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3 years ago

12

Avery wants to put a percentage of muffins in a display case. There are 60 muffins total. 40% are blueberry, 20% are pumpkin, an

d 30% are cranberry. how many blueberry muffin can she put in the display

1 answer:

padilas [110]3 years ago

5 0

i cant do this either

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Joe's summer camp had 81 attendees when it first opened and has grown by 92 attendees per year since then.

pychu [463]

Answer:

A = 92y + 81

Step-by-step explanation:

Because A = number of attendees and if it adds 92 each year, you times the number of years by 92 and add 81 for the ones that were already there

4 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 :

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

The largest possible circle is cut out of a square whose side length is 8 feet. What will be the approximate area, in square fee

valentina_108 [34]

<h3>Therefore the area of remaining board =13.76 square feet</h3>

Step-by-step explanation:

Given , The length of side of the square is 8 feet.

Since a circle is inscribed in the square. Then the diameter of the circle is equal to the length of side of the square .

Therefore the diameter of the circle is = 8 feet.

Radius of the circle is(r) = $\frac{8}{2}$ feet = 4 feet

The area of the circle is= 3.14 r²

= 3.14 × 4² square feet

= 50.24 square feet

The area of the square is = side × side

= 8×6 square feet

=64 square feet

Therefore the area of remaining board = (64- 50.24)square feet

=13.76 square feet

4 0

2 years ago

a cow is tied to a pole fixed at the mid-point of a side of a square field of side 40m by means of a 14m long rope find the area

svp [43]

Step-by-step explanation:

The area that cow can graze is in the form of semicircle.

Radius of semicircle

Length of rope =14 m

Required area = 1/2 ×πr

=1/2×22/7×r^2

=1/2×22/7×14×14

=308m2

4 0

2 years ago

After each soccer practice Scott Runs 4 sprints of 10 yards each complete exclamation to find how many practices it will take fo

Tpy6a [65]

Answer:

Scott will have to do 44 practices

Step-by-step explanation:

Let X be the number of yards per practice.

Let P = number of practice Scott needs to do.

Multiply 20 yards by 4 sprints

X = 20yards × 4 sprints = 80 yards

Number of yards he had to sprint per practice will be:

1 mile = 1760 yards

Converting from miles to yards

X = 1760 × 2 miles = 3520 yards

Number of practice,P Scott need to do = (3520/80)yards

Number of Practice,P = 44

5 0

3 years ago

Read 2 more answers