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Paraphin [41]
3 years ago
12

For a rectangular prism, if the base length was shrunk by a factor of two-thirds, the width was quadrupled, and height was cut i

n half, how would the changes affect the surface area formula? The attachment has the problem and the answer choices. Thanks.

Mathematics
1 answer:
Luden [163]3 years ago
5 0
Surface area = 2(wl + hl + hw) = 2wl + 2hl + 2hw

Conditions:
base length is shrunk by a factor of 2/3
width is quadrupled
height is cut in half.

l ⇒ 2l/3 w ⇒ 4w ; h ⇒ h/2

SA = <span>2wl + 2hl + 2hw
</span>SA = 2(4w)(2l/3) + 2(h/2)(2l/3) + 2(h/2)(4w)
SA = (16wl/3) + 4hl/6 + 8hw/2

Simplify:

SA = 16/3 wl + 2/3 hl + 4hw   Choice C.


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why do we need imaginary numbers?explain how can we expand (a+ib)^5. finally provide the expanded solution of (a+ib)^5.(write a
zheka24 [161]

Answer:

a. We need imaginary numbers to be able to solve equations which have the square-root of a negative number as part of the solution.

b. (a + ib)⁵ = a⁵ + 5ia⁴b - 10a³b² - 10ia²b³ + 5ab⁴ + ib⁵

Step-by-step explanation:

a. Why do we need imaginary numbers?

We need imaginary numbers to be able to solve equations which have the square-root of a negative number as part of the solution. For example, the equation of the form x² + 2x + 1 = 0 has the solution (x - 1)(x + 1) = 0 , x = 1 twice. The equation x² + 1 = 0 has the solution x² = -1 ⇒ x = √-1. Since we cannot find the square-root of a negative number, the identity i = √-1 was developed to be the solution to the problem of solving quadratic equations which have the square-root of a negative number.

b. Expand (a + ib)⁵

(a + ib)⁵ =  (a + ib)(a + ib)⁴ = (a + ib)(a + ib)²(a + ib)²

(a + ib)² = (a + ib)(a + ib) = a² + 2iab + (ib)² = a² + 2iab - b²

(a + ib)²(a + ib)² = (a² + 2iab - b²)(a² + 2iab - b²)

= a⁴ + 2ia³b - a²b² + 2ia³b + (2iab)² - 2iab³ - a²b² - 2iab³ + b⁴

= a⁴ + 2ia³b - a²b² + 2ia³b - 4a²b² - 2iab³ - a²b² - 2iab³ + b⁴

collecting like terms, we have

= a⁴ + 2ia³b + 2ia³b - a²b² - 4a²b² - a²b² - 2iab³  - 2iab³ + b⁴

= a⁴ + 4ia³b - 6a²b² - 4iab³ + b⁴

(a + ib)(a + ib)⁴ = (a + ib)(a⁴ + 4ia³b - 6a²b² - 4iab³ + b⁴)

= a⁵ + 4ia⁴b - 6a³b² - 4ia²b³ + ab⁴ + ia⁴b + 4i²a³b² - 6ia²b³ - 4i²ab⁴ + ib⁵

= a⁵ + 4ia⁴b - 6a³b² - 4ia²b³ + ab⁴ + ia⁴b - 4a³b² - 6ia²b³ + 4ab⁴ + ib⁵

collecting like terms, we have

= a⁵ + 4ia⁴b + ia⁴b - 6a³b² - 4a³b² - 4ia²b³ - 6ia²b³ + ab⁴ + 4ab⁴ + ib⁵

= a⁵ + 5ia⁴b - 10a³b² - 10ia²b³ + 5ab⁴ + ib⁵

So, (a + ib)⁵ = a⁵ + 5ia⁴b - 10a³b² - 10ia²b³ + 5ab⁴ + ib⁵

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3 years ago
87.99 minusss 52.46 HELPPPPPPPPPPPP
torisob [31]
35.53 is the answer I hoped that helped
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mackenzie made 33 out of 50 throws. what is the experimental probability that mackenzie will not make the next free throw she at
siniylev [52]

answer:

1.94117647058

Step-by-step explanation:

33/50 her free throw % is 66% at the moment based on how many she missed you'd do 33 / by 17 you get 1.94117647058

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Answer:

12 months because $50 for 12 months is $600

Step-by-step explanation:

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2 years ago
Given the function f(x) = 2x, find the value of f−1(32).
Oliga [24]

Answer:

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Step-by-step explanation:

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