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2 years ago

Carla packed this box with 1-centimeter cubes. what is the volume of the box?

Mathematics

1 answer:

Yuki888 [10]2 years ago

7 0

Answer: 60 cm three squared

You can observe in the picture attached that the box is a rectangular prism.

The volume of a rectangular prism can be found with this formula:

Where "l" is the length, "w" is the width and "h" is the height.

You know that the lenght of each side of those cubes is 1 centimeter. Therefore, you can multiply the number of cubes on each side of the box by 1 centimeter in order to find the lenght, the width and the height of the box:

Now you can substitute the lenght, the width and the height of the box into the formula shown at the beginning of the explanation:

Finally, evaluating, you get that the volume of the box is:

223 units

Step-by-step explanation:

brainly.com/question/14536184

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Which equation represents a proportional relationship that has a constant of proportionality equal to 2?

Softa [21]

you didn't give the options but constant of proportionality is a number you have to multiply x by to get y.

y=kx is the equation that expresses the proportionality of x and y

the constant of proportionality is k, so k=2

y= kx becomes y=2x

so y = 2x should be the answer

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2 years ago

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Suppose bug A lands on the end of the blade farthest from the pivot. Assume the wiper turns through an angle of 120°. In one cyc

ruslelena [56]

Answer:

s = 21.33*π in

Step-by-step explanation:

Given:

- The complete data is given in the figure (attached):

Solution:

- The bugs lands on the end of the wiper blade furthest to the pivot. The arc length (s) swept by a wiper in one cycle i.e θ = 120° would be given by:

s = 2*r*θ

- Where, r: The distance between the bug and the pivot = 16 in

θ : Angle swept in radians

- The distance travelled by the bug is s:

s = 2*(16)*( 120 / 180 ) * π

s = 21.33*π in

3 0

1 year ago

Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices (0,0,0),(5,0,0),(0,9,0),(0,0,4).

Elan Coil [88]

Answer: $\int\limits^a_E {\int\limits^a_E {\int\limits^a_E {xy} } \, dV$ = 1087.5

Step-by-step explanation: To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedon is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.

An equation of a plane is found with a point and a normal vector. Normal vector is a perpendicular vector on the plane.

Given the points, determine the vectors:

P = (5,0,0); Q = (0,9,0); R = (0,0,4)

vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)

vector QR = (0,9,0) - (0,0,4) = (0,9,-4)

Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:

n = PQ × QR = $\left[\begin{array}{ccc}i&j&k\\5&-9&0\\0&9&-4\end{array}\right]$ $\left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right]$

n = 36i + 0j + 45k - (0k + 0i - 20j)

n = 36i + 20j + 45k

Equation of a plane is generally given by:

$a(x-x_{0}) + b(y-y_{0}) + c(z-z_{0}) = 0$

Then, replacing with point P and normal vector n:

$36(x-5) + 20(y-0) + 45(z-0) = 0$

The equation is: 36x + 20y + 45z - 180 = 0

Second, in evaluating the triple integral, set limits:

In terms of z:

$z = \frac{180-36x-20y}{45}$

When z = 0:

$y = 9 + \frac{-9x}{5}$

When z=0 and y=0:

x = 5

Then, triple integral is:

$\int\limits^5_0 {\int\limits {\int\ {xy} \, dz } \, dy } \, dx$

Calculating:

$\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx$

$\int\limits^5_0 {\int\limits {\int\ {xy(\frac{180-36x-20y}{45} - 0 )} \, dy } \, dx$

$\frac{1}{45} \int\limits^5_0 {\int\ {180xy-36x^{2}y-20xy^{2}} \, dy } \, dx$

$\frac{1}{45} \int\limits^5_0 {90xy^{2}-18x^{2}y^{2}-\frac{20}{3} xy^{3} } \, dx$

$\frac{1}{45} \int\limits^5_0 {2430x-1458x^{2}+\frac{94770}{125} x^{3}-\frac{23490}{375}x^{4} } \, dx$

$\frac{1}{45} [30375-60750+118462.5-39150]$

$\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx$ = 1087.5

The volume of the tetrahedon is 1087.5 cubic units.

3 0

1 year ago

Alana and two of her friends evenly split the cost of a meal. They determine that each person owes $14.68. How much was the enti

AlekseyPX

Answer:

44.04 bucks

Step-by-step explanation:

14.68 times 3 because 1 plus 2 is 3 friends. And 14.68 is how much they EACH paid.

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1 year ago

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Which equation is the inverse of y = 2x2 – 8?

natita [175]

The inverse of the function is $y=\pm \sqrt{\frac{x+8}{2}}$

Explanation:

To find the inverse of the equation $y=2x^{2} -8$ , we need to interchange the variables x and y for the variables y and x.

Thus, the equation becomes

$x=2y^{2} -8$

Now, we shall find the value of y.

Now, adding 8 to both sides of the equation, we have,

$x+8=2y^{2}$

Interchanging the sides,

$2y^{2} =x+8$

Dividing by 2 on both sides,

$y^{2} =\frac{x+8}{2}$

Taking square root on both sides,

$y=\pm \sqrt{\frac{x+8}{2}}$

Thus, the inverse of the function is $y=\pm \sqrt{\frac{x+8}{2}}$

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2 years ago