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3 years ago

Find the distance between the points E(3, 7) and F(6, 5).

Mathematics

1 answer:

V125BC [204]3 years ago

7 0

Answer:

root 13 units

Step-by-step explanation:

There is a formula that you use to solve these types of questions.

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Diagram 5 shows a right cylinder with a diameter of 2xcm. Given that the total surface area of the cylinder is 96cm³.Find the ma

Paraphin [41]

Given:

The diameter of the right cylinder is 2x cm.

The total surface area is 96 cm cube.

The radius is calculated as,

$\begin{gathered} r=\frac{d}{2} \\ r=\frac{2x}{2} \\ r=x\text{ cm} \end{gathered}$

The total surface area is,

$\begin{gathered} S=2\pi rh+2\pi(r)^2 \\ 96=2\pi xh+2\pi(x^2) \\ h=\frac{96-2\pi(x^2)}{2\pi x} \end{gathered}$

Volume is,

$\begin{gathered} V=\pi(r)^2h \\ =\pi(x^2)\frac{96-2\pi(x^2)}{2\pi x} \\ =\frac{x(96-2\pi(x^2)}{2} \end{gathered}$

Now, differentiate with respect to x,

$\begin{gathered} \frac{dV}{dx}^{}=\frac{d}{dx}(\frac{x(96-2\pi(x^2)}{2}) \\ =\frac{d}{dx}\mleft(x\mleft(-\pi x^2+48\mright)\mright) \\ =\frac{d}{dx}\mleft(x\mright)\mleft(-\pi x^2+48\mright)+\frac{d}{dx}\mleft(-\pi x^2+48\mright)x \\ =1\cdot\mleft(-\pi x^2+48\mright)+\mleft(-2\pi x\mright)x \\ =84-3\pi(x^2)\ldots\ldots\ldots\ldots\text{.}(1) \end{gathered}$

Now,

$\begin{gathered} \frac{dV}{dx}=0 \\ 84-3\pi(x^2)=0 \\ x^2=\frac{16}{\pi} \\ x=\sqrt[]{\frac{16}{\pi}} \end{gathered}$

Now, differentiate (1) with respect to x again,

$\begin{gathered} \frac{d^2V}{dx^2}=\frac{d}{dx}(84-3\pi(x^2)) \\ =-6\pi x \\ At\text{ x=}\sqrt[]{\frac{16}{\pi}} \\ \frac{d^2V}{dx^2}=-6\pi\sqrt[]{\frac{16}{\pi}}$

Since, the double derivative is negative.

$So,\text{ the volume is maximum at }\sqrt[]{\frac{16}{\pi}}$

So, the volume becomes,

$\begin{gathered} V=\pi(x^2)h \\ V=\pi(\sqrt[]{\frac{16}{\pi}})^2h \\ V=\frac{16h}{\pi} \end{gathered}$

Answer: maximum volume of the cylinder is,

6 0

1 year ago

Write the sum of 18+27 as the product of their gcf and another sum

Serjik [45]

One <em>possible answer</em> is:

9×(2+3)

Explanation:

First we find the sum of 18 and 27. 18+27 = 45.

Next we find the GCF of 18 and 27. We do this by finding the prime factorization of each:

18 = 2*9

9 = 3*3

Thus, 18 = 2*3*3.

27 = 3*9

9 = 3*3

Thus, 27 = 3*3*3

We want the common factors; there are 2 3's in common, so 3*3 = 9 is the GCF. This makes the product 9×( ). The missing number would be 5, since 9*5 = 45. Writing this as a sum, we can use 2+3; this gives us 9×(2+3).

4 0

3 years ago

Read 2 more answers

What is 1 more than 23.14

Alina [70]

Answer:

24.14

Step-by-step explanation:

more than means to add. So,

23.14 + 1 = 24.14

5 0

3 years ago

Lin has a drawing with an area of 20 in2. If she increases all the sides by a scale factor of 3, what will the new area be?

vodomira [7]

I forget what I was going to put

5 0

3 years ago

Graph y=−5/6x−4 .<br><br> Use the line tool and select two points on the line.

creativ13 [48]

$y = \frac{ - 5}{6x - 4}$
so I think I fill 0 in for Y and 0 in for X so:
$0 = \frac{ - 5}{6x - 4}$
you multiply 6x-4 to the 0
0 = -5

no solution

then you do the same but with X

$y = \frac{ - 5}{6(0) - 4}$
$y = \frac{ - 5}{0 - 4}$
$y = \frac{ - 5}{ - 4}$
negatives cancel out
$y = \frac{5}{4}$

I would check this! I am not totally sure!!

4 0

3 years ago

Read 2 more answers