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2 years ago

(50 POINTS)

Mathematics

1 answer:

inna [77]2 years ago

8 0

The formula of a function is the rise over run.

The slope would be 2/5.

Hope this helps!

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Mrs. Barnes cuts1/2 of a piece of construction paper. She uses 1/6

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Step-by-step explanation:

what fraction?? she uses 1/6 of the construction paper

if you are referring to how much paper is left, its 2/6 aka 1/3

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2 years ago

The indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Th

Fantom [35]

Answer:

∫ $6x^5(x^6-2)\,dx$ = $\frac{1}{2}(x^6-2)^2+C$

Step-by-step explanation:

To find:

∫ $6x^5(x^6-2)\,dx$

Solution:

Method of substitution:

Let $x^6-2=t$

Differentiate both sides with respect to $t$

$6x^5\,dx=dt$

[use $(x^n)'=nx^{n-1}$ ]

So,

∫ $6x^5(x^6-2)\,dx$ = ∫ $t\,dt$ = $\frac{t^2}{2}+C_1$ where $C_1$ is a variable.

(Use ∫ $t^n\,dt=\frac{t^{n+1} }{n+1}$ )

Put $t=x^6-2$

∫ $6x^5(x^6-2)\,dx$ = $\frac{1}{2}(x^6-2)^2+C_1$

Use $(a-b)^2=a^2+b^2-2ab$

So,

∫ $6x^5(x^6-2)\,dx$ = $\frac{1}{2}(x^6-2)^2+C_1=\frac{1}{2}(x^{12}+4-4x^6)+C_1=\frac{x^{12} }{2}-2x^6+2+C_1=\frac{x^{12} }{2}-2x^6+C$

where $C=2+C_1$

Without using substitution:

∫ $6x^5(x^6-2)\,dx$ = ∫ $6x^{11}-12x^5\,dx$ = $\frac{6x^{12} }{12}-\frac{12x^6}{6}+C=\frac{x^{12} }{2}-2x^6+C$

So, same answer is obtained in both the cases.

7 0

2 years ago

Using the formula in model 1, choose the correct answers for the total amount and amount of interest earned in the following com

DIA [1.3K]

The total amount is $ 1015.82 and interest amount is $ 165.82

Solution:

The formula for amount when interest is compounded annually is:

$\mathrm{A}=P\left(1+r}\right)^{n}$

Where,

"A" is the total amount

"P" is the principal

"r" is the rate of interest in decimal form

"n" is the number of years

From given, $850 at 2% for 9 years, compounded annually

P = 850

t = 9 years

$r = 2 \% = \frac{2}{100} = 0.02$

Substituting the given values we get,

$A = 850(1+0.02)^9\\\\A = 850 \times 1.02^9\\\\A = 850 \times 1.1950\\\\A = 1015.82$

Thus total amount is $ 1015.82

Interest amount = Total amount - principal

Interest amount = 1015.82 - 850

Interest amount = 165.82

Thus total amount earned is $ 1015.82 and interest amount is $ 165.82

7 0

3 years ago