Is it possible for two planes to intersect in exactly one point

Three more than twice the sum of a number and half the number equals 105. Which equation models this relationship?

Umnica [9.8K]

Answer:

The correct answer is A or 2(x+1/2x)=105

Step-by-step explanation:

3+2(x+1/2x)=105

3 0

2 years ago

A contractor bought 6.4 ft2 of sheet metal. He has used 2.1 ft2 so far and has $77.40 worth of

son4ous [18]

Answer:

$18

Step-by-step explanation:

Given:

6.4x - 2.1x = 77.4

Where,

x = cost of sheet metal per square foot

How much does sheet metal cost per square foot?

6.4x - 2.1x = 77.4

4.3x = 77.4

Divide both sides by 4.3

x = 77.4 / 4.3

= 18

x = $18

Sheet metal per square foot cost $18

8 0

3 years ago

You deposit $1200 in an account. The account earns $120 simple

iVinArrow [24]

We have to find the unit rate, so we have to divide what you earned in interest by the amount of months.

120/8=15

So you earn $15 per month

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sorry if this doesn't help

7 0

2 years ago

Find the next three terms in the geometric sequence: 400, 200, 100, 50

Elena-2011 [213]

It's dividing by 2.

Next 3 would be: 25, 25/2, 25/4 or converting those into decimals.

7 0

3 years ago

Read 2 more answers

g A manufacturer is making cylindrical cans that hold 300 cm3. The dimensions of the can are not mandated, so to save manufactur

sdas [7]

Answer:

The dimensions that minimize the cost of materials for the cylinders have radii of about 3.628 cm and heights of about 7.256 cm.

Step-by-step explanation:

A cylindrical can holds 300 cubic centimeters, and we want to find the dimensions that minimize the cost for materials: that is, the dimensions that minimize the surface area.

Recall that the volume for a cylinder is given by:

$\displaystyle V = \pi r^2h$

Substitute:

$\displaystyle (300) = \pi r^2 h$

Solve for <em>h: </em>

$\displaystyle \frac{300}{\pi r^2} = h$

Recall that the surface area of a cylinder is given by:

$\displaystyle A = 2\pi r^2 + 2\pi rh$

We want to minimize this equation. To do so, we can find its critical points, since extrema (minima and maxima) occur at critical points.

First, substitute for <em>h</em>.

$\displaystyle \begin{aligned} A &= 2\pi r^2 + 2\pi r\left(\frac{300}{\pi r^2}\right) \\ \\ &=2\pi r^2 + \frac{600}{ r} \end{aligned}$

Find its derivative:

$\displaystyle A' = 4\pi r - \frac{600}{r^2}$

Solve for its zero(s):

$\displaystyle \begin{aligned} (0) &= 4\pi r - \frac{600}{r^2} \\ \\ 4\pi r - \frac{600}{r^2} &= 0 \\ \\ 4\pi r^3 - 600 &= 0 \\ \\ \pi r^3 &= 150 \\ \\ r &= \sqrt[3]{\frac{150}{\pi}} \approx 3.628\text{ cm}\end{aligned}$

Hence, the radius that minimizes the surface area will be about 3.628 centimeters.

Then the height will be:

$\displaystyle \begin{aligned} h&= \frac{300}{\pi\left( \sqrt[3]{\dfrac{150}{\pi}}\right)^2} \\ \\ &= \frac{60}{\pi \sqrt[3]{\dfrac{180}{\pi^2}}}\approx 7.25 6\text{ cm} \end{aligned}$

In conclusion, the dimensions that minimize the cost of materials for the cylinders have radii of about 3.628 cm and heights of about 7.256 cm.

7 0

2 years ago