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3 years ago

Determine whether the expression is a polynomial. If it is a polynomial, find the degree

Mathematics

1 answer:

ZanzabumX [31]3 years ago

5 0

Answer:

This expression is a polynomial. The largest exponent is 2, therefore, it is in the quadratic degree. It is a binomial because it has two parts: 3y² and -2.

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What value of m does the graph y = 18x2 + mx + 2 have exactly one x-intercept?

Vlada [557]

To get the graph to have one x-intercept, we must find the m value where the discriminant of the equation will equal 0.

The discriminant for a graph with one x-intercept is found with the following formula:

$b^2 - 4ac = 0$

Plug in the values of the equation into this formula:

$\text{a = 18, b = m, c = 2}$
$m^2 - 4(18)(2) = 0$
$m^2 - 144 = 0$

Add 144 to both sides:

$m^2 = 144$

Square root both sides to get m by itself:

$\sqrt{144} = \pm 12$
$m = 12, \ m = -12$

In order for the graph to have one x-intercept, m must equal -12 or 12.

7 0

3 years ago

Verify that P = Ce^t /1 + Ce^t is a one-parameter family of solutions to the differential equation dP dt = P(1 − P).

NemiM [27]

Answer:

See verification below

Step-by-step explanation:

We can differentiate P(t) respect to t with usual rules (quotient, exponential, and sum) and rearrange the result. First, note that

$1-P=1-\frac{ce^t}{1+ce^t}=\frac{1+ce^t-ce^t}{1+ce^t}=\frac{1}{1+ce^t}$

Now, differentiate to obtain

$\frac{dP}{dt}=(\frac{ce^t}{1+ce^t})'=\frac{(ce^t)'(1+ce^t)-(ce^t)(1+ce^t)'}{(1+ce^t)^2}$

$=\frac{(ce^t)(1+ce^t)-(ce^t)(ce^t)}{(1+ce^t)^2}=\frac{ce^t+ce^{2t}-ce^{2t}}{(1+ce^t)^2}=\frac{ce^t}{(1+ce^t)^2}$

To obtain the required form, extract a factor in both the numerator and denominator:

$\frac{dP}{dt}=\frac{ce^t}{1+ce^t}\frac{1}{1+ce^t}=P(1-P)$

3 0

4 years ago

4897 to the nerest 100

vagabundo [1.1K]

900 I think you need to try

6 0

3 years ago

On Monday, a factory used 11/15 a ton of grapes to make grape juice. Tuesday required 14/30 a ton more than the amount on Monday

Rudiy27

Answer:

1 ton on wednesday!

Step-by-step explanation:

We need to go step by step for this one.

On monday the factory used 11/15 of a ton, while tuesday required 14/30 a ton more than that. To find tuesday's amount we must take 11/15 and add 14/30 to that.

11/15 + 14/30 = 1 1/5

Tuesday = 1 1/5 of a ton

On wednesday the factory uses 5/6 of the amount used on tuesday, which is 1 and 1/5 of a ton.

1 1/5 times 5/6 = 6/5 times 5/6

Anything multiplied by their reciprocal is 1, so the answer is 1. On wednesday 1 ton of grapes was used on wednesday!

5 0

3 years ago

A data set contains an independent and a dependent variable. Which must be true of the data set if a linear function can be

Rom4ik [11]

When we have dependent and independent variables we will have a linear relationship.

Let x be the independent variable and y be the dependent variable.

To write the relationship we will have :

y = kx + c

Where k and c are constants.

In the case of a line the constant k is the gradient.

A multiplicative change is a log form and it is given by :

Y = Ck^x

The relationship is not linear but exponential.

The correct answer is thus :

Additive rate of change.

5 0

3 years ago