Write an expression equal to " 5 less than the product of 64 and a number"

Classify the following polynomials by the highest

Molodets [167]

Answer:

1. quadratic

2. cubic

3. linear

4. constant

Step-by-step explanation:

7 0

3 years ago

A manufacturer is planning to sell a new product at the price of 210 dollars per unit and estimates that if x thousand dollars i

sattari [20]

Answer:

Development costs: $2757

Promotion costs: $3155

Step-by-step explanation:

This might seem like a two-variable problem, but in actuality it's not - because the demand function is a sum of two components, each being independent and using only one variable, we can solve for the two separately.

Moreover, the price per unit and cost per unit is constant, so each product yields exactly $80 ($210 - $130).

Let's solve separately.

We need to maximize:

$80 * 160y/(y+4) - 1000y = $12800 * y/(y+4) - $1000*y

$80 * 170x/(x+7) - 1000x = $13600 * x/(x+7) - $1000*x

Let's go:

$12800 * y/(y+4) - $1000*y = $12800 * (1 - 4/(y+4)) - $1000y = $12800 - $51200/(y+4) - $1000*y

we analyze the derivative. $12800 is a constant, so we can skip it. Derivative of 1/(y+4) is -(y+4)^-2, derivative of $1000y is $1000.

deriv = $51200/(y+4)/(y+4) - $1000

We find the changepoints by analyzing $51200/(y+4)/(y+4) - $1000 = $0. We don't need to worry about y+4 = 0 because we cannot spend negative money on development/advertisement.

(y+4)^2 = $51.2

y+4 ~= 7.155417528 (or -y-4 = 7.1554... but it doesn't make sense because negative budget so we don't analyze).

y ~= 3.155417528

lastly, we should check that it's actually a maximum there - but it is, the original function goes to negative infinity.

rounding $1000y to the nearest dollar gives us $3155

Let's do the same for x:

$13600 * x/(x+7) - $1000*x = $13600 * (1 - 7/(x+7)) - $1000x = $13600 - $95200/(x+7) - $1000*x

deriv = $95200/(x+7)/(x+7) - $1000

$95200/(x+7)/(x+7) - $1000 = $0

(x+7)^2 = 95.2

(x+7) ~= 9.75704873412

x ~= 2.75704...

rounding $1000x to the nearest dollar yields $2757

3 0

3 years ago

What is 2.1 divided by 1.488

vekshin1

Answer:

= 0.708

Step-by-step explanation:

3 0

2 years ago

the height of a triangle is 4 meters less than the base. if the area of the triangle is 6 m^2 what is the height of the triangle

inna [77]

Answer:

$2m$

Step-by-step explanation:

Alrighty let's do this.

We know that formula for the Area of a triangle is:

$A = \frac{1}{2}bh$

They give us the area as $6m^2$ , so let's include it in the equation.

$6 = \frac{1}{2}bh$

Now we reach a stage where we have 2 unknown variables! That means we can't solve it in its current state. So the idea you should have in cases like these where you have 2 or more unknown variables is, "Can I represent this one variable in terms of another variable?" In this case you can do exactly that. You can represent height in terms of length of the base. We are told the height of the triangle is 4 meters less than the base. That is telling us that $h = b-4$

So replace $h$ in the equation with $b-4$ .

You will now get:

$6 = \frac{1}{2}b(b-4)$

Now we can work towards solving. Let's get simplifying.

$12 = b(b-4)\\12 = b^2 - 4b\\$

bring everything to one side so we can make a quadratic and factor:

$0 = b^2 - 4b - 12\\0 = (b-6)(b+2)\\\\b = 6\\b\neq -2$

We get that $b=6$ .

Since we need the height of the triangle we'll need to call back on what h is. We found earlier that $h = b - 4$ , so to find h, we just sub in our b value into that.