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2 years ago

What is the following difference?

Mathematics

1 answer:

Svetllana [295]2 years ago

7 0

Answer:

$-7ab\sqrt[3]{3ab^2}$

Step-by-step explanation:

Remove perfect cubes from under the radical and combine like terms.

$2ab\sqrt[3]{192ab^2}-5\sqrt[3]{81a^4b^5}=2ab\sqrt[3]{4^3\cdot 3ab^2}-5\sqrt[3]{(3ab)^3\cdot 3ab^2}\\\\=(8ab -15ab)\sqrt[3]{3ab^2}=\boxed{-7ab\sqrt[3]{3ab^2} }$

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The coordinates of parallelogram PVWZ are P(0, 0), V(-p, q), and W(-p - r, q). Find the coordinates of Z without using any new v

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For the answer to the question above asking to f<span>ind the coordinates of Z without using any new variables.
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Vector WZ equals vector VP, which is (p, -q)
So Z is (-p - r + p, q - q) which is (-r, 0)
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2 years ago

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It takes 32 hours for a motorboat moving downriver to get from pier A to pier B. The return journey takes 48 hours. How long doe

lina2011 [118]

Answer:

Time taken by the un powered raft to cover this distance is T = 192.12 hr

Step-by-step explanation:

Let speed of boat = u $\frac{km}{hr}$

Speed of current = v $\frac{km}{hr}$

Let distance between A & B = 100 km

Time taken in downstream = 32 hours

$32 = \frac{100}{u +v}$

$u + v = \frac{100}{32}$

u + v = 3.125 ------ (1)

Time taken in upstream = 48 hours

$48 = \frac{100}{u -v}$

$u -v = \frac{100}{48}$

u - v = 2.084 ------- (2)

By solving equation (1) & (2)

u = 2.6045 $\frac{km}{hr}$

v = 0.5205 $\frac{km}{hr}$

Now the time taken by the un powered raft to cover this distance

$T = \frac{100}{v}$

Because un powered raft travel with the speed of the current.

$T = \frac{100}{0.5205}$

T = 192.12 hr

Therefore the time taken by the un powered raft to cover this distance is

T = 192.12 hr

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2 years ago

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Hair Color/Height Less than 175 cm 175 to 180 cm Above 180 cm Total

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I think the answers A

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Rewrite each statement using the appropriate mathematical language 1. There exists a number b belonging to the set B 2. Even num

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Answer:

1. b ∈ B 2. ∀ a ∈ N; 2a ∈ Z 3. N ⊂ Z ⊂ Q ⊂ R 4. J ≤ J⁻¹ : J ∈ Z⁻

Step-by-step explanation:

1. Let b be the number and B be the set, so mathematically, it is written as

b ∈ B.

2. Let a be an element of natural number N and 2a be an even number. Since 2a is in the set of integers Z, we write

∀ a ∈ N; 2a ∈ Z

3. Let N represent the set of natural numbers, Z represent the set of integers, Q represent the set of rational numbers, and R represent the set of rational numbers.

Since each set is a subset of the latter set, we write

N ⊂ Z ⊂ Q ⊂ R .

4. Let J be the negative integer which is an element if negative integers. Let the set of negative integers be represented by Z⁻. Since J is less than or equal to its inverse, we write

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2 years ago

jack bought 4 rulers and 5 compasses for $18.92 altogether. If Jacks brother bought 2 rulers and 4 compasses for $14.98, what wa

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Answer:

Price of each compass = $3.68

Price of each ruler = $0.13

Step-by-step explanation:

Let R denote rulers and C denotes compasses

Jack bought 4 rulers and 5 compasses for $18.92

which algebraically translates to

4R + 5C = 18.92 eq. 1

Jack's brother bought 2 rulers and 4 compasses for $14.98

which algebraically translates to

2R + 4C = 14.98 eq. 2

Now we have two equations and two unknowns R and C

Choose any of the above equation and make any of the unknown the subject of the equation.

Choosing eq. 1

4R + 5C = 18.92

4R = 18.92 - 5C

R = (18.92 - 5C)/4 eq. 3

Now put this value of R into eq. 2

2R + 4C = 14.98

2((18.92 - 5C)/4) +4C = 14.98

9.46 - 2.5C + 4C = 14.98

1.5C = 5.52

C = 5.52/1.5

C = 3.68

So the price of each compass is $3.68

We can verify whether our answer is right or not. First we have to find the cost of R

Put this value of C into eq. 3

R = (18.92 - 5C)/4

R = (18.92 - 5*3.68)/4

R = (18.92 - 18.4)/4

R = 0.52/4

R = 0.13

So the price of each ruler is $0.13

Now let us verify:

from eq. 1

4R + 5C = 18.92

4(0.13) + 5(3.68) = 18.92

0.52 + 18.4 = 18.92

18.92 = 18.92 (hence proved)

from eq. 2

2R + 4C = 14.98

2(0.13) + 4(3.68) = 14.98

0.26 + 14.72 = 14.98

14.98 = 14.98 (hence proved)

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2 years ago