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2 years ago

Addison walked 6 miles in 4 hours what was her walking rate in hours per mile

Mathematics

1 answer:

Marizza181 [45]2 years ago

8 0

Answer: 0.66 hours per mile

Step-by-step explanation:

You know that in 4 hours Addison walked 6 miles.

Now, you need to calculate the amount of hours she walked in 1 mile.

Let be "x" the amount of hours she walked in 1 mile.

Then, to calculate the value of "x" you need to multiply 1 mile by 4 hours and divide by 6 miles:

$x=\frac{(1mile)(4hours)}{6miles}\\\\x=\frac{2}{3}\ hours$

$x$ ≈ $0.66\ hours$

Therefore, her walking rate in hours per mile was:

0.66 hours per mile

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The staff at a company went from 40 to 29 employees. what is the percent decrease in staff

topjm [15]

Number of employees outside of company=40-29=11

we can calculate the percent decrease in staff by the rule of 3

40 employees-----------------100%
11 employees---------------- x

x=(11 employees*100%) / 40 employees=27.5%

The percent decrease in staff was: 27.5%

5 0

2 years ago

(a) Find a vector-parametric equation r⃗ 1(t)=⟨x(t),y(t),z(t)⟩r→1(t)=⟨x(t),y(t),z(t)⟩ for the shadow of the circular cylinder x2

motikmotik

Answer: (a) r1(t) = <2cost , 0 , 2sint>

(b) <2cost , (1 - 12sint - 10cost)/8 , 2sint>

Step-by-step explanation:

x2+z2=4

Now, in the xz plane, we know that y = 0...

So, x^2 + z^2 = 4 will simply be a circle centered at (0,0)..

This can be easily parameterized as

x = 2cos(t)

z = 2sin(t)

So, the required parameterization is :

r1(t) = <2cost , 0 , 2sint>

Cylinder : x^2 + z^2 = 4

Plane : 5x+8y+6z=1

Easily enough, the x^2 + z^2 = 4 can again be parameterized as

x = 2cost , z = 2sint

With this, we can find y using plane equation...

5x+8y+6z=1

5(2cost) + 8y + 6(2sint) = 1

8y = 1 - 12sint - 10cost

y = (1 - 12sint - 10cost)/8

So, the parameterization is :

<2cost , (1 - 12sint - 10cost)/8 , 2sint>

6 0

2 years ago

A hackberry tree has roots that reach a depth of

Degger [83]

Answer:

24.6967 meters

Step-by-step explanation:

The roots of the tree go 6 and 5 over 12 meters below the ground level.

Now, 6 and 5 over 12 meters is equivalent to 6.4167 meters.

Again the top of the tree is 18.28 meters high from the ground level.

Therefore, the total height of the tree from the bottom of the root to the top is

(6.4167 +18.28) = 24.6967 meters (Answer)

5 0

2 years ago

What is the domain of validity for csctheta =start fraction 1 over sine theta end fraction? (1 point) all real numbers all real

dem82 [27]

We know the following relationship:

$csc(\theta)=\frac{1}{sin(\theta)}$

The domain of a function are the inputs of the function, that is, a function $f$ is a relation that assigns to each element $x$ in the set A exactly one element in the set B. The set A is the domain (or set of inputs) of the function and the set B contains the range (or set of outputs).Then applying this concept to our function $csc(\theta)$ we can write its domain as follows:

1. Domain of validity for $csc(\theta)$ :

$D: \{\theta \in R/ sin(\theta) \neq 0 \} \\ In words: All \ \theta \ that \ are \ real \ values \ except \ those \ that \ makes \ sin(\theta)=0$

When:

$sin(\theta)=0$ ?

when:

$\theta=..., -2\pi,-\pi,0,\pi,\2pi,3pi,...,k\pi$

where k is an integer either positive or negative. That is:

$sin(k\theta)=0 \ for \ k=...,-2,-1,0,1,2,3,...$

To match this with the choices above, the answer is:

"All real numbers except multiples of $\pi$ "


2. which identity is not used in the proof of the identity $1+cot^{2}(\theta)=csc^{2}(\theta)$ :

This identity can proved as follows:

$sin^2{\theta}+cos^{2}(\theta)=1 \ Dividing \ by \ sin^{2}(\theta) \\ \\ \therefore \frac{sin^2{\theta}}{sin^{2}(\theta)}+\frac{cos^{2}(\theta)}{sin^{2}(\theta)}=\frac{1}{sin^{2}(\theta)} \\ \\ \therefore 1+cot^{2}(\theta)=csc^{2}(\theta)$

The identity that is not used is as established in the statement above:

"1 +cos squared theta over sin squared theta= csc2theta"

Written in mathematical language as follows:

 $\frac{1+cos^{2}(\theta)}{sin^{2}(\theta)}=csc^{2}(\theta)$

4 0

2 years ago

Read 2 more answers

Given that $A = (\sqrt{2008}+\sqrt{2009}),$ $B = (-\sqrt{2008}-\sqrt{2009}),$ $C = (\sqrt{2008}-\sqrt{2009}),$ and $D = (\sqrt{2

kipiarov [429]

Answer:

ABCD = 0.803

Step-by-step explanation:

$A = \sqrt{2008}+\sqrt{2009} \\A = 44.81 + 44.82\\A = 89.63$