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2 years ago

6

An oil-well contractor drills a shaft 7 meters deeper into the ground every 2 hours. Which graph has a slope that best represent

s this rate?

2 answers:

pentagon [3]2 years ago

8 0

Answer:

Graph G

Step-by-step explanation:

The graphs are attached

Given that the oil-well contractor drills a shaft 7 meters deeper into the ground every 2 hours, hence the rate at which the shaft drills = 7 meter / 2 hours = 3.5 meters per hour

Since the drill goes into the ground, hence the rate is negative that is -3.5 meters per secong

The slope (rate of change) of a line (m) is given by:

$m=\frac{y_2-y_1}{x_2-x_1}$

a) For graph F, the line passes through the point (0,0) and (10, -20). Hence:

$Slope\ of\ line\ F=\frac{-20-0}{10-0} =-2\ meters\ per\ second$

b) For graph G, the line passes through the point (0,0) and (10, -70). Hence:

$Slope\ of\ line\ G=\frac{-70-0}{10-0} =-7\ meters\ per\ second$

c) For graph H, the line passes through the point (0,0) and (10, -35). Hence:

$Slope\ of\ line\ H=\frac{-35-0}{10-0} =-3.5\ meters\ per\ second$

d) For graph J, the line passes through the point (0,-3.5) and (10, -3.5). Hence:

$Slope\ of\ line\ j=\frac{-3.5-(-3.5)}{10-0} =0\ meters\ per\ second$

umka2103 [35]2 years ago

6 0

Answer:The answer is H , It is the graph where -10 is right below the 0 on the y.

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Brad is hoping to package exactly 48 baseballs together. He sees the side of a box in his storeroom that is 2 x 3. What is he ho

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The given dimensions of the base of the box are 2 x 3 units.

Let h be the height of the box.

So, the volume of the box = 2 x 3 x h ...(i)

The shape of baseball is spherical and one baseball fits in a cubical box having the minimum dimensions equal to the diameter of the spherical ball.

Assuming the diameter of the baseball is d units.

So, the volume occupied by one baseball= volume of the cubical box having the side $d$ units.

$=d^3$ cubic units

So, the volume required to pack 48 baseballs

$= 48 d^3 \cdots(ii)$

Assuming that all the baseballs fit in the box, i.e peripheral balls in every horizontal and vertical layer touched the box as shown in the figure.

So, the length, 3 units and the width, 2 units, must be the integral multiple of the diameter, $d$ units, of the baseball. i.e

The length, $3 = ad\cdots(iii)$

The width, $2=bd\cdots(iv)$

The height, $h=cd\cdots(iv)$

where $a,b$ and $c$ belong to the natural number.

This required volume must be equals to the volume of the box.

From equations (i) and (ii),

$2\times 3\times h=48d^3$

[from (iii) and (iv)]

$\Rightarrow abhd^2=48d^3$

$\Rightarrow h=\frac{48d^3}{6abd^2}$

$\Rightarrow h=\frac{48}{ab}d$

On comparing with the equation (iv)

$c=\frac{48}{ab}\cdots(v)$

Now, if the diameter of the baseball is unity,i.e, d=1 unit

( integer) and (integer) [from (iii) and (iv)]

(also an integer) [from (v)]

Now, the height of the box,

$h=8 \times 1= 8$ unit.

Hence, the other dimension of the box, is 8 units corrosponding to the unity diameter of the baseball.

Note the height of the box depends on the diameter of the baseball, so it will have infinite possible value for different value of the diameter.

For example, the value of height for d=1 unit has been shown.

and another example may be if units, then (integer) and (integer)

(also an integer) [from (v)]

Now, the height of the box,

$h=2 \times 0.5= 1$ unit. [from (iv)]

Here, the height of the box is 2 units corrosponding to 0.5 unit diameter of the baseball.

The possivle values of d can be taken for which $a,b$ and $c$ must be integers.

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2 years ago

A group of campers is going to occupy 3 campsites at a campground. There are 17 campsites from which to choose. In how many ways

Alexeev081 [22]

Answer:

Campsites be chosen in 680 ways.

Step-by-step explanation:

Given:

Number of campsites= 17

Number of campsites that are to be occupied=3

To Find:

Number of ways can the campsites be chosen=?

Solution:

Combination:

In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter. Suppose we have a set of three numbers P, Q and R. Then in how many ways we can select two numbers from each set, is defined by combination.

nCr = n(n - 1)(n - 2) ... (n - r + 1)/r! = n! / r!(n - r)!

No of ways in which campsites can be chosen= $\frac{17!}{3!(17-3)!}$ 17C3

=> $\frac{17!}{3!(14!)}$

=> $\frac{15\times16\times17}{3\times 2\times 1}$

=> $\frac{4080}{6}$

=>680

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So the volume is

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2 years ago

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Sati [7]

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2 years ago

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