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2 years ago

The circumference of a circle is 28 x inches. What is the length of the radius of this circle?

Mathematics

1 answer:

meriva2 years ago

4 0

Answer: 14

Explanation: The radius is half of the value of the circumference.

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What is the maximum volume in cubic inches of an open box to be made from a 12-inch by 16-inch piece of cardboard by cutting out

Romashka-Z-Leto [24]

If you start with a 12x16 rectangle and cut square with side length x, when you bend the sides you'll have an inner rectangle with sides $12-2x$ and $16-2x$ , and a height of x.

So, the volume will be given by the product of the dimensions, i.e.

$(12-2x)(16-2x)x = 4x^3-56x^2+192x$

The derivative of this function is

$12x^2-112x+192$

and it equals zero if and only if

$12x^2-112x+192=0 \iff x = \dfrac{14\pm 2\sqrt{13}}{3}$

If we evaluate the volume function at these points, we have

$f\left(\dfrac{14-2\sqrt{13}}{3}\right) = \dfrac{64}{27}(35+13\sqrt{13})> f\left(\dfrac{14-2\sqrt{13}}{3}\right) = -\dfrac{64}{27}(13\sqrt{13}-35)$

So, the maximum volume is given if you cut a square with side length

$x=\dfrac{14-2\sqrt{13}}{3}\approx 2.7$

5 0

2 years ago

Help!!<br> What is the relationship between the corresponding angle bisectors BD and XZ?

Harrizon [31]

Answer:

XZ = 2.5 BD

Step-by-step explanation:

Comparing the two triangles,

$\frac{BD}{BC}$ = $\frac{XZ}{XY}$

$\frac{6}{8}$ = $\frac{XZ}{20}$

⇒ XZ = $\frac{20*6}{8}$

= 15

XZ = 15

So that,

BD:XZ = 6:15

= 1:2.5

Therefore, the relationship between BD and XZ is XZ = 2.5 BD.

8 0

2 years ago

1. Find 3 equivalent fraction for the following: a) 5/6 b) 7/11 c) 9/7

SOVA2 [1]

Answer:

Step-by-step explanation:

To find equivalent fractions, multiply the numerator and the denominator by the same table.

a) 5/6

$\frac{5*2}{6*2}=\frac{10}{12}\\\\\frac{5*3}{6*3}=\frac{15}{18}\\\\\frac{5*4}{6*4}=\frac{20}{24}$

b) 7/11

$\frac{7*3}{11*3}=\frac{21}{33}\\\\\frac{7*4}{11*4}=\frac{28}{44}\\\\\frac{7*5}{11*5}=\frac{35}{55}$

c)9/7

$\frac{9*2}{7*2}=\frac{18}{14}\\\\\frac{9*5}{7*5}=\frac{45}{35}\\\\\frac{9*10}{7*10}=\frac{90}{70}$

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2 years ago

Fark earns 2.5% interest on savings account each year if Clark device is 2 mm in to a savings account

raketka [301]

Answer:

Step-by-step explanation:

4 0

2 years ago

Tell whether the sequence is arithmetic. If it is, what is the common difference?

denis23 [38]

Idek sorry have a nice day

6 0

2 years ago