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2 years ago

Simplify the following.

Mathematics

1 answer:

GalinKa [24]2 years ago

8 0

Answer:

(2f-17h)/24k

Step-by-step explanation:

We can make the common denominator for 3k and 8k in the form of 24k, so we get (multiply the first fraction by 8 and the second one by 3 to get 24k on each denominator) (8f-32h)/3k-(6f-15h)/24k. Now we can just subtract the numerators :

8f-32h-6f+15h (sign gets flipped on 6f and 15h), so we get

(2f-17h)/24k

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(x + 1 < -1) ∩ (x + 1 < 1)

stealth61 [152]

Answer: ok that’s confusing

Step-by-step explanation:

3 0

3 years ago

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

The answer to this problem

katovenus [111]

D.) 2cm, 12cm, 16cm
'cause the sum of two small sides must be greater than that of longest side.

Hope this helps!

5 0

2 years ago

PLEASE HELP!!!! Will mark brainlesst!

Alexxandr [17]

Step-by-step explanation:

a. y=mx+c

m = rise/run

3/2=m

1.5=m

b. y=1.5x+3

c. y int. x=0 x int. y=0

y=1.5(0)+3 0= 1.5x+3

y= 3 -3=1.5×

1.5x/1.5=-3/1.5

x= 2

d. y-y1 =m(x-x1)

y-3=1.5(×-2)

y-3 =1.5x-3

y-3+3=1.5x-3+3

y=1.5x +0

y int =3 x int =2

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2 years ago

What is the value of the expression below

givi [52]

Answer:

9/50

Step-by-step explanation:

gjccgkcgkgckkcgkgcgckgckgck

5 0

2 years ago