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Vladimir79 [104]
3 years ago
5

Which equation is modeled by the graph? Using the equation, about how many more cars are in the deck at 9:00 a.m. than at 8:30 a

.m.?
A) y = 3x + 50; 90 cars
B) y = 4x + 50; 75 cars
C) y = x + 50; 100 cars
D) y = 3x - 50; 120 cars

Mathematics
2 answers:
omeli [17]3 years ago
6 0
The correct answer is Choice A.

You can see from the graph that the y-intercept is 50 because it cross on the left at 50.

To find the slope, we can use the following two points (0, 50) and (20, 110). This will give a slope of 3.

Put the 50 and 3 together and you will have the equation:
y = 3x + 50
Stells [14]3 years ago
6 0

Answer:

y = 3x + 50

Step-by-step explanation:

Substitute the y-intercept (0, 50) and an estimated point (40, 170) into the slope formula and simplify.

m =  

y2 - y1

x2 - x1

m =  

170 - 50

40 - 0

m = 3

Substitute slope and y-intercept into slope- intercept form.

y = mx + b

y = 3x + 50

The slope represents the change in the number of cars in the parking garage per minute, which is 3.  

To find the number of cars in the parking garage at 8:30 a.m., substitute 30 into the equation for x (number of minutes after 8:00 a.m.) and simplify:  

y = 30(3) + 50 = 140

To find the number of cars in the parking garage at 9:00 a.m., substitute 60 into the equation for x (number of minutes after 8:00 a.m.) and simplify:  

y = 60(3) + 50 = 230

Find the difference: 230 - 140 = 90 cars

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erik [133]

Hey there!

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113.04/3.14=36

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Our radius is six. To find the circumference, we need to multiply the diameter by pi. The diameter is twice the radius.

6*2=12

12*3.14=37.68

Therefore, we will need 37.68 feet of trim to around the edge of the quilt.

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6 0
3 years ago
Marine biologists have determined that when a shark detectsthe presence of blood in the water, it will swim in the directionin w
siniylev [52]

Solution :

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$e^{-(x^2+2y^2)/10^4}=k$

where k is a positive constant.

The equation is equivalent to

$x^2+2y^2=K$

$\Rightarrow \frac{x^2}{(\sqrt K)^2}+\frac{y^2}{(\sqrt {K/2})^2}=1, \text{ where}\ K = -10^4 \ln k$

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We sketch the level curves for K =1,2,3 and 4.

If the shark always swim in the direction of maximum increase of blood concentration, its direction at any point would coincide with the gradient vector.

Then we know the shark's path is perpendicular to the level curves it intersects.

b). We have :

$\triangledown C= \frac{\partial C}{\partial x}i+\frac{\partial C}{\partial y}j$

$\Rightarrow \triangledown C =-\frac{2}{10^4}e^{-(x^2+2y^2)/10^4}(xi+2yj),$ and

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$r(t)=x(t)i+y(t)j$  is a parametrization of the most $\text{rapid increase curve}$ , then

$\frac{dx}{dt}=\frac{dx}{dt}i+\frac{dy}{dt}j$ is a tangent to the curve.

So then we have that $\frac{dr}{dt}=\lambda \triangledown C$

$\Rightarrow \frac{dx}{dt}=-\frac{2\lambda x}{10^4}e^{-(x^2+2y^2)/10^4}, \frac{dy}{dt}=-\frac{4\lambda y}{10^4}e^{-(x^2+2y^2)/10^4} $

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$\frac{dy}{y}=2\frac{dx}{x}$

$\int\frac{dy}{y}=2\int \frac{dx}{x}$

$\ln y=2 \ln x$

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but we know that $y(x_0)=y_0$

$\Rightarrow kx_0^2=y_0$

$\Rightarrow k =\frac{y_0}{x_0^2}$

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luda_lava [24]

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B)

B)

D)

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The polynomial within the bracket can not be factorized further hence this is our final answer. Option (B) is the right answer

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4 0
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7 0
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