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3 years ago

Maria has a cube-shaped box that measures 9 inches along each edge. Can she fit 1,000 square-inch cubes inside the box? Explain.

Mathematics

1 answer:

kumpel [21]3 years ago

7 0

Answer:

No, she cannot fit it into the box

Step-by-step explanation:

The way to know is this is simply find the total surface area of the cube. This helps to know the capacity of the cube.

From the question, the side length of the cube is 9 inches;

Mathematically, the area of a cube is 6l^2

Thus, the total surface area of the cube = 6 * 9 * 9 = 486 square inches

Seeing that what she is trying to fix is less than the total surface area, then we can say that she cannot fix 1,000 square-inch cubes inside the box

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A car travels 55 miles per hour for two hours. Complete the table.

iogann1982 [59]

Answer:

1/2 hr 27.5

1 1/2 hr 82.5

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Step-by-step explanation:

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3 years ago

A moving truck company charges a flat fee of $75 to rent the truck, plus $15 per day. 1:What is the total cost (flat fee and dai

Paraphin [41]

Answer:

Step-by-step explanation:

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3 years ago

Read 2 more answers

(sqrt3-sqrt3i)^4

Ludmilka [50]

The increasing order of the complex numbers is (√2 - i)⁶ < (√2 - √2i)⁸ = (√3 - i)⁶ = (-1 + √3i)¹² < (√3 - √3i)⁴.

<h3>Absolute values of the complex numbers</h3>

The absolute values of the complex numbers are determined as follows;

(sqrt3-sqrt3i)^4 = (√3 - √3i)⁴

$|z| = \sqrt{(\sqrt{3} )^2 + (\sqrt{3 }\times1 )^2} } \\\\|z| = \sqrt{6}$

(-1+sqrt3i)^12 = (-1 + √3i)¹²

$|z| = \sqrt{(-1)^2 + (\sqrt{3)^2} } \\\\|z| = \sqrt{4} \\\\|z| = 2$

(sqrt 3-i)^6 = (√3 - i)⁶

$|z| = \sqrt{(\sqrt{3})^2 + (-1)^2 } \\\\|z| = \sqrt{4} \\\\|z| = 2$

(sqrt2-sqrt2i)^8 = (√2 - √2i)⁸

$|z| = \sqrt{(\sqrt{2} )^2 + (\sqrt{2})^2 } \\\\|z| = 2$

(sqrt2-i)^6 = (√2 - i)⁶

$|z| = \sqrt{(\sqrt{2})^2 + (-1)^2} } \\\\|z| = \sqrt{3}$

Increasing order of the complex numbers;

(√2 - i)⁶ < (√2 - √2i)⁸ = (√3 - i)⁶ = (-1 + √3i)¹² < (√3 - √3i)⁴.

Learn more about complex numbers here: brainly.com/question/10662770

#SPJ1

3 0

3 years ago

PLEASEEEEEEE HELP I NEED SERIOUS HELP AT THIS

Sergeu [11.5K]

Answer:

Ok, so I think I may have got it right.

Step-by-step explanation:

So in each row going left to right is the following numbers

1st row: 2, 3, 4, 5

2nd row: 3, 4, 5, 6

3rd row: 4, 5, 6, 7

4th row: 5, 6, 7, 8

b) 1/16

c) 6/16

I'm not exactly sure if I got everything right, but I hope this helps :)

5 0

4 years ago

The tangent of the graph of y=<img src="https://tex.z-dn.net/?f=e%5E%7Bax%7D" id="TexFormula1" title="e^{ax}" alt="e^{ax}" align

bearhunter [10]

a) The tangent to $y=e^{ax}$ at $x=p$ has slope

$y' = ae^{ax} \implies y'(p) = ae^{ap}$

and $y=e^{ap}$ at this point. It passes through the origin, so its equation is

$y - 0 = ae^{ap} (x - 0) \implies y = ae^{ap} x$

It also passes through the point $(p,e^{ap})$ on the curve, so

$y - e^{ap} = ae^{ap} (x - p) \implies y = e^{ap} + ae^{ap} x - ape^{ap}$

By substitution,

$ae^{ap} x = e^{ap} + ae^{ap} x - ape^{ap} \implies e^{ap} = ape^{ap} \implies ap=1 \\\\ \implies \boxed{p=\dfrac1a}$

b) The normal to $y=e^{ax}$ at $x=2p$ has slope

$-\dfrac1{y'(2p)} = -\dfrac1{ae^{2ap}} = -1 \implies ae^{2ap} = 1$

It follows that

$ae^{2ap} = ae^2 = 1 \implies \boxed{a = \dfrac1{e^2} \text{ and } p = e^2}$

c) The tangent line equation is then

$y = \dfrac1{e^2} e^1 x \implies \boxed{y = \dfrac xe}$

7 0

2 years ago