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2 years ago

How are the values of -4^3 and 4^-3 alike and how do they differ?

Mathematics

1 answer:

BartSMP [9]2 years ago

4 0

Answer:

(-4)³ = -64

(4)⁻³ = 1/64

Step-by-step explanation:

$( - 4) {}^{3} = ( - 4) \times ( - 4) \times ( - 4) = - 64 \\$

${4}^{ - 3} = (\frac{1}{4} ) {}^{3} \\$

$({ \frac{1}{4} )}^{3} = \frac{1}{4} \times \frac{1}{4} \times \frac{1}{4} = \frac{1}{64} \\$

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The difference of two perfect cubes is 386. If the cube root of the smaller of the two numbers is 7, then the cube root of the l

choli [55]

Answer:

Step-by-step explanation:

Let the two perfect cubes be x and y where x > y.

According to the given conditions:

${x}^{3} - {y}^{3} = 386...(1) \\ y = 7...(2) \\ plug \: y = 7 \: in \: equation \: (1) \\ {x}^{3} - {7}^{3} = 386 \\ {x}^{3} - 343 = 386 \\ {x}^{3} = 343 + 386 \\ {x}^{3} = 343 + 386 \\ {x}^{3} = 729 \\ x = \sqrt[3]{729} \\ x = 9$

Thus the cube root of the larger number is 9.

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3 years ago

A local high school held a two-day fundraiser selling lunches. The equations shown represent the amount of money the school coll

Over [174]

Answer:

Step-by-step explanation:

The two equations appear to be ...

12x +4y = 152
32x +12y = 420

These can be solved for y using Cramer's rule:

y = (152(32) -420(12))/(4(32) -12(12)) = -176/-16 = 11

The cost of the vegetarian lunch is 11.

_____

<em>Comment on Cramer's Rule</em>

For equations ...

ax +by =c

dx +ey = f

The solutions are ...

x = (bf -ey)/(bd -ea)

y = (cd -fa)/(bd -ea) . . . . note the denominators are the same expression

Once you memorize the pattern of products, this can be the simplest way to solve a pair of equations--especially if you only need one of the variable values.

6 0

3 years ago

The volume of a cube is 27 cubic inches. What is the length of one edge of the cube?

hjlf

The volume for any cube is length x width x height,
so in this case because all side of cube is the same, let it be y.
y x y x y = 27
y = 3
so each side will be 3 inches

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3 years ago

Let the function f be defined by f(x)=12-5x b)evaluate f(-1)

Alexxx [7]

F(-1) = 12 - 5(-1)
f(-1) = 12 + 5
Solution: f(-1) = 17

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2 years ago

Read 2 more answers

A crate that is 10 inches long, 8 inches wide, and 3 inches high is shown above. The floor and the four walls are all one inch t

miskamm [114]

Answer:

Step-by-step explanation:

The exterior of the crate is 10 inches long, meaning that the inside measurement is 8 inches. Next, the 8 inch width corresponds to 6 inches inside. Finally, the 3 inch height corresponds to 1 inch interior height.

Thus the inside floor of the box is 8 by 6 inches, or 48 square inches.

Since the inside height is only 1 inch, this means that 48 one-inch cubical blocks will fit inside the crate.

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3 years ago