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MakcuM [25]
3 years ago
10

2. A small square garden has an area of 25 square yards. How long is each side of

Mathematics
1 answer:
gizmo_the_mogwai [7]3 years ago
3 0
It’s C, because a square has 4 sides so you divide 25 by 4 and get 5
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If the perimeter of a rectangle or piece of glass is 26 inches and the length is 4 inches longer than twice the width and what a
cricket20 [7]
2(2w+4+w)=26; 6w+8=26; w=3, l=10

5 0
3 years ago
The teacher has 11 apples and seven oranges. Does he have more apples or oranges? How much more
Drupady [299]
Ok well since it said “how much more we subtract 11-7=4
6 0
2 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 :

a). The level curves of the function :

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

are actually the curves

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

where k is a positive constant.

The equation is equivalent to

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

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

which is a family of ellipses.

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

$\triangledown C$ points in the direction of most rapid increase in concentration, which means $\triangledown C$ is tangent to the most rapid increase curve.

$r(t)=x(t)i+y(t)j$  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} $

∴ $\frac{dy}{dx}=\frac{dy/dt}{dx/dt}=\frac{2y}{x}$

Using separation of variables,

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

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

$\ln y=2 \ln x$

⇒ y = kx^2 for some constant k

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

$\Rightarrow kx_0^2=y_0$

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

∴ The path of the shark will follow is along the parabola

$y=\frac{y_0}{x_0^2}x^2$

$y=y_0\left(\frac{x}{x_0}\right)^2$

7 0
2 years ago
Someone help me with this. I forgot my notes in class
Nonamiya [84]

Answer:

see explanation

Step-by-step explanation:

Since AB = BC the the triangle is isosceles and thus

∠ A = ∠ C = 8x

The sum of the 3 angles in a triangle = 180°

Sum the 3 angles and equate to 180

44x + 8x + 8x = 180, that is

60x = 180 ( divide both sides by 60 )

x = 3

Thus

∠ A = ∠ C = 8x = 8(3) = 24°

∠ B = 44x = 44(3) = 132°

6 0
3 years ago
Read 2 more answers
X^2-11x+30=2 <br> Solve using quadratic formula or factoring
Pavel [41]
X^2-11x+28=0

(x-7)(x-4)=0

x-7=0
x=7

x-4=0
x=4
7 0
3 years ago
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