Ask question

Ask question

All categories

2 years ago

9

The volume of the fish tank needs to be tripled. What scale factor should be applied to the dimensions to produce a fish tank wi

th three times the volume

1 answer:

joja [24]2 years ago

4 0

Answer:

assuming it's a perfect world and that the fish lives in a 1 cubic meter fish tank 1*1.4422 will increase the volume my a factor of 3

You might be interested in

Hi please do this answer and please show the (steps) on how you got it. ❤️

zhenek [66]

This is the answer!!!!!!

4 0

3 years ago

Is this solvable or simplifiable

sashaice [31]

Answer:

hello please follow me I am new and thanks for free points

8 0

2 years ago

Read 2 more answers

A graphing calculator is recommended. A function is given. g(x) = x4 − 5x3 − 14x2 (a) Find all the local maximum and minimum val

Taya2010 [7]

Answer:

The local maximum and minimum values are:

Local maximum

$g(0) = 0$

Local minima

$g(5.118) = -350.90$

$g(-1.368) = -9.90$

Step-by-step explanation:

Let be $g(x) = x^{4}-5\cdot x^{3}-14\cdot x^{2}$ . The determination of maxima and minima is done by using the First and Second Derivatives of the Function (First and Second Derivative Tests). First, the function can be rewritten algebraically as follows:

$g(x) = x^{2}\cdot (x^{2}-5\cdot x -14)$

Then, first and second derivatives of the function are, respectively:

First derivative

$g'(x) = 2\cdot x \cdot (x^{2}-5\cdot x -14) + x^{2}\cdot (2\cdot x -5)$

$g'(x) = 2\cdot x^{3}-10\cdot x^{2}-28\cdot x +2\cdot x^{3}-5\cdot x^{2}$

$g'(x) = 4\cdot x^{3}-15\cdot x^{2}-28\cdot x$

$g'(x) = x\cdot (4\cdot x^{2}-15\cdot x -28)$

Second derivative

$g''(x) = 12\cdot x^{2}-30\cdot x -28$

Now, let equalize the first derivative to solve and solve the resulting equation:

$x\cdot (4\cdot x^{2}-15\cdot x -28) = 0$

The second-order polynomial is now transform into a product of binomials with the help of factorization methods or by General Quadratic Formula. That is:

$x\cdot (x-5.118)\cdot (x+1.368) = 0$

The critical points are 0, 5.118 and -1.368.

Each critical point is evaluated at the second derivative expression:

x = 0

$g''(0) = 12\cdot (0)^{2}-30\cdot (0) -28$

$g''(0) = -28$

This value leads to a local maximum.

x = 5.118

$g''(5.118) = 12\cdot (5.118)^{2}-30\cdot (5.118) -28$

$g''(5.118) = 132.787$

This value leads to a local minimum.

x = -1.368

$g''(-1.368) = 12\cdot (-1.368)^{2}-30\cdot (-1.368) -28$

$g''(-1.368) = 35.497$

This value leads to a local minimum.

Therefore, the local maximum and minimum values are:

Local maximum

$g(0) = (0)^{4}-5\cdot (0)^{3}-14\cdot (0)^{2}$

$g(0) = 0$

Local minima

$g(5.118) = (5.118)^{4}-5\cdot (5.118)^{3}-14\cdot (5.118)^{2}$

$g(5.118) = -350.90$

$g(-1.368) = (-1.368)^{4}-5\cdot (-1.368)^{3}-14\cdot (-1.368)^{2}$

$g(-1.368) = -9.90$

7 0

3 years ago

A rectangular rug has an area of 84 square feet. If its length is 2 feet more than twice its width, find the dimensions of the

weeeeeb [17]

L=2W+2

W=(L-2)/2

A=LW, using W from above makes this

A=L(L-2)/2

2A=L^2-2L

L^2-2L-2A=0, given A=84

L^2-2L-168=0

(L-14)(L+12)=0, since L>0

L=14

The length of the rug is 14 ft

(W=(L-2)/2=6 ft)

3 0

3 years ago

What is the answer to this problem if you need to find out the area?

PolarNik [594]

Answer:

17.28in

Step-by-step explanation:

To find the area of a triangle, multiply the base by the perpendicular height (the length from the point opposite the base, to the base, which makes a 90-degree angle with the base), and half it:

7.2*4.8=34.56

34.56/2=17.28

8 0

3 years ago