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2 years ago

How do you factor 6x^2+6x

Mathematics

1 answer:

Andreyy892 years ago

7 0

I think it might be 2

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cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup. The material for the sides of the can costs 0

Dafna11 [192]

Answer:

Radius=2.09 cm

Height,h=14.57 cm

Step-by-step explanation:

We are given that

Volume of cylinderical shaped can=200 cubic cm.

Cost of sides of can=0.02 cents per square cm

Cost of top and bottom of the can =0.07 cents per square cm

Curved surface area of cylinder= $2\pi rh$

Area of circular base=Area of circular top= $\pi r^2$

Total cost,C(r)= $0.02\times 2\pi rh+2\pi r^2\times 0.07$

Volume of cylinder, $V=\pi r^2 h$

$200=\pi r^2 h$

$h=\frac{200}{\pi r^2}$

Substitute the value of h

$C(r)=0.02\times 2\pi r\times \frac{200}{\pi r^2}+2\pi r^2\times 0.07$

$C(r)=\frac{8}{r}+0.14\pi r^2$

Differentiate w.r.t r

$C'(r)=-\frac{8}{r^2}+0.28\pi r$

$C'(r)=0$

$-\frac{8}{r^2}+0.28\pi r=0$

$0.28\pi r=\frac{8}{r^2}$

$r^3=\frac{8}{0.28\pi}=9.095$

$r=(9.095)^{\frac{1}{3}}=2.09$

Again, differentiate w.r.t r

$C''(r)=\frac{16}{r^3}+0.28\pi$

Substitute the value of r

$C''(2.09)=\frac{16}{(2.09)^3}+0.28\pi=2.63>0$

Therefore,the product cost is minimum at r=2.09

h= $\frac{200}{\pi (2.09)^2}=14.57$

Radius of can,r=2.09 cm

Height of cone,h=14.57 cm

4 0

2 years ago

Write 53 minutes to 4 hours as a ratio.

Hoochie [10]

Answer:

The minutes wouldn't it be hours?

Step-by-step explanation:

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5x² + 4x - 20 = 0<br> Solve this using the quadratic formula

Natali [406]

Here's the answer, using the quadratic formula

8 0

2 years ago

Simplify the expression 3.5(1.2x+0.8)-0.5(4.6-1.2x)

luda_lava [24]

Answer:

4.8x + 0.5

Step-by-step explanation:

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2 years ago

Calculate the slope of the line given the points (2,1) and (1,-4)

Dmitrij [34]

The equation for the slope of a line is:

y2-y1/x2-x1

So:

-4-1/1-2 = -5/-1 =5

The slope of the line is 5.

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