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3 years ago

The archway of the main entrance of a university is modeled by the quadratic equation

Mathematics

1 answer:

Scilla [17]3 years ago

3 0

Answer:

B. (1,5) and (5.25, 3.94)

Step-by-step explanation:

The answer is where the 2 equations intersect.

We need to solve the following system of equations:

y = -x^2 + 6x

4y = 21 - x

From the second equation:

x = 21 - 4y

Plug this into the first equation:

y = -(21 - 4y)^2 + 6(21 - 4y)

y = -(441 - 168y + 16y^2)+ 126 - 24y

y = -441 + 168y - 16y^2 + 126 - 24y

16y^2 + y - 168y + 24y + 441 - 126 = 0

16y^2 - 143y + 315 = 0

y = [-(-143) +/- sqrt ((-143)^2 - 4 * 16 * 315)]/ (2*16)

y = 5, 3.938

When y = 5:

x = 21 - 4(5) = 1

When y = 3.938

x = 21 - 4(3.938) = 5.25.

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Alexxandr [17]

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3 years ago

Use green's theorem to find integral subscript c left parenthesis y space plus space e to the power of square root of x end expo

Flauer [41]

My best interpretation of the math here is that you're talking about the line integral,

$\displaystyle \int_C \left(y+e^{\sqrt x}\right) \, dx + \left(2x + \cos\left(y^2\right)\right) \, dy$

I won't bother trying to decipher what look like multiple choice solutions.

By Green's theorem, the line integral above is equivalent to

$\displaystyle \iint_D \frac{\partial\left(2x+\cos\left(y^2\right)\right)}{\partial x} - \frac{\partial\left(y+e^{\sqrt x}\right)}{\partial y} \, dx \, dy$

where D is the set

$D = \left\{ (x, y) : 0 \le x \le 1 \text{ and } 0 \le y \le x^2 \right\}$

Compute the double integral:

$\displaystyle \int_0^1 \int_0^{x^2} \left(2 - 1\right) \, dy \, dx = \int_0^1 \int_0^{x^2} dy \, dx = \int_0^1 x^2 \, dx = \boxed{\frac13}$

7 0

3 years ago

Find the intercepts to graph the line. x + 3y = -6

qwelly [4]

Answer:

X-Intercepts (-6,0) Y-intercepts(0,-2)

Step-by-step explanation:

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5 0

3 years ago

Need help please answer ASAP!

Dmitrij [34]

Answer:

46. (3) 29

47. (1) y = -4x + 3

48. (3) 3

49. (3) -1/2

50. (4) 25x - 75

Step-by-step explanation:

Question 46

Let red marbles be 2x + 3 and black marbles be x
2x + 3 + x = 42
3x = 39
x = 13
No. of red = 2(13) + 3 = 29 marbles
(3) 29

Question 47

Parallel to a line means the slope is the same
(1) y = -4x + 3

Question 48

For the expression to be undefined, the denominator has to be 0
x - 3 = 0
x = 3
(3) 3

Question 49

Slope = -4 - 1 / 4 + 6
Slope = -5/10
Slope = -1/2
(3) -1/2

Question 50

Total = 25x
Left 3 boxes at home = -3x = -3(25) = -75
(4) 25x - 75

6 0

2 years ago

If h(x) = x^3+ x and g(x) = 2x + 3, then g(h(2)) = ?

leonid [27]

Answer:

The proper answer is in the picture.

Step-by-step explanation:

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3 0

3 years ago