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3 years ago

What is the leading coefficient in 1-2x+5x^4 when in standard form

1 answer:

4 0

That's a lot of points for this question. You don't have to offer that much.

Leading Coefficient: When written in standard form (starting with the variable with the highest power, going to the variable with the next highest power ... all the way down to a number with no variable), the leading coefficient is the number in front of the variable with the highest power.

Let me put this less technically. Find the variable with the highest power. The number in front of that variable is the leading coefficient.

Write this in standard form. 5x^4 -2x + 1
The number in front of the x^4 is the answer.
5 <<<<< answer

You might be interested in

Find all of the equilibrium solutions. Enter your answer as a list of ordered pairs (R,W), where R is the number of rabbits and

zloy xaker [14]

Answer:

$(0,0)$ $(4000,0)$ and $(500,79)$

Step-by-step explanation:

Given

See attachment for complete question

Required

Determine the equilibrium solutions

We have:

$\frac{dR}{dt} = 0.09R(1 - 0.00025R) - 0.001RW$

$\frac{dW}{dt} = -0.02W + 0.00004RW$

To solve this, we first equate $\frac{dR}{dt}$ and $\frac{dW}{dt}$ to 0.

So, we have:

$0.09R(1 - 0.00025R) - 0.001RW = 0$

$-0.02W + 0.00004RW = 0$

Factor out R in $0.09R(1 - 0.00025R) - 0.001RW = 0$

$R(0.09(1 - 0.00025R) - 0.001W) = 0$

Split

$R = 0$ or $0.09(1 - 0.00025R) - 0.001W = 0$

$R = 0$ or $0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

Factor out W in $-0.02W + 0.00004RW = 0$

$W(-0.02 + 0.00004R) = 0$

Split

$W = 0$ or $-0.02 + 0.00004R = 0$

Solve for R

$-0.02 + 0.00004R = 0$

$0.00004R = 0.02$

Make R the subject

$R = \frac{0.02}{0.00004}$

$R = 500$

When $R = 500$ , we have:

$0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

$0.09 -2.25 * 10^{-5} * 500 - 0.001W = 0$

$0.09 -0.01125 - 0.001W = 0$

$0.07875 - 0.001W = 0$

Collect like terms

$- 0.001W = -0.07875$

Solve for W

$W = \frac{-0.07875}{ - 0.001}$

$W = 78.75$

$W \approx 79$

$(R,W) \to (500,79)$

When $W = 0$ , we have:

$0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

$0.09 - 2.25 * 10^{-5}R - 0.001*0 = 0$

$0.09 - 2.25 * 10^{-5}R = 0$

Collect like terms

$- 2.25 * 10^{-5}R = -0.09$

Solve for R

$R = \frac{-0.09}{- 2.25 * 10^{-5}}$

$R = 4000$

So, we have:

$(R,W) \to (4000,0)$

When $R =0$ , we have:

$-0.02W + 0.00004RW = 0$

$-0.02W + 0.00004W*0 = 0$

$-0.02W + 0 = 0$

$-0.02W = 0$

$W=0$

So, we have:

$(R,W) \to (0,0)$

Hence, the points of equilibrium are:

$(0,0)$ $(4000,0)$ and $(500,79)$

4 0

3 years ago

A parallelogram has an area of 60 square inches. If the base of the parallelogram is 12 inches, what is the height of the parall

Vikentia [17]

How to find the area of a parallelogram is length times height. 12 times what gets you to 60? 5 does. 12 times 5 is 60.

HEIGHT: 5

8 0

3 years ago

What is the fifth term in the geometric sequence described by this explicit formula y=40×(-2)^(n-1)

cupoosta [38]

Answer:

The fifth term is 620

Step-by-step explanation:

y=40×(-2)^(n-1)

The 5th terms means n=5

y = 40 * (-2) ^ (5-1)

= 40 * (-2) ^4

= 40 * (16)

= 640

5 0

3 years ago

2. The 7th term of an A.P is 27 and the 12th term is 47, what is the sequence?

Vera_Pavlovna [14]

Answer:

Step-by-step explanation:

let r be the common differenc of the sequence

Term 12 - Term 7 = (12 - 7)r

then

47 - 27 = 5r

then

20 = 5r

then

r = 4

term 7 = term 1 + (7 - 1)r

then

27 = term 1 + 6r = term 1 + 24

then

Term1 = 27 - 24 = 3

<em><u>therefore </u></em>

the standard explicit formula of the sequence is :

term 1 + (n - 1)r = 3 + 4(n - 1)

8 0

3 years ago

A certain city with population of 132,000 is to be divided into 11 voting districts, and no district is to have a population tha

galben [10]

Answer: Therefore, Option 'D' is correct.

Step-by-step explanation:

Since we have given that

Number of population = 132000

Number of voting districts = 11

According to question, no district is to have a population that is more than 10 percent greater than the population of any other district.

Let the number of population that the least populated district could have be 'x'.

So, it becomes,

$x+10(1.1x)=132000\\\\x+11x=13200\\\\12x=132000\\\\x=\dfrac{132000}{12}\\\\x=11000$

Hence, there are 11000 population that the least populated district could have.

Therefore, Option 'D' is correct.

4 0

3 years ago