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3 years ago

Solve x3 = 160. help

Mathematics

1 answer:

Bad White [126]3 years ago

5 0

Answer: 5.43

Step-by-step explanation:

Given :

$x^{3} = 160$

To find x , we will find the cube root of both sides , that is

$x = \sqrt[3]{160}$

$x = 5.428835233$

$x$ ≈ 5.43

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Latanya leaves her house at 12:30 p.M. And bikes at 12 mi/h to Marta's house. She stays at Marta's house for 90 minute. Both gir

Llana [10]

Answer:

Marta's house is 3.10 miles from Latanya's house

Step-by-step explanation:

* Lets explain how to solve the problem

- Latanya leaves her house at 12:30 p.M.

- She bikes at 12 mi/hr to Marta's house

- She stays at Marta's house for 90 minute

- Both girls walk back to latanya's house at 2.5 mi/h

- They arrive at latanya's house at 3:30 p.M.

- We need to know how far is Marta's house from latanya's house

∵ Latanya starts her trip at 12:30 p.M.

∵ She returns her home at 3:30 p.M.

∴ The time of her trip is → 3:30 - 12:30 = 3 hours

- But she stays at at Marta's house for 90 minutes

∵ 1 hour = 60 minutes

∴ 90 minutes = 90 ÷ 60 = 1.5 hours

∴ The time from her house to Marta's house and from Marta's house

to her house is → 3 - 1.5 = 1.5 hours

- Assume that the distance from her house to Marta's house is d

and the time from her house to Marta's house is $t_{1}$ ,

the time from Marta's house to her house is $t_{2}$

∵ Latanya bikes at 12 mi/h to Marta's house

∵ Distance = speed × time

∴ d = 12 × $t_{1}$

∵ Both girls walk back to latanya's house at 2.5 mi/h

∴ d = 2.5 × $t_{2}$

- Equate the two expressions of d

∴ 12 $t_{1}$ = 2.5 $t_{2}$ ⇒ (1)

∵ $t_{1}$ + $t_{2}$ = 1.5

- Subtract $t_{1}$ from both sides

∴ $t_{2}$ = 1.5 - $t_{1}$ ⇒ (2)

- Substitute equation (2) in equation (1)

∴ 12 $t_{1}$ = 2.5(1.5 - $t_{1}$ )

∴ 12 $t_{1}$ = 3.75 - 2.5 $t_{1}$

- Add 2.5 $t_{1}$ to both sides

∴ 14.5 $t_{1}$ = 3.75

- Divide both sides by 14.5

∴ $t_{1}$ = $\frac{15}{58}$ hour

∴ She spends 15/58 hour to bike to Marta's house

- Lets find d

∵ d = 12 $t_{1}$

∴ d = $12*\frac{15}{58}=3.10$ miles

* <em>Marta's house is 3.10 miles from Latanya's house</em>

6 0

4 years ago

Use mathematical induction to prove the following statement: 8"-1 is a multiple of 7 for all neN

Ket [755]

Answer:

Step-by-step explanation:

To prove that $8^n-1$ is a multiple of 7.

Proof by induction:

Let n =1. Then we have 8-1 =7 is a multiple of 7

Thus the P(1) is true.

Let us assume that P(n) is true.

$8^n-1$ = 7l is true for some integer l

To check for P(n+1)

$8^{n+1} -1$ =LHS

= $8^n(8)-1\\=(7l+1)8-1\\=56l+7\\=7(8l+1)$

Thus we find that this is also a multiple of 7.

If true for n, then true for n+1

Hence we find that since true for 1, we have it is true for all natural numbers.

5 0

3 years ago

Read 2 more answers

A circular region has a population of about 260000 people and a population density of about 135 people per square mine . find th

ValentinkaMS [17]

Answer:

24.76 mine

Step-by-step explanation:

The first thing is to calculate the area of the region, which we can calculate since we have the density and the population. The area would be the quotient between population and density:

260000/135 = 1925.93

The area would be 1925.93 square mine

We know that the area is given by:

A = pi * r ^ 2

we solve to r

r ^ 2 = A / pi

r ^ 2 = 1925.92 / 3.14

r ^ 2 = 613.3

r = 24.76

the radius is equal to 24.76 mine

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3 years ago

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Dmitriy789 [7]

12=3x+12
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4 years ago

How to do -4x+5y+6z?

Gala2k [10]

Answer:

There are no like terms to therefore the answer is -4x+5y+6z

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3 years ago