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Citrus2011 [14]

3 years ago

5

Fred’s birthday party will be in a room at the community center. The room can hold no more than 75 people. He wants to use tabl

es that seat 5 people each. Which inequality can be used to find the maximum number of tables he can use?
A. 5 + t >= 75
B. 5t >= 75
C. 5 + t <= 75
D. 5t <=75

1 answer:

Zepler [3.9K]3 years ago

6 0

Answer:

I think it's D? However I'm not sure.

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before the use of calculators, mathematicians developed and used detailed tables of values of the sine, cosine and tangent ratio

Debora [2.8K]

Answer:

the answer is bc of my knowledge XD XD XD hahaha

Step-by-step explanation:

nbhgutfyctygvuhbijnk mjbguvyfccvguhbijnk bvf vhnjhbvtcdxtcrftygbhjnhbgvfctytguhb vgc

3 0

3 years ago

Determine the value of x

KATRIN_1 [288]

Answer:

The value of x is 12 feet

Step-by-step explanation:

The shape in question is a composite shape. We can see that x is both the base of the triangle and the breadth of the rectangle.

To get the area of the shape, we will have to add the area of the rectangle to the area of the triangle.

Area of rectangle = length X breadth

Area of triangle = 1/2 base X height.

However, to calculate the area of the triangle, we need to find its height first.

The next step is to get the height of the triangle. Observing the shape properly, we can see that we can get the height by subtracting the length of the rectangle from the overall length of the shape.

Height of triangle = 16 ft - 10 ft = 6 ft

recall area = 156 square feet.

We now have most of our missing dimensions

We can now set up an equation as follows:

$(10 \times x) +0.5 \times x \times 6 = 156$

$10x +3x=156\\13x=156\\x=12 feet$

Therefore the value of x is 12 feet

8 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

Which of these story problem describes the sum 19 + (-12)? Check all that apply. Show your work to justify your answer.

MatroZZZ [7]

-19 + (-12) = 7

Remove Parentheses
( -a ) = -a

= 19 - 12
Subtract The Numbers
19-12 = 7

8 0

3 years ago

Katie wants to buy some popcorn for her family at the theater. Each small tub of popcorn costs $3 and each large tub of popcorn

Molodets [167]

For this case we propose a system of equations:

x: Represents the amount of small popcorn tubs

y: Represents the amount of large popcorn tubs

According to the data we have to:

$3x + 4y = 24$ (Spending all the money in your wallet)

$x + y = 7$ (Buying 7 popcorn tubs)

From the second equation we have:

$x = 7-y$

Substituting in the first equation:

$3 (7-y) + 4y = 24\\21-3y + 4y = 24\\21 + y = 24\\y = 24-21\\y = 3$

Thus, Katie can buy 3 large tubs of popcorn.

So:

$x = 7-3\\x = 4$

In addition, you can buy 4 small tubs of popcorn.

Answer:

3 large popcorn tubs.

4 small popcorn tubs.

8 0

2 years ago