me please someone

LuckyWell [14K]

Answer:

B is Geometric and its next terms are 81, 243, 729...

See example below to complete other problems.

Step-by-step explanation:

Geometric sequences have a pattern that is exponential. Because of this, they do not have a constant rate of change using addition or subtraction. Instead, they have a constant rate through multiplication and division called a common ratio. Problem B is geometric because as you subtract each y value you get a different value each time. It is not a common difference. But if you divide, you find a common ratio.

Example: 27-9= 18 27/9 = 3

9-3 = 6 9/3 = 3

etc. Common ratio of 3

7 0

3 years ago

Janissa bought 50 cupcake cases for baking. She used 2/5 of the cases to bake vanilla cupcakes. She then used 5/6 of the remaini

tensa zangetsu [6.8K]

<u>Jessica has 5 cupcake cases left.</u>

<em>First, divide 50 into groups of five. Next, subtract two groups of five from 50. Third, divide the remaining cases into groups of six. Finally, subtract 5 groups of six from the remains from the last subtraction equation. </em>

4 0

4 years ago

Line CD passes through points C(3, -5) And D(6, 0). What is the equation of line CD in standard form?

Fynjy0 [20]

Y = mx + b
m = (0 - -5)/(6 - 3) = 5/3
y = 5/3x + b
0 = 5/3(6) + b
b = -10
(y = 5/3x - 10)3
3y = 5x - 30
3y - 5x = -30
5x - 3y = 30

8 0

3 years ago

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