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2 years ago

5

5000 people attended a football game. 2350 of the people attending supported the home team, while 2650 supported the visiting te

am. What percentage of people attending supported the home team?

1 answer:

Otrada [13]2 years ago

3 0

Answer:

47%

2350 out of 5000=0.47

move the decimal 2 times

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Choose the quadratic equation that has a leading coefficient of 8 and solutions -10 and 7/8

Maru [420]

Answer:

$f(x)=8x^2+73x-70$

Step-by-step explanation:

We are given

zeros as -10 and 7/8

now, we can set up function as

$f(x)=a(x-(-10))(x-\frac{7}{8})$

now, we are given that

leading coefficient is 8

so, a=8

now, we can plug it

$f(x)=8(x-(-10))(x-\frac{7}{8})$

now, we can simplify it

$f(x)=8\left(x^2+\frac{73x}{8}-\frac{35}{4}\right)$

so, we get

$f(x)=8x^2+73x-70$

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lora16 [44]

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Step-by-step explanation:

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2 years ago

3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k

Andreas93 [3]

a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

$\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt$

Evaluate the integral to solve for y :

$\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt$

$\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x$

$\displaystyle y = x^3+2x^2+kx - 2$

Use the other known value, f(2) = 18, to solve for k :

$18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}$

Then the curve C has equation

$\boxed{y = x^3 + 2x^2 + 2x - 2}$

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

$\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2$

The slope of the given tangent line $y=x-2$ is 1. Solve for a :

$3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1$

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).

Decide which of these points is correct:

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Bess [88]

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Step-by-step explanation:

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