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3 years ago

I need help ASAP 120>10n+20

Mathematics

1 answer:

Burka [1]3 years ago

4 0

Answer:n = 10 can make the inequality true

Step-by-step explanation:

The given inequality is

120 greater than or equal to 10n + 20. This means that the least value of n that would make the inequality true would be 10.

If we substitute n = 10 into the right hand side of the given inequality, it would result to 120.

So n = 10 can make the inequality true.

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The following integral requires a preliminary step such as long division or a change of variables before using the method of par

shtirl [24]

Division yields

$\dfrac{x^4+7}{x^3+2x} = x-\dfrac{2x^2-7}{x^3+2x}$

Now for partial fractions: you're looking for constants a, b, and c such that

$\dfrac{2x^2-7}{x(x^2+2)} = \dfrac ax + \dfrac{bx+c}{x^2+2}$

$\implies 2x^2 - 7 = a(x^2+2) + (bx+c)x = (a+b)x^2+cx + 2a$

which gives a + b = 2, c = 0, and 2a = -7, so that a = -7/2 and b = 11/2. Then

$\dfrac{2x^2-7}{x(x^2+2)} = -\dfrac7{2x} + \dfrac{11x}{2(x^2+2)}$

Now, in the integral we get

$\displaystyle\int\frac{x^4+7}{x^3+2x}\,\mathrm dx = \int\left(x+\frac7{2x} - \frac{11x}{2(x^2+2)}\right)\,\mathrm dx$

The first two terms are trivial to integrate. For the third, substitute y = x ² + 2 and dy = 2x dx to get

$\displaystyle \int x\,\mathrm dx + \frac72\int\frac{\mathrm dx}x - \frac{11}4 \int\frac{\mathrm dy}y \\\\ =\displaystyle \frac{x^2}2+\frac72\ln|x|-\frac{11}4\ln|y| + C \\\\ =\displaystyle \boxed{\frac{x^2}2 + \frac72\ln|x| - \frac{11}4 \ln(x^2+2) + C}$

7 0

2 years ago

Maddie and Leah both play offense for their school's soccer team. This year, they decided to keep track of their goals and assis

n200080 [17]

Answer:

no they don't

Step-by-step explanation:

leah has a higher goal-assist ratio with 1 more assist than maddie

6 0

3 years ago

A menu has three meat choices,

wolverine [178]

Answer:

18 ways

Step-by-step explanation:

Number of Meat choices = 3

Number of Vegetable choices = 3

Number of Desserts = 2

Number of ways dinner can be chosen :

Number of meat choices * Number of vegetable choices * number of desserts

3 * 3 * 2

= 18

Hence, dinner can be chosen in 18 different choices.

4 0

2 years ago

The product of two consecutive odd intergers is 1 less than four times thier sum. Find the two integers.

seraphim [82]

Consecutive odd integers are 2 apart
they are x and x+2
the product (x times (x+2)) is 1 less than 4 times their sum

x(x+2)=-1+4(x+x+2)
$x^2+2x=-1+4(2x+2)$
$x^2+2x=-1+8x+8$
$x^2+2x=8x+7 minus (8x+7) from both sides [tex]x^2-6x-7=0$
factor
what numbers multliply to get -7 and add to get -6?
-7 and 1
(x-7)(x+1)=0
set equal to 0
x-7=0
x=7

x+1=0
x=-1

so the x can be 7 or -1
the other number (x+2) can be 7 or 1

test each

7 and 9
7(9)=-1+4(7+9)
63=-1+4(16)
63=-1+64
63=63
true

-1 and 1
-1(1)=-1+4(-1+1)
-1=-1+4(0)
-1=-1+0
-1=-1
true

the 2 integers can be 7 and 9 or -1 and 1 (both pairs of numbers work)

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kirill115 [55]

Step-by-step explanation:

❤️❤️needed this thank u!!!

5 0

3 years ago