All categories

3 years ago

Suppose the circumference of a circle is 15pi. What is its diameter?

1 answer:

7 0

The circumference of a circle is proportional to its diameter.

$C\propto d\\ \\ \therefore \quad C=kd$

Now, when d=1, C=π, therefore:

k=π

This means that:

$C=\pi d$

If C=15π:

15π=πd

Therefore:

d=15

You might be interested in

uppose we want to build a rectangular storage container with open top whose volume is $$ cubic meters. Assume that the cost of m

Ainat [17]

Answer:

a = length of the base = 2.172 m

b = width of the base = 1.357 m

c = height = 4.072 m

Step-by-step explanation:

Suppose we want to build a rectangular storage container with open top whose volume is 12 cubic meters. Assume that the cost of materials for the base is 12 dollars per square meter, and the cost of materials for the sides is 8 dollars per square meter. The height of the box is three times the width of the base. What’s the least amount of money we can spend to build such a container?

lets call a = length of the base

b = width of the base

c = height

V = a.b.c = 12

Area without the top:

Area = ab + 2bc + 2ac

Cost = 12ab + 8.2bc + 8.2ac

Cost = 12ab + 16bc + 16ac

height = 3.width

c = 3b

Cost = 12ab + 16b.3b + 16a.3b = 12ab + 48b² + 48ab = 48b² + 60ab

abc = 12 → ab.3b = 12 → 3ab² = 12 → ab² = 4 → a = 4/b²

Cost = 48b² + 60ab = 48b² + 60b.4/b² = 48b² + 240/b

C(b) = 48b² + 240/b

C'(b) = 96b - 240/b²

Minimum cost: C'(b) = 0

96b - 240/b² = 0

(96b³ - 240)/b² = 0

96b³ - 240 = 0

96b³ = 240

b³ = 240/96

b³ = 2.5

b = 1.357m

c = 3b = 3*1.357 = 4.072m

a = 4/b² = 2.172m

6 0

3 years ago

What 223 x 12 explain

geniusboy [140]

Answer: 2676

Step-by-step explanation:

223 x 12 = 2676

This is because 223 12 times equals 2676.

*I will attach my work for the problem so you can see the solving process more clearly :).

Hope this helps :).

4 0

1 year ago

Please help me answer this. I think that for the first one the answer is A, but I am not sure. There are two parts to the questi

Anika [276]

Vector $PQ=(7-5, 3-4)=(2, -1)$ . $4RS=4 \cdot (4-8, 1-6) = 4 \cdot (-4, -5) = (-16, -20)$ . So the sum is $(-14, -21)$ .

For the second, the magnitude is the square root of the sum of the squares of the components. This is equal to $\sqrt{(-14)^2+(-21)^2} = \sqrt{637}=7\sqrt{13}$ .

4 0

2 years ago

Read 2 more answers

Describe Cullen's mistake

gizmo_the_mogwai [7]

Answer:Cullen did not add 4n to the -6n he added -4n.

Step-by-step explanation:When you go to move the -4n you want to add 4n to make the -4n turn to 0. This is because we need n on one side and what it is equaled to on the other.

8 0

2 years ago

Read 2 more answers

Solve 3x2 + 4x = −5.

Alla [95]

Move the -5 over by adding 5 to both sides
3x^2+4x+5=0
must use quadratic formula

for an equation in the form
ax^2+bx+c=0
x= $\frac{-b+/- \sqrt{b^2-4ac} }{2a}$

a=3
b=4
c=5

x= $\frac{-4+/- \sqrt{4^2-4(3)(5)} }{2(3)}$
x= $\frac{-4+/- \sqrt{16-60} }{6}$
x= $\frac{-4+/- \sqrt{-44} }{6}$
x= $\frac{-4+/- 2\sqrt{-11} }{6}$
remember that√-1=i
x= $\frac{-4+/- 2i\sqrt{-11} }{6}$
x= $\frac{-2+/- i\sqrt{-11} }{3}$

x= $\frac{-2+ i\sqrt{-11} }{3}$ or x= $\frac{-2- i\sqrt{-11} }{3}$

4 0

2 years ago