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4 years ago

If A = 3x^2 + 5x - 6 and B = -2x^2 - 6x + 7, then A - B equals

1 answer:

7 0

$A=3x^2+5x-6 \\
B=-2x^2-6x+7 \\ \\
A-B= \\ 3x^2+5x-6-(-2x^2-6x+7)=\\
 3x^2+5x-6+2x^2+6x-7= \\ 5x^2+11x-13$

The answer is (2).

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Answer:

1.) 1/2 or 50%

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3 years ago

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3 years ago

What is the 101st term for the sequence 13, 9, 5, 1... ?

NeX [460]

Step-by-step explanation:

a=13
d=13-9=4

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3 years ago

Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges.

Arisa [49]

Answer: $S_n=5(1-\dfrac{1}{n+1})$ ; 5

Step-by-step explanation:

Given series : $[\dfrac{5}{1\cdot2}]+[\dfrac{5}{2\cdot3}]+[\dfrac{5}{3\cdot4}]+....+[\dfrac{5}{n\cdot(n+1)}]$

Sum of series = $S_n=\sum^{\infty}_{1}\ [\dfrac{5}{n\cdot(n+1)}]=5[\sum^{\infty}_{1}\dfrac{1}{n\cdot(n+1)}]$

Consider $\dfrac{1}{n\cdot(n+1)}=\dfrac{n+1-n}{n(n+1)}$

$=\dfrac{1}{n}-\dfrac{1}{n+1}$

⇒ $S_n=5\sum^{\infty}_{1}\dfrac{1}{n\cdot(n+1)}=5\sum^{\infty}_{1}[\dfrac{1}{n}-\dfrac{1}{n+1}]$

Put values of n= 1,2,3,4,5,.....n

⇒ $S_n=5(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+......-\dfrac{1}{n}+\dfrac{1}{n}-\dfrac{1}{n+1})$

All terms get cancel but First and last terms left behind.

⇒ $S_n=5(1-\dfrac{1}{n+1})$

Formula for the nth partial sum of the series :

$S_n=5(1-\dfrac{1}{n+1})$

Also, $\lim_{n \to \infty} S_n = 5(1-\dfrac{1}{n+1})$

$=5(1-\dfrac{1}{\infty})\\\\=5(1-0)=5$

4 0

3 years ago

Triangle ABC has a perimeter of 22cm I WILL MARK YOU AS BRAINLIEST

Andreyy89

Answer:

Step-by-step explanation:

Number of vertices

Variable constraints

a>0 and b>0

Diagonal lengths

(data not available)

Height

Area

A = (a b)/2

Centroid

x^_ = (a/3, b/3)

Mechanical properties:

Area moment of inertia about the x-axis

J_x invisible comma x = (a b^3)/12

Area moment of inertia about the y-axis

J_y invisible comma y = (a^3 b)/12

Polar moment of inertia

J_zz = 1/12 a b (a^2 + b^2)

Product moment of inertia

J_x invisible comma y = -1/24 a^2 b^2

Radii of gyration about coordinate axes

r_x = b/sqrt(6)

r_y = a/sqrt(6)

Distance properties:

Side lengths

a | sqrt(a^2 + b^2) | b

Hypotenuse

sqrt(a^2 + b^2)

Perimeter

p = sqrt(a^2 + b^2) + a + b

Inradius

r = 1/2 (-sqrt(a^2 + b^2) + a + b)

Circumradius

R = 1/2 sqrt(a^2 + b^2)

Generalized diameter

sqrt(a^2 + b^2)

Convexity coefficient

χ = 1

Mean triangle area

A^_ = (a b)/24

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3 years ago