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2 years ago

Find the slope of the line that passes through the points (-6, 2) and (-10, 2).

Mathematics

1 answer:

Alex Ar [27]2 years ago

4 0

Answer:

m = 0

Step-by-step explanation:

$m=\frac{rise}{run}=\frac{2-2}{-10-6}=\frac{0}{-16} =0$

Hope this helps.

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. A right cylindrical drum is to hold 7.35 cubic feet of liquid. Find the dimensions (radius of the base and height) of the drum

Drupady [299]

Answer:

$r=1.05\ \text{ft}$

$h=2.12\ \text{ft}$

$20.91\ \text{ft}^3$

Step-by-step explanation:

r = Radius

h = Height

Volume of cylinder = $7.35\ \text{ft}^3$

$V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{7.35}{\pi r^2}$

Surface area is given by

$A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi r^2+2\pi r\dfrac{7.35}{\pi r^2}\\\Rightarrow A=2\pi r^2+\dfrac{14.7}{r}$

Differentiating with respect to radius we get

$\dfrac{dA}{dr}=4\pi r-\dfrac{14.7}{r^2}$

Equating with zero we get

$0=4\pi r-\dfrac{14.7}{r^2}\\\Rightarrow 4\pi r=\dfrac{14.7}{r^2}\\\Rightarrow r^3=\dfrac{14.7}{4\pi}\\\Rightarrow r=(\dfrac{14.7}{4\pi})^{\dfrac{1}{3}}\\\Rightarrow r=1.05$

$\dfrac{d^2A}{dr^2}=4\pi-2\times \dfrac{14.7}{r^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=4\pi+2\times \dfrac{14.7}{1.05^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=37.96>0$

So, the value of the function is minimum at $r=1.05$

$h=\dfrac{7.35}{\pi r^2}=\dfrac{7.35}{\pi 1.05^2}\\\Rightarrow h=2.12$

So, the radius and height which would minimize the surface area is 1.05 feet and 2.12 feet respectively.

Surface area

$A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi \times 1.05^2+2\pi 1.05\times 2.12\\\Rightarrow A=20.91\ \text{ft}^3$

The minimum surface area is $20.91\ \text{ft}^3$ .

8 0

3 years ago

Kimiya has four times as many marbles as Ramneet. If kimiya gave 18 to Ramneet they would have the same number. How many marbles

RSB [31]

Answer:

Kimiya has 48 marbles, Ramneet has 12 marbles

Step-by-step explanation:

kimiya has 4x marbles ramneet has x marbles then 4x - 18 = x + 18 because if you give 18 marbles from kimiya to ramneet then you subtract 18 from kimiya and add 18 to ramneet by solving the equation you will get x as 12.So kimiya has 48 marbles, ramneet has 12 marbles.

<h2 /><h2>Hope it helps.</h2><h3>Thank you.</h3>

7 0

2 years ago

Which of the following scenarios demonstrates sampling bias? (A) To estimate the ethnic background distribution of residents of

ankoles [38]

Answer:

Option C.

Step-by-step explanation:

Sampling bias is a problem during the initial data gathering step of a survey.

When the first step is wrong, then the survey cannot produce non biased results.

The problem occurs when the design of the study is wrong the data collection procedure is wrong.

So, here answer seems C, because the starting point is not selected at random in this survey.

(C) Jean wants to estimate the mean amount of money spent on clothes per week by mall shoppers. She collects data from every 10th person entering a clothing store at the mall.

6 0

3 years ago

Logs are stacked in a pile. The top row has 15 logs and the bottom row has 24 logs. How many logs are there in the stack?

ziro4ka [17]

There are two ways you can do this. You can use the longer way:
15+16+17+18+19+20+21+22+23+24 = 195 (starting from the top row, which has 15 logs, up until the bottom row, which has 24 logs, on condition that each second row has one log more than the previous one)

You can also use the formula (where n is the number of rows)
x= (n(first term+last term))/2
x= (10(15+24))/2
x= (10*39)/2
x=390/2
x=195

Either way, there are 195 logs in the stack.

8 0

2 years ago

Read 2 more answers

If m<1=4x+2and m<2=110 what is x

Rina8888 [55]

Answer:

4x2+110=180

4x=68

x=17

4 0

3 years ago