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soldi70 [24.7K]
1 year ago
15

50 points to whoever gets this right .

Mathematics
1 answer:
katrin2010 [14]1 year ago
3 0

We have the two equivalent expressions:

( (2.3)⁵/(0.9)⁴)³ = (2.3)¹⁵/(0.9)¹²

From this, we conclude that the correct option is the last one.

<h3>Which expression is equivalent to the given one?</h3>

Here we start with the expression:

( (2.3)⁵/(0.9)⁴)³

Remember the rule for exponents:

(aⁿ)ˣ = aⁿ*ˣ

Now we can use the above rule to simplify the large parenthesis we will get:

( (2.3)⁵/(0.9)⁴)³ = (2.3)⁵*³/(0.9)⁴*³ =  (2.3)¹⁵/(0.9)¹²

Then we have the two equivalent expressions:

( (2.3)⁵/(0.9)⁴)³ = (2.3)¹⁵/(0.9)¹²

From this, we conclude that the correct option is the last one.

If you want to learn more about exponents:

brainly.com/question/847241

#SPJ1

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Consider this sphere inside the cylinder. Which statements are true? Check all that apply. NEED HELP ASAP​
-Dominant- [34]

Option A: The height of the cylinder is equal to the diameter of the sphere.

Option C: The radius of the sphere is half the height of the cylinder.

Option E: The volume of the sphere is two-thirds the volume of the cylinder.

Solution:

The sphere is inside the cylinder.

Let r be the radius of the sphere.

Option A: The height of the cylinder is equal to the diameter of the sphere.

The sphere is fully occupied the cylinder.

If we draw the vertical line through enter of the sphere, which is equal to the height of cylinder.That is h = d. It is true.

Option B: The height of the cylinder is two times the diameter of the sphere.

That is h = 2d. From the above option, we know that h = d.

So, it is not true.

Option C: The radius of the sphere is half the height of the cylinder.

we know that diameter = 2 × radius (d = 2r)

From option A, we have h = d.

Substitute d = 2r, we get

⇒ h = 2r

Divide by 2 on both sides, we get

$\Rightarrow \frac{h}{2}=r

Therefore, it is true.

Option D: The diameter of the sphere is equal to the radius of the cylinder.

It is not true, because diameters of both cylinder and sphere are equal.

Option E: The volume of the sphere is two-thirds the volume of the cylinder.

Radius of cylinder and sphere = r

Height of cylinder h = 2r (by option C)

Volume of cylinder = Volume of sphere

  $\Rightarrow \pi r^2 h = \frac{4}{3} \pi r^3 (formula)

$\Rightarrow \pi r^2 (2r) = \frac{2\times2}{3} \pi r^3

$\Rightarrow 2 \pi r^3= \frac{2}{3} \times 2\pi r^3

Hence it is true.

Option A, option C and option E are true.

6 0
3 years ago
Read 2 more answers
1. Consider f(x) = 3x - 5
Rzqust [24]

Answer:

3

Step-by-step explanation:

Here we have the function

f(x)=3x-5

We want to find the following ratio:

\frac{f(x+h)-f(x)}{h}

Note that the limit of this for h\rightarrow 0 is equivalent to the derivative of the function.

Here we have:

f(x+h)=3(x+h)-5=3x+3h-5

And

f(x)=3x-5

Therefore we have

f(x+h)-f(x)=3x+3h-5-(3x-5)=3h

And therefore,

\frac{f(x+h)-f(x)}{h}=\frac{3h}{h}=3

4 0
3 years ago
Find the product of all positive divisors of 288.
irinina [24]

Answer:

<em>The</em><em> </em><em>answer</em><em> </em><em>is</em><em> </em><em>1</em><em>.</em><em>5</em><em>1</em><em>4</em><em>5</em><em>7</em><em>1</em><em>8</em><em>9</em><em>4</em><em>×</em><em>1</em><em>0</em><em>^</em><em>2</em><em>1</em><em>.</em>

Step-by-step explanation:

<em>Here</em><em>, </em><em> </em><em>the</em><em> </em><em>divisors</em><em> </em><em>of</em><em> </em><em>2</em><em>8</em><em>8</em><em> </em><em>are</em><em>,</em>

<em>1</em><em>,</em><em>2</em><em>,</em><em>3</em><em>,</em><em>4</em><em>,</em><em>6</em><em>,</em><em>8</em><em>,</em><em>9</em><em>,</em><em>1</em><em>2</em><em>,</em><em>1</em><em>6</em><em>,</em><em>1</em><em>8</em><em>,</em><em>2</em><em>4</em><em>,</em><em>3</em><em>2</em><em>,</em><em>3</em><em>6</em><em>,</em><em>4</em><em>8</em><em>,</em><em>7</em><em>2</em><em>,</em><em>9</em><em>6</em><em>,</em><em>1</em><em>4</em><em>4</em><em>,</em><em>2</em><em>8</em><em>8</em><em>.</em>

<em>now</em><em>,</em><em> </em><em>their</em><em> </em><em>product</em><em> </em><em>=</em><em>1</em><em>×</em><em>2</em><em>×</em><em>3</em><em>×</em><em>4</em><em>×</em><em>6</em><em>×</em><em>8</em><em>×</em><em>9</em><em>×</em><em>1</em><em>2</em><em>×</em><em>1</em><em>6</em><em>×</em><em>1</em><em>8</em><em>×</em><em>2</em><em>4</em><em>×</em><em>3</em><em>2</em><em>×</em><em>3</em><em>6</em><em>×</em><em>4</em><em>8</em><em>×</em><em>7</em><em>2</em><em>×</em><em>9</em><em>6</em><em>×</em><em>1</em><em>4</em><em>4</em><em>×</em><em>2</em><em>8</em><em>8</em>

<em>=</em><em>1</em><em>.</em><em>5</em><em>1</em><em>4</em><em>5</em><em>7</em><em>1</em><em>8</em><em>9</em><em>4</em><em>×</em><em>1</em><em>0</em><em>^</em><em>2</em><em>1</em><em>.</em>

<em>is</em><em> </em><em>answer</em><em>. </em>

<em><u>Hope</u></em><em><u> </u></em><em><u>it helps</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em>

6 0
3 years ago
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40 pts!! Simplify the expression in the picture.
tino4ka555 [31]

Answer:

D.   (27x^6y^9) / x^9.

Step-by-step explanation:

(3x^2y^3 / z^3 )^3

=  3^3 x^(2*3)y(3*3) / z^(3^3)

= 27 x^6y^9 / x^9.

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