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3 years ago

Is the answer true or false? I need to get this correct

Mathematics

2 answers:

Pavlova-9 [17]3 years ago

8 0

True because the plus 2 increases the x by negative 2

DaniilM [7]3 years ago

6 0

Vertex is the lower or highest point.

That is the correct answer. Go to desmos and put in the equation and look at where the lowest point is. :)

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Math question

strojnjashka [21]

Answer:

The candle has a radius of 8 centimeters and 16 centimeters and uses an amount of approximately 1206.372 square centimeters.

Step-by-step explanation:

The volume ( $V$ ), in cubic centimeters, and surface area ( $A_{s}$ ), in square centimeters, formulas for the candle are described below:

$V = \pi\cdot r^{2}\cdot h$ (1)

$A_{s} = 2\pi\cdot r^{2} + 2\pi\cdot r \cdot h$ (2)

Where:

$r$ - Radius, in centimeters.

$h$ - Height, in centimeters.

By (1) we have an expression of the height in terms of the volume and the radius of the candle:

$h = \frac{V}{\pi\cdot r^{2}}$

By substitution in (2) we get the following formula:

$A_{s} = 2\pi \cdot r^{2} + 2\pi\cdot r\cdot \left(\frac{V}{\pi\cdot r^{2}} \right)$

$A_{s} = 2\pi \cdot r^{2} +\frac{2\cdot V}{r}$

Then, we derive the formulas for the First and Second Derivative Tests:

First Derivative Test

$4\pi\cdot r -\frac{2\cdot V}{r^{2}} = 0$

$4\pi\cdot r^{3} - 2\cdot V = 0$

$2\pi\cdot r^{3} = V$

$r = \sqrt[3]{\frac{V}{2\pi} }$

There is just one result, since volume is a positive variable.

Second Derivative Test

$A_{s}'' = 4\pi + \frac{4\cdot V}{r^{3}}$

If $\left(r = \sqrt[3]{\frac{V}{2\pi}}\right)$ :

$A_{s} = 4\pi + \frac{4\cdot V}{\frac{V}{2\pi} }$

$A_{s} = 12\pi$ (which means that the critical value leads to a minimum)

If we know that $V = 3217\,cm^{3}$ , then the dimensions for the minimum amount of plastic are:

$r = \sqrt[3]{\frac{V}{2\pi} }$

$r = \sqrt[3]{\frac{3217\,cm^{3}}{2\pi}}$

$r = 8\,cm$

$h = \frac{V}{\pi\cdot r^{2}}$

$h = \frac{3217\,cm^{3}}{\pi\cdot (8\,cm)^{2}}$

$h = 16\,cm$

And the amount of plastic needed to cover the outside of the candle for packaging is:

$A_{s} = 2\pi\cdot r^{2} + 2\pi\cdot r \cdot h$

$A_{s} = 2\pi\cdot (8\,cm)^{2} + 2\pi\cdot (8\,cm)\cdot (16\,cm)$

$A_{s} \approx 1206.372\,cm^{2}$

The candle has a radius of 8 centimeters and 16 centimeters and uses an amount of approximately 1206.372 square centimeters.

3 0

3 years ago

A group of four boys (Alex, Bryan, Chris, and David) and five girls (Megan, Nancy, Olivia, Pauline, and Rebecc?

aliina [53]

Answer:

a) P = 362880 ways

b) P = 2880 ways

Step-by-step explanation:

a) We have four boys and five girls, they are going to sit together in a row of 9 theater seats, without restrictions

We have a permutation of 9 elements

P = 9!

P = 9*8*7*6*5*4*3*2*1

P = 362880 ways

b) Boys must seat together, we have two groups of people

4 boys they can seat in 4! different ways

P₁ = 4!

P₁ = 4*3*2*1

P₁ = 24

And girls can seat in 5! dfferent ways

P₂ = 5!

P₂ = 5*4*3*2*1

P₂ = 120

To get total ways in the above mentioned condition, we have to multiply P₁*P₂

P = 24*120

P = 2880 ways

4 0

3 years ago

297 words in 5.5 minutes ? im confused again

Vedmedyk [2.9K]

Answer:

The unit rate of 297 words for 5.5 minutes is, 54 words per minutes

hope this helps :-)

5 0

3 years ago

H + 1/3 when h= 1 2/3

Bess [88]

2. Because if 1/3 + 2/3 is 1 then 1+1=2

8 0

3 years ago

Read 2 more answers

If Callum is consuming his utility maximizing bundle and the price of one good rises, what happens to the marginal utility per d

monitta

Answer:

MU/P has decreased and Callum should buy less of the good.

Step-by-step explanation:

8 0

3 years ago