Ask question

Ask question

All categories

MA_775_DIABLO [31]

2 years ago

13

The Xianren Bridge is located in Guangxi Province, China. This arch is the world’s longest natural arch, with a length of 400 fe

et. Write and graph an inequality that represents the lengths l (in inches) of all other natural arches.

2 answers:

KengaRu [80]2 years ago

7 0

Length of Xianren Bridge is 400 feet.

l represents the length of other natural arches.

Since, Xianren Bridge is the longest arch, we have,

l < 400

Let's graph this inequality.

Take the other natural arches along x-axis and the lengths along y-axis.

Clearly, the graph of l = 400 is a straight line parallel to x-axis.

So, l < 400 is the region below the line l = 400.

Drupady [299]2 years ago

6 0

Answer: $400>l\ \text{or}\ l$

Step-by-step explanation:

Given : The Xianren Bridge is located in Guangxi Province, China.

This arch is the world’s longest natural arch, with a length of 400 feet.

if the length of all other natural arches ( in inches) is represented by 'l'.

Then, the required inequality will be :-

$400>l\ \text{or}\ l$

Hence, the inequality that represents the lengths l (in inches) of all other natural arches : $400>l\ \text{or}\ l$

The graph for this inequality is given below:

For strictly less than or more than we use circle to exclude that value from the interval.

Also, the length cannot be negative so the line(orange in color) is stopped at 0 .

You might be interested in

The population p of a small community on the outskirts of a city grows rapidly over a 20-year period: t05101520p1002004509502000

myrzilka [38]

Answer:

The population of the small community, 5 years into the future, after the initial 20-year period = 4268.

Step-by-step explanation:

t | 0 | 5 | 10 | 15 | 20

p | 100 | 200 | 450 | 950 | 2000

The exponential function will look like

p = aeᵏᵗ

where a and k are constants.

Take the natural logarithms of both sides

In p = In aeᵏᵗ

In p = In a + In eᵏᵗ

In p = In a + kt

In p = kt + In a.

We then use linear regression to fit the data of In p against t to obtain k and In a.

t | 0 | 5 | 10 | 15 | 20

p | 100 | 200 | 450 | 950 | 2000

In p | 4.605 | 5.298 | 6.109 | 6.856 | 7.601

In p = kt + In a.

y = mx + b

m = k and b = In a

Performing a linear regression analysis on the now-linear relationship between In p and t and also plotting a graph of the variables.

The regression equation obtained is

y = 0.151x + 4.584

The first attached image shows the equations necessary for the estimation of the linear regression parameters.

The second attached image shows the use of regression calculator and the plot of the function In p versus t.

Comparing

y = 0.151x + 4.584

With

In p = kt + In a.

y = In p

k = 0.151

x = t

In a = 4.584

a = 97.905

The exponential function relating p and t,

p = aeᵏᵗ now becomes

p = 97.905 e⁰•¹⁵¹ᵗ

So, to predict the population 5 years into the future, that is 5 years after the 20 year period.

we need p at t=25 years.

0.151 × 25 = 3.775

p(t=25) = 97.905 e³•⁷⁷⁵ = 4268.41 = 4268.

Hope this Helps!!!

7 0

2 years ago

Question 5 (3 points) The soccer team is planning to sell health bars for a fundraiser. The prices of purchasing health bars fro

Ierofanga [76]

The correct answer is 40 bars.

In order to find this amount we have to find when the y values are worth the same. Since both equations are equal to y, we can set them equal to each other to find a time when the y values are the same.

Company A = Company B
.75x = 10 + .50x ---> Now subtract .50x from both sides.
.25x = 10 ---> Now divide both sides by .25
x = 40

When x = 40 it will cost $30 from both companies.

3 0

2 years ago

Read 2 more answers

Three people guess the number of cherries in a bag rounded to the nearest 10 Alex guesses 80 cherries Jess guesses 60 cherries a

Marrrta [24]

Jess guessed correctly because the number of cherries in a bag is 63. 7x9=63 and 6+3= 9. 63 rounded to the nearest 10 is 60.

6 0

2 years ago

Find the equation of the plane through the point (2,5,7) that is parallel to the line r=(3i+2j−2k)+t(i+2j+9k) and perpendicular

insens350 [35]

The plane we want to find has general equation

$a(x-2)+b(y-5)+c(z-7)=0$

with $a,b,c$ not equal to 0, and has normal vector

$\vec n=a\,\vec\imath+b\,\vec\jmath+c\,\vec k$

$\vec n$ is perpendicular to both the normal vector of the other plane, which is $4\,\vec\imath+5\,\vec\jmath+6\,\vec k$ , as well as the tangent vector to the line $\vec r(t)$ , which is $\vec\imath+2\,\vec\jmath+9\,\vec k$ .

This means the dot product of $\vec n$ with either vector is 0, giving us

$\begin{cases}4a+5b+6c=0\\a+2b+9c=0\end{cases}$

Suppose we fix $c=1$ . Then the system reduces to

$\begin{cases}4a+5b=-6\\a+2b=-9\end{cases}$

and we get

$(4a+5b)-4(a+2b)=-6-4(-9)\implies-3b=30\implies b=-10$

$a+2(-10)=-9\implies a=11$

Then one equation for the plane could be

$\boxed{11(x-2)-10(y-5)+(z-7)=0}$

or in standard form,

$\boxed{11x-10y+z=-21}$

The solution is unique up to non-zero scalar multiplication, which is to say that any equation $(11x-10y+z)k=-21k$ would be a valid answer. For example, suppose we instead let $c=2$ ; then we would have found $a=22$ and $b=-20$ , but clearly dividing both sides of the equation

$22(x-2)-20(y-5)+2(z-7)=0$

by 2 gives the same equation as before.

7 0

2 years ago

Chris invested some money at a rate of 5% per year compound interest.

max2010maxim [7]

Step-by-step explanation:

the answer is in the picture ☝️

6 0

2 years ago