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3 years ago

What is the end behavior of f(x) = (x − 3)2(x + 5)(x − 2)3?

1 answer:

6 0

The total power of the polynomial is 6 so it would take on the same end behavior as a parabola. As x approaches infinity y approaches infinity, as x approaches negative infinity y approaches infinity.
I hope this helps.

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Linear Programming:

tatuchka [14]

Let the number of large bookcases be x and number of small bookcases be y, then
Maximise P = 80x + 50y;
subkect to:
6x + 2y ≤ 24
x, y ≥ 2

The corner points are (2, 2), (2, 6), (3.333, 2)
For (2, 2): P = 80(2) + 50(2) = 160 + 100 = 260
For (2, 6): P = 80(2) + 50(6) = 160 + 300 = 460
For (3.333, 2): P = 80(3.333) + 50(2) = 266.67 + 100 = 366.67

Therefore, for maximum profit, he should produce 2 large bookcases and 6 small bookcases.

7 0

3 years ago

. A pitcher’s mound on a women’s softball field is 43 feet from home plate and the distance between the bases is 60 feet. How fa

butalik [34]

Answer:

42.43 ft

Step-by-step explanation:

Please find attached an image of the softball pitch

h² = p² + f² -2x p×f×cos45

h² = 43² + 60² - 2x (43)(60) x 0.7071

h² = 1849 + 3600 - 3648.636

h² = 1800.364

h = √1800.364

h = 42.43 feet

8 0

2 years ago

ed fills his sports bottle with 1.2 liters of water after his bike ride he drinks 200 millimeters of water how much water is lef

Iteru [2.4K]

1,2 liters of water = 1.200 millimeters so if he drinks 200 millimeters he has 1,000 millimeters left or 1 liter of water left

6 0

3 years ago

Find the area of this trapezoid. Be sure to include the correct unit in your answer.

melisa1 [442]

Answer:

12x9=108

108x7=756

756×17=12,852

The answer is 12,852.

3 0

3 years ago

Read 2 more answers

Find an asymptote of this conic section. 9x^2-36x-4y^2+24y-36=0

ki77a [65]

We will begin by grouping the x terms together and the y terms together so we can complete the square and see what we're looking at. $(9x^2-36x)-(4y^2+24y)-36=0$ . Now we need to move that 36 over by adding to isolate the x and y terms. $(9x^2-36x)-(4y^2+24y)=36$ . Now we need to complete the square on the x terms and the y terms. Can't do that, though, til the leading coefficients on the squared terms are 1's. Right now they are 9 and 4. Factor them out: $9(x^2-4x)-4(y^2-6y)=36$ . Now let's complete the square on the x's. Our linear term is 4. Half of 4 is 2, and 2 squared is 4, so add it into the parenthesis. BUT don't forget about the 9 hanging around out front there that refuses to be forgotten. It is a multiplier. So we are really adding in is 9*4 which is 36. Half the linear term on the y's is 3. 3 squared is 9, but again, what we are really adding in is -4*9 which is -36. Putting that altogether looks like this thus far: $9(x^2-4x+4)-4(y^2-6y+9)=36+36-36$ . The right side simplifies of course to just 36. Since we have a minus sign between those x and y terms, this is a hyperbola. The hyperbola has to be set to equal 1. So we divide by 36. At the same time we will form the perfect square binomials we created for this very purpose on the left: $\frac{(x-2)^2}{4}- \frac{(y-3)^2}{9}=1$ . Since the 9 is the bigger of the 2 values there, and it is under the y terms, our hyperbola has a horizontal transverse axis. a^2=4 so a=2; b^2=9 so b=3. Our asymptotes have the formula for the slope of $m=+/- \frac{b}{a}$ which for us is a slope of negative and positive 3/2. Using the slope and the fact that we now know the center of the hyperbola to be (2, 3), we can solve for b and rewrite the equations of the asymptotes. $3= \frac{3}{2}(2)+b$ give us a b of 0 so that equation is y = 3/2x. For the negative slope, we have $3=- \frac{3}{2}(2)+b$ which gives us a b value of 6. That equation then is y = -3/2x + 6. And there you go!

8 0

3 years ago