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madreJ [45]
3 years ago
15

Which point is a solution to y<4x+5

Mathematics
1 answer:
Alla [95]3 years ago
3 0

Answer:

(1,-1)

Step-by-step explanation:

y < 4x+5

x = 1, y = -1 => -1 < -4+5 (T)

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3/20 as a decimal equivalent is <span>0.15</span>
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What is 2.20 rounded to the nearest tenth?
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2.20 rounded to the nearest tenth is 2.2 it is already rounded if it was 2.29 it would be 2.3 
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The radius of a circle 6 cm what is the circles area?
dolphi86 [110]

Answer:

113.04 cm

Step-by-step explanation:

We know the formula to find the area of a circle is

A= pi(r^{2})

And we are told to use 3.14 instead of pi so what we have now is,

A=3.14(r^{2})

We are also told the radius, r, is 6. So our equation now looks like this,

A=3.14(6^{2})\\\\6^{2}is the same as 36, because 6x6 is 36.

Now we have,

A=3.14(36)  

Which equals 113.04 and that is the area!

Hope that helps and have a great day!

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You have been asked to design a can shaped like right circular cylinder that can hold a volume of 432π-cm3. What dimensions of t
rosijanka [135]

Answer:

Height = 12cm

Radius = 6cm

Step-by-step explanation:

Given

Represent volume with v, height with h and radius with r

V = 432\pi

Required

Determine the values of h and r that uses the least amount of material

Volume is calculated as:

V = \pi r^2h\\

Substitute 432π for V

432\pi = \pi r^2h

Divide through by π

432 = r^2h

Make h the subject:

h = \frac{432}{r^2}

Surface Area (A) of a cylinder is calculated as thus:

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

Substitute \frac{432}{r^2} for h in A=2\pi rh+2\pi r^2

A=2\pi r(\frac{432}{r^2})+2\pi r^2

A=2\pi (\frac{432}{r})+2\pi r^2

Factorize:

A=2\pi (\frac{432}{r} + r^2)

To minimize, we have to differentiate both sides and set A' = 0

A'=2\pi (-\frac{432}{r^2} + 2r)

Set A' = 0

0=2\pi (-\frac{432}{r^2} + 2r)

Divide through by 2\pi

0= -\frac{432}{r^2} + 2r

\frac{432}{r^2} = 2r

Cross Multiply

2r * r^2 = 432

2r^3 = 432

Divide through by 2

r^3 = 216

Take cube roots of both sides

r = \sqrt[3]{216}

r = 6

Recall that:

h = \frac{432}{r^2}

h = \frac{432}{6^2}

h = \frac{432}{36}

h = 12

Hence, the dimension that requires the least amount of material is when

Height = 12cm

Radius = 6cm

3 0
3 years ago
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