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monitta
3 years ago
12

HELP!!! A LOT OF POINTS!!!

Mathematics
1 answer:
Tpy6a [65]3 years ago
7 0

Answer: Last option.

Step-by-step explanation:

For this exercise you need to find the Discriminant.

The formula used to find the Discriminant, is the following:

D=b^2-4ac

In this case, given the Quadratic equation:

6x^2-2x+7=0

You can identify that:

a=6\\b=-2\\c=7

Knowing those values, you must substitute them into the formula and then you must evaluate in order to find the Discriminant.

You get that this is:

D=(-2)^2-4(6)(7)\\\\D=-164

By definition, if:

 D

Then the Quadraitc equation has 2 nonreal solutions.

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I'm have some issues with the problem shown in the screenshot and would love some help.
KiRa [710]

The dimensions and volume of the largest box formed by the 18 in. by 35 in. cardboard are;

  • Width ≈ 8.89 in., length ≈ 24.89 in., height ≈ 4.55 in.

  • Maximum volume of the box is approximately 1048.6 in.³

<h3>How can the dimensions and volume of the box be calculated?</h3>

The given dimensions of the cardboard are;

Width = 18 inches

Length = 35 inches

Let <em>x </em>represent the side lengths of the cut squares, we have;

Width of the box formed = 18 - 2•x

Length of the box = 35 - 2•x

Height of the box = x

Volume, <em>V</em>, of the box is therefore;

V = (18 - 2•x) × (35 - 2•x) × x = 4•x³ - 106•x² + 630•x

By differentiation, at the extreme locations, we have;

\frac{d V }{dx}  =  \frac{d( 4 \cdot \:  {x}^{3}  - 106 \cdot \:  {x}^{2}  + 630\cdot \:  {x} )  }{dx} = 0

Which gives;

\frac{d V }{dx}  =12\cdot \:  {x}^{2}  -  212\cdot \:  {x} + 630 = 0

6•x² - 106•x + 315 = 0

x  =  \frac{ - 6 \pm \sqrt{106 ^2 - 4 \times 6 \times 315} }{2 \times 6}

Therefore;

x ≈ 4.55, or x ≈ -5.55

When x ≈ 4.55, we have;

V = 4•x³ - 106•x² + 630•x

Which gives;

V ≈ 1048.6

When x ≈ -5.55, we have;

V ≈ -7450.8

The dimensions of the box that gives the maximum volume are therefore;

  • Width ≈ 18 - 2×4.55 in. = 8.89 in.

  • Length of the box ≈ 35 - 2×4.55 in. = 24.89 in.

  • Height = x ≈ 4.55 in.

  • The maximum volume of the box, <em>V </em><em> </em>≈ 1048.6 in.³

Learn more about differentiation and integration here:

brainly.com/question/13058734

#SPJ1

7 0
1 year ago
Given g(x)=-x-1, find g(-4)
Molodets [167]

Answer:

g(-4)=3

Step-by-step explanation:

g(x)=-x-1

g(-4)=-(-4)-1

g(-4)=4-1

g(-4)=3

6 0
3 years ago
Write 9 as a power of the base 3
malfutka [58]
9 = 3^2
Since 3 squared equals 9, that is how 9 as a power of the base 3 should be written. 
4 0
2 years ago
sammy's bicycle and tricycles. clarence went to Sammy's and counted 37 sets of handlebars and 95 wheels. How many bicycles and t
Trava [24]

Answer:

16 bicycles and 21 tricycles

Step-by-step explanation:

Both bicycles and tricycles have 1 set of handlebars. Bicycles have 2 wheels while tricycles have 3.

Using this information, set up a system of equations, where b is the number of bicycles and t is the number of tricycles:

b + t = 37

2b + 3t = 95

Solve by elimination by multiplying the top equation by -2:

-2b - 2t = -74

2b + 3t = 95

t = 21

Then, plug in 21 as t into one of the equations:

b + t = 37

b + 21 = 37

b = 16

So, there are 16 bicycles and 21 tricycles

4 0
3 years ago
The sum of two numbers is 27. One number is 2 times as large as the other. What are the numbers?
Alex

Answer:

9 and 18

Step-by-step explanation:

x+y=27\\x=2y\\2y+y=27\\3y=27\\y=27/3=9\\x=27-9=18

6 0
1 year ago
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