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olga2289 [7]
3 years ago
11

The path followed by a roller coaster as it climbs up and descends down from a peak can be modeled by a quadratic function, wher

e h(x) is the height, in feet, and x is the horizontal distance, also in feet. The path begins and ends at the same height, covers a total horizontal distance of 100 feet, and reaches a maximum height of 250 feet. Which of the functions could be used to model this situation? A. h(x)=-0.1x^2-50x+250 B. h(x)=-0.1(x-50)^2+250 C. h(x)=-0.1(x-100)^2+250 D. h(x)=-0.1x^2+100x+250
Mathematics
1 answer:
nirvana33 [79]3 years ago
7 0

Answer:

C

Step-by-step explanation:

0.1(x - 100)² + 250

0.1[(x - 100)(x - 100)] + 250

0.1(x² -200x + 10000) + 250

0.1x² - 20x + 1000 + 250

0.1x² - 20x + 1250

0.1x² - 25x + 5x + 1250

0.1x(x - 250) + 5(x + 250)

∴ (0.1x + 5)(x - 250) or (0.1x + 5)(x + 250)

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balu736 [363]

Answer:

Step-by-step explanation:

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8 0
2 years ago
Find the LCM of k2 + 3k + 2 and 2k2 + 14k + 20.
Archy [21]

Answer:

2(k+1)(k+2)(k+5)

5 0
2 years ago
If x^2y-3x=y^3-3, then at the point (-1,2), (dy/dx)?
zavuch27 [327]
If you're using the app, try seeing this answer through your browser:  brainly.com/question/2866883

_______________


          dy
Find  ——  for an implicit function:
          dx


x²y – 3x = y³ – 3


First, differentiate implicitly both sides with respect to x. Keep in mind that y is not just a variable, but it is also a function of x, so you have to use the chain rule there:

\mathsf{\dfrac{d}{dx}(x^2 y-3x)=\dfrac{d}{dx}(y^3-3)}\\\\\\&#10;\mathsf{\dfrac{d}{dx}(x^2 y)-3\,\dfrac{d}{dx}(x)=\dfrac{d}{dx}(y^3)-\dfrac{d}{dx}(3)}


Applying the product rule for the first term at the left-hand side:

\mathsf{\left[\dfrac{d}{dx}(x^2)\cdot y+x^2\cdot \dfrac{d}{dx}(y)\right]-3\cdot 1=3y^2\cdot \dfrac{dy}{dx}-0}\\\\\\&#10;\mathsf{\left[2x\cdot y+x^2\cdot \dfrac{dy}{dx}\right]-3=3y^2\cdot \dfrac{dy}{dx}}


                        dy
Now, isolate  ——  in the equation above:
                        dx

\mathsf{2xy+x^2\cdot \dfrac{dy}{dx}-3=3y^2\cdot \dfrac{dy}{dx}}\\\\\\&#10;\mathsf{2xy+x^2\cdot \dfrac{dy}{dx}-3-3y^2\cdot \dfrac{dy}{dx}=0}\\\\\\&#10;\mathsf{x^2\cdot \dfrac{dy}{dx}-3y^2\cdot \dfrac{dy}{dx}=-\,2xy+3}\\\\\\&#10;\mathsf{(x^2-3y^2)\cdot \dfrac{dy}{dx}=-\,2xy+3}


\mathsf{\dfrac{dy}{dx}=\dfrac{-\,2xy+3}{x^2-3y^2}\qquad\quad for~~x^2-3y^2\ne 0}


Compute the derivative value at the point (– 1, 2):

x = – 1   and   y = 2


\mathsf{\left.\dfrac{dy}{dx}\right|_{(-1,\,2)}=\dfrac{-\,2\cdot (-1)\cdot 2+3}{(-1)^2-3\cdot 2^2}}\\\\\\&#10;\mathsf{\left.\dfrac{dy}{dx}\right|_{(-1,\,2)}=\dfrac{4+3}{1-12}}\\\\\\&#10;\mathsf{\left.\dfrac{dy}{dx}\right|_{(-1,\,2)}=\dfrac{7}{-11}}\\\\\\\\ \therefore~~\mathsf{\left.\dfrac{dy}{dx}\right|_{(-1,\,2)}=-\,\dfrac{7}{11}}\quad\longleftarrow\quad\textsf{this is the answer.}


I hope this helps. =)


Tags:  <em>implicit function derivative implicit differentiation chain product rule differential integral calculus</em>

6 0
2 years ago
kaitlin is participating in a 5-day cross country biking challenge. She biked for 55,67,56,and 49 miles on the first four days.
SOVA2 [1]
The mean of a set of values is the sum of the data divided by the number of entries. So in this case:

\frac{55+67+56+49+x}{5} =55

Solve for x:

55 + 67 + 56 + 49 + x = 5(55)

227 + x = 275

x = 48

The answer is 48 miles.
7 0
2 years ago
Monica earned $60 from a bonus plus $8.50 per hour (h) she worked this week. Which of the following expressions best represents
maria [59]
60 +8.50 x 24 x 7 = ?
3 0
2 years ago
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