All categories

3 years ago

What is the volume of an aquarium that is 1 yard wide, .5 yard deep, and .75 yard long?

2 answers:

8 0

The volume of the aquarium is calculated using the formula of rectangular prism volume
v = l × w × h

From the question, we know that
l = 0.75 yard
w = 1 yard
h = 0.5 yard

Input the numbers to the formula
v = l × w × h
v = 0.75 × 1 × 0.5
v = 0.75 × 0.5
v = 0.375

The volume of the aquarium is 0.375 cube yard

Helga [31]3 years ago

3 0

0.375 is the answer hope this helps

You might be interested in

which expression shows the result of applying the distributive property to 12 (5y + 4) ? A. 60y + 48 B. 5y + 48 C. 17y + 16 D. 6

PSYCHO15rus [73]

A because you just distribute the 12 to both

7 0

3 years ago

Read 2 more answers

Max makes $612 every three months. At the same rate, how much does Max make in one year (12 months)?

Lostsunrise [7]

Ok!

Lets find out how much he makes per month.

You do this by dividing 612 and 3. so 612 / 3 = 204.
Max makes 204 per month.

2. Now that you have the per month, you multiply it by 12.

204 x 12 = 2448

Answer: 2,448

I hope this helped you understand!

7 0

3 years ago

Based on the table of values below, find the slope between points where x = 5 and where x = 10.

horsena [70]

Hello!

$\large\boxed{m = 1}$

Use the slope formula to determine the slope between the points:

m = (y2 - y1) / (x2 - x1)

Plug in the values:

m = (7 - 2) / (10 - 5)

m = 5 / 5

m = 1

7 0

3 years ago

Find the critical points of the surface f(x, y) = x3 - 6xy + y3 and determine their nature.

Vedmedyk [2.9K]

Compute the gradient of $f$ .

$\nabla f(x,y) = \left\langle 3x^2 - 6y, -6x + 3y^2\right\rangle$

Set this equal to the zero vector and solve for the critical points.

$3x^2-6y = 0 \implies x^2 = 2y$

$-6x+3y^2=0 \implies y^2 = 2x \implies y = \pm\sqrt{2x}$

$\implies x^2 = \pm2\sqrt{2x}$

$\implies x^4 = 8x$

$\implies x^4 - 8x = 0$

$\implies x (x-2) (x^2 + 2x + 4) = 0$

$\implies x = 0 \text{ or } x-2 = 0 \text{ or } x^2 + 2x + 4 = 0$

$\implies x = 0 \text{ or } x = 2 \text{ or } (x+1)^2 + 3 = 0$

The last case has no real solution, so we can ignore it.

Now,

$x=0 \implies 0^2 = 2y \implies y=0$

$x=2 \implies 2^2 = 2y \implies y=2$

so we have two critical points (0, 0) and (2, 2).

Compute the Hessian matrix (i.e. Jacobian of the gradient).

$H(x,y) = \begin{bmatrix} 6x & -6 \\ -6 & 6y \end{bmatrix}$

Check the sign of the determinant of the Hessian at each of the critical points.

$\det H(0,0) = \begin{vmatrix} 0 & -6 \\ -6 & 0 \end{vmatrix} = -36 < 0$

which indicates a saddle point at (0, 0);

$\det H(2,2) = \begin{vmatrix} 12 & -6 \\ -6 & 12 \end{vmatrix} = 108 > 0$

We also have $f_{xx}(2,2) = 12 > 0$ , which together indicate a local minimum at (2, 2).

3 0

2 years ago

Sam had $24.75 to spend on flowers for his mother. each rose cost $2.50 and each daisy cost $1.75. what are his options for the

diamong [38]

<span>The equation for the flowers Sam can purchase for his mother is 2.5x + 1.75y < 24.75. There are many acceptable answers for this, such as buying only 1 to 9 roses. If Sam wants to spend all of his $24.75 budget, he can get 5 roses and 7 daisies for a bouquet: 5*$2.50 = $12.50, 7*$1.75= $12.25, $12.50+$12.25 = $24.75</span>

3 0

3 years ago