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4 years ago

I need help answering number 8 please

Mathematics

1 answer:

swat324 years ago

5 0

The diagram of the triangle is shown below

One interior angle is 56°
One exterior angle is 103° ⇒ we can work out one interior angle 180°-103° = 77°

The other interior angle is 180° - (56°+77°) = 44°

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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:

<u>Average Value of a Function</u>

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

Polygon ABCDE is dilated by a scale factor of 3 with the center of dilation at the origin to create polygon A′B′C′D′E′. If the e

solmaris [256]

Short answer: B'C' has the same as BC
Let the slope of BC have a slope of m

m = (y2 - y1) / (x2 - x1)
y2 = 10
y1 = 5
x2 = 5
x1 = 3

m = (10 - 5)/(5 - 3)
m = 5 / 2
m = 2.5

Since the slope of BC is 2.5
The slope of B'C' = 2.5 <<<<<<<<<< answer

6 0

4 years ago

An item is regularly priced at $55 . It is now priced at a discount of 80% off the regular price. What is the price now

Goshia [24]

The answer is 44 dollars

3 0

3 years ago

Read 2 more answers

The experimental probability that Amir will make a basket is 0.4 the experimental probability that juju with make the same baske

AVprozaik [17]

Answer:

30 baskets

Step-by-step explanation:

The experimental probability Pa that Amir will make a basket is 0.4;

Pa = 0.4

the experimental probability Pj that juju with make the same basket is 0.6;

Pj = 0.6

Total number of shoot Nt = 150

Number of basket Amir will make is;

Na = Pa × Nt

Na = 0.4 × 150

Na = 60 basket

Number of basket juju will make is;

Nj = Pj × Nt

Nj = 0.6 × 150

Nj = 90 basket

how many more baskets will juju make;

Nd = Nj - Na = 90 - 60 = 30 baskets

8 0

3 years ago

Write following in y=mx+b form<br> 1/2 x-y= 4<br> 2y= x+ 6

Zigmanuir [339]

Lets do this.
$\frac{1}{2} *x-y=4$ /- $\frac{1}{2}x$
-y= $- \frac{1}{2}x+4$ /*(-1)
y= $\frac{1}{2}x-4$ - its the result

2y=x+6 /:2 (divide both sides by2 )
y= $\frac{1}{2} x+3$ - its the result

3 0

3 years ago