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3 years ago

Give the degree of the polynomial -3w+x^6y^5-2+5y^4w^3x^2

Mathematics

1 answer:

Jlenok [28]3 years ago

5 0

Answer:

Here the degree of the polynomial is 11.

Step-by-step explanation:

To find the degree of the multivariate polynomials, we need to add up the powers of all the variables. So the total degree is given by the sum of all the powers of the highest powers terms.

Now in the given polynomial $-3w+x^6y^5-2+5y^4w^3x^2$

the term with the highest total powers is $x^6y^5$ and thus the total power is 6+5=11.

And hence the degree of this polynomial is 11.

You might be interested in

Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by

a_sh-v [17]

Answer:

Dimension of the box is $16.1\times 7.1\times 2.45$

The volume of the box is 280.05 in³.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the box?

Solution :

Let h be the height of the box which is the side length of a corner square.

According to question,

A sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

The length of the box is $L=21-2h$

The width of the box is $W=12-2h$

The volume of the box is $V=L\times W\times H$

$V=(21-2h)\times (12-2h)\times h$

$V=(21-2h)\times (12h-2h^2)$

$V=252h-42h^2-24h^2+4h^3$

$V=4h^3-66h^2+252h$

To maximize the volume we find derivative of volume and put it to zero.

$V'=12h^2-132h+252$

$0=12h^2-132h+252$

Solving by quadratic formula,

$h=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$h=\frac{-(-132)\pm\sqrt{132^2-4(12)(252)}}{2(12)}$

$h=\frac{132\pm72.99}{24}$

$h=2.45,8.54$

Now, substitute the value of h in the volume,

$V=4h^3-66h^2+252h$

When, h=2.45

$V=4(2.45)^3-66(2.45)^2+252(2.45)$

$V\approx 280.05$

When, h=8.54

$V=4(8.54)^3-66(8.54)^2+252(8.54)$

$V\approx -170.06$

Rejecting the negative volume as it is not possible.

Therefore, The volume of the box is 280.05 in³.

The dimension of the box is

The height of the box is h=2.45

The length of the box is $L=21-2(2.45)=16.1$

The width of the box is $W=12-2(2.45)=7.1$

So, Dimension of the box is $16.1\times 7.1\times 2.45$

6 0

3 years ago

A rectangular box has faces with areas of 12,15, and 20 square units. What is the volume of the box?

miv72 [106K]

First find the side lengths of the box by factoring each area:

12: 1, 2, 3, 4, 6, 12
15: 1, 3, 5, 15
20: 1, 2, 4, 5, 10, 20

Find 3 numbers that both have 2 sides have in common and can multiply to make the areas of the faces:

12: 3 * 4
15: 3 * 5
20: 4 * 5

Sides: 3, 4, and 5

Then multiply to get the volume:

3 * 4 * 5 = 60 units^2

6 0

3 years ago

Can someone help me with this f(g(x))=2(3x-4)^2+5?

Greeley [361]

Answer:

f(x)=349525

Step-by-step explanation:

f(x)=2(3x-4)^2+5

f(x)= 6x - 8^7

f(x)= 6x - 2,097,152

f(-6x)= - 2,097,152

/-6x /-6x

f(x)=349525

I hope I am not terribly wrong but I probably am good luck

7 0

3 years ago

HELP FAST PLEASE 50 POINTS TO BRAINLIEST

weqwewe [10]

Is there any positive 3 or not if not,
The answer for A is .....
The answer for B is ......
The answer for C is ......

8 0

3 years ago

Read 2 more answers

Juno is taking a taxi. The table represents a linear function and shows the amount she owed after various numbers of miles trave

Gennadij [26K]

(B) - Yes, because the amount owed changes by 2.25 every time the miles change by 1.

Starting at 1 mile the price is 2.5 dollars.

Mile 2 is 4.75 dollars. What is the difference between 4.75 and 2.5? 2.25

Mile 3 is 7 dollars. What is the difference between 7 and 4.75? 2.25

Mile 4 is 9.25 dollars. What is the difference between 9.25 and 7? 2.25

Mule 5 is 11.5 dollars. What is the difference between 11.5 and 9.25? 2.25

The change is always 2.25 dollars.

The change is 2.25 dollars per mile.

One way to solve for this is (11.5 - 2.5)/(5-1)=2.25

This is (y2-y1)/(x2-x1). By picking 2 points, (x1,y1) and (x2,y2) you can solve for the slope (rate of change) between them.

7 0

3 years ago

Read 2 more answers