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3 years ago

The quadratic function y = -x2 + 10x - 8 models the height of a trestle on a bridge. The x-axis represents ground level.

Mathematics

1 answer:

Scilla [17]3 years ago

6 0

Answer: 0.876, 9.123

Step-by-step explanation:

The function is $y=-x^2+10-8$

It meets the ground level when $y$ is 0

$\Rightarrow -x^2+10x-8=0\\\Rightarrow x^2-10x+8=0\\\\\Rightarrow x=\dfrac{10\pm \sqrt{(-10)^2-4(1)(8)}}{2}\\\\\Rightarrow x=\dfrac{10\pm \sqrt{68}}{2}\\\\\Rightarrow x=5\pm \sqrt{17}\\\Rightarrow x=0.876,\ 9.123$

Thus, it touches the ground at two points given above

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Answer:

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Step-by-step explanation:

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1 year ago

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A bakery sells 3642 pastries in 2010. The bakery sells 8422 pastries in 2015. Write a linear model that represents the number y

Simora [160]

Answer:

y = 936x + 3742

Step-by-step explanation:

If it is a linear model, then we should have a slope and y-intercept with the equation representing the model as;

y = mx + c

where m is the slope and c is the y-intercept

Thus, we have for the slope;

(8422-3742)/(2015-21010) = 4680/5 = 936

So the equation will be;

y = 936x + c

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So the linear model is;

y = 936x + 3742

7 0

3 years ago

(15 pts) 4. Find the solution of the following initial value problem: y"-10y'+25y = 0 with y(0) = 3 and y'(0) = 13

jolli1 [7]

Answer:

$y(x)=3e^{5x}-2xe^{5x}$

Step-by-step explanation:

The given differential equation is $y''-10y'+25y=0$

The characteristics equation is given by

$r^2-10r+25=0$

Finding the values of r

$r^2-5r-5r+25=0\\\\r(r-5)-5(r-5)=0\\\\(r-5)(r-5)=0\\\\r_{1,2}=5$

We got a repeated roots. Hence, the solution of the differential equation is given by

$y(x)=c_1e^{5x}+c_2xe^{5x}...(i)$

On differentiating, we get

$y'(x)=5c_1e^{5x}+5c_2xe^{5x}+c_2e^{5x}...(ii)$

Apply the initial condition y (0)= 3 in equation (i)

$3=c_1e^{0}+0\\\\c_1=3$

Now, apply the initial condition y' (0)= 13 in equation (ii)

$13=5(3)e^{0}+0+c_2e^{0}\\\\13=15+c_2\\\\c_2=-2$

Therefore, the solution of the differential equation is

$y(x)=3e^{5x}-2xe^{5x}$

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3 years ago

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Darya [45]

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3 years ago

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3 years ago