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3 years ago

What is 7 over 8 eaqual to

Mathematics

2 answers:

777dan777 [17]3 years ago

8 0

0.875
I hope this helps

elena-14-01-66 [18.8K]3 years ago

4 0

Your answer is 56

hope it helps

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A pendulum is set swinging. its first oscillation is through 30 and each succeeding oscillation is through 95% of the angle of t

Marat540 [252]

<u>Answer-</u>

<em>After 76 swings</em><em> the angle through which it swings less than 1°</em>

<u>Solution-</u>

From the question,

Angle of the first of swing = 30° and then each succeeding oscillation is through 95% of the angle of the one before it.

So the angle of the second swing = $(30\times \frac{95}{100})^{\circ}$

Then the angle of third swing = $(30\times (\frac{95}{100})^2)^{\circ}$

So, this follows a Geometric Progression.

$(30,\ 30\cdot \frac{95}{100},\ 30\cdot (\frac{95}{100})^2............,0)$

a = The initial term = 30

r = Common ratio = $\frac{95}{100}$

As we have to find the number swings when the angle swept by the pendulum is less than 1°.

So we have the nth number is the series as 1, applying the formula

$T_n=ar^{n-1}$

Putting the values,

$\Rightarrow 1=30(\frac{95}{100})^{n-1}$

$\Rightarrow \frac{1}{30} =(\frac{95}{100})^{n-1}$

Taking logarithm of both sides,

$\Rightarrow \log \frac{1}{30} =\log (\frac{95}{100})^{n-1}$

$\Rightarrow \log \frac{1}{30} =(n-1)\log (\frac{95}{100})$

$\Rightarrow -1.5=(n-1)(-0.02)$

$\Rightarrow 1.5=(n-1)(0.02)$

$\Rightarrow n-1=\dfrac{1.5}{0.02}$

$\Rightarrow n-1=75$

$\Rightarrow n=76$

Therefore, after 76 swings the angle through which it swings less than 1°

8 0

3 years ago

The side of each of the equilateral triangles in the figure is twice the side of the central regular hexagon. What fraction of t

lana [24]

Answer:

The fraction is 1/4

Step-by-step explanation:

we know that

The area of an equilateral triangle, using the law of sines is equal to

$A=\frac{1}{2}x^{2}sin(60^o)$

$A=\frac{1}{2}x^{2}(\frac{\sqrt{3}}{2})$

$A=x^{2}\frac{\sqrt{3}}{4}$

where

x is the length side of the triangle

In this problem

Let

b ----> the length side of the regular hexagon

2b ---> the length side of the equilateral triangle

step 1

Find the area of the six triangles

Multiply the area of one triangle by 6

$A=6[x^{2}\frac{\sqrt{3}}{4}]$

$A=3x^{2}\frac{\sqrt{3}}{2}$

we have

$x=2b\ units$

substitute

$A=3(2b)^{2}\frac{\sqrt{3}}{2}\\\\A=6b^{2}\sqrt{3}\ units^2$

step 2

Find the area of the regular hexagon

Remember that, a regular hexagon can be divided into 6 equilateral triangles

The area of the regular hexagon is the same that the area of 6 equilateral triangles

$A=3x^{2}\frac{\sqrt{3}}{2}$

we have

$x=b\ in$

substitute

$A=3(b)^{2}\frac{\sqrt{3}}{2}$

step 3

To find out what fraction of the total area of the six triangles is the area of the hexagon, divide the area of the hexagon by the total area of the six triangles

$3(b)^{2}\frac{\sqrt{3}}{2}:6b^{2}\sqrt{3}=\frac{3}{2} :6=\frac{3}{12}=\frac{1}{4}$

3 0

3 years ago

What is the domain of the function on the graph

sergey [27]

Answer:

<h3>Domain [-3 , ∞ ]</h3>

Step-by-step explanation:

Domain is the set of all inputs for which the given function is defined.

graphically it represents the shadow of the graph taken on the x axis from above and below the x axis

Here is the shadow will be formed from -3 till +∞, hence we have our domain as [-3 , ∞ ]

5 0

1 year ago

Okay have reposted it.

Delvig [45]

Answer:

Step-by-step explanation:

6 0

2 years ago

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(4x^2+3x −5)+(x^2 −7x+10)

olga nikolaevna [1]

Answer:

$5x^{2} -4x +5$

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers