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3 years ago

Find the area of this triangle..

Mathematics

1 answer:

Phoenix [80]3 years ago

3 0

Answer:

Step-by-step explanation:

Use the Pythagorean theorem to find the altitude.

h^2 = 9^2 - 6.4^2

h^2 = 40.04

h = 6.328

area = base * height/2

area = (2 * 6.4) * 6.328/2

area = 40.5 square units

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Find the generating function for the sequence 1,1,1,2,3,4,5,6,....

marin [14]

Answer:

$P(x)=\dfrac{1}{1-x}+\dfrac{x^3}{(1-x)^2} \quad \text{for} \mid x \mid < 1$ [/tex]

Step-by-step explanation:

The generating function of a sequence is the power series whose coefficients are the elements of the sequence. For the sequence

$1,1,1,2,3,4,5,6,...$

the generating function would be

$P(x)=1+x+x^2+2x^3+3x^4+4x^5+5x^6+...\\$

we can multiply P(x) by x to get

$xP(x)=x+x^2+x^3+2x^4+3x^5+4x^6+...$

Note that

$P(x)-xP(x)=1+(2x^3-x^3)+(3x^4-2x^4)+(4x^5-3x^5)+(5x^6-4x^6)+...\\ \\=1+x^3+x^4+x^5+x^6+...=1+x^3(1+x+x^2+x^3+x^4+...)$

which for $\mid x \mid < 1$ can be rewritten as

$(1-x)P(x)=1+\dfrac{x^3}{(1-x)} \quad \Rightarrow \\\\P(x)=\dfrac{1}{(1-x)}+\dfrac{x^3}{(1-x)^2}$

8 0

3 years ago

A salesperson receives a 3% commission on sales. The salesperson receives $180 in commission. What is the amount of sales?

erastova [34]

Let sales be x
.03x = 180 
divide both sides by .03 
x = 180/.03 = 6000

6 0

3 years ago

If the Lafita family deposits 8500$ ina savings account at 6.75% interest, compounded continuously, how much will be the account

julsineya [31]

A=pe^rt
A=8,500×e^(0.0675×25)
A=45,950.57

8 0

4 years ago

John bikes at a speed of 10 miles per hour. His friend Brian is slower, his biking speed is only 8 miles per hour. d Tomorrow bo

skad [1K]

Answer:

6 miles

Step-by-step explanation:

Given

John's speed = 10 mph
Brian's speed = 8 mph
Time 3 hours

Solution

The difference in distance covered:

3*(10 - 8) = 6 miles

3 0

3 years ago

Convert 3/4 to decimal leaving the answer in 1S.f

GuDViN [60]

Answer:

0.8

Step-by-step explanation:

3/4 =0.75

~0.8(to 1s.f)

3 0

3 years ago