Simplify -3/2 * 9/6 A. -4 B. -1 C. 4 D. 1

Talia had a rope that measured 4 2/5 inches. How 1/8 inch pieces of rope can she cut from the larger piece?

spin [16.1K]

Step-by-step answer:

1/8" long piece is not very much. However, mathematically,

we divide the total length by the length of each piece to get the number of pieces. So

4 2/5 / (1/8)

= (5*4+2)/5 * (8/1) [convert to fraction, and division to multiplication

= (22/5) * (8/1)

= 176/5

= 35 pieces with 1/5" left over.

3 0

4 years ago

Find the average value of the function g(x) = <img src="https://tex.z-dn.net/?f=%5Cfrac%7Blnx%7D%7Bx%7D" id="TexFormula1" title=

aleksley [76]

Answer:

$\displaystyle average=\frac{1}{2(e-1)}$

Step-by-step explanation:

Average Value of a Function

Given a function g(x), we can compute the average value of g in a given interval (a,b) with the equation:

$\displaystyle average=\frac{1}{b-a}\int_{a}^{b} g(x)dx$

We use the given data

$\displaystyle average=\frac{1}{e-1}\int_{1}^{e} \frac{lnx}{x}dx$

We now compute the indefinite integral with a u-substitution

$\displaystyle I=\int \frac{lnx}{x}dx$

We'll use the substitution u=lnx, du=dx/x. Then

$\displaystyle I=\int u.du$

Integrating

$\displaystyle I=\frac{u^2}{2}$

Since u=lnx

$\displaystyle I=\frac{ln^2x}{2}$

The average value is

$\displaystyle average=\frac{1}{e-1}\left|\frac{ln^2x}{2} \right|_1^e$

$\displaystyle average=\frac{1}{e-1}\left(\frac{ln^2e}{2}-\frac{ln^21}{2} \right )$

Since lne=1, and ln1=0

$\displaystyle average=\frac{1}{e-1}\left(\frac{1}{2}-0 \right )$

$\displaystyle average=\frac{1}{2(e-1)}$

3 0

4 years ago

Choose the possible descriptions of cross sections formed by the intersection of a plane and a cylinder.

Rus_ich [418]

Answer:

Ellipses (special case is called a circle), hyperbolas, parabolas.

Step-by-step explanation:

These are all conic sections.

A conic section is defined by the cross section of a plane and a double-napped cone. There are other special cases called degenerate conics, which are lines and points (occurs when the equation does not follow the usual pattern, however, these are not considered main conics). The main types of conics are: ellipses, hyperbolas, and parabolas.

The illustration below gives more insight into the question.

I hope this helps.

6 0

3 years ago

Write each of the below number in an ascending order. 3.4 4.7 2.9 2.69

Serjik [45]

Answer:

2.69 2.9 3.4 4.7

is the order

7 0

3 years ago

The cost of Samantha's 15th birthday party depends on the number guest. The hall charges $250 for the use of the hall plus $12 p

Scorpion4ik [409]

Answer:

Equation: y=x(12)+250

Total cost: $550

3 0

3 years ago