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4 years ago

It's cost $3.99 for 25 fl. oz. of detergent or $6.99 for 90 fl. oz. Which is a better buy?

Mathematics

1 answer:

Gemiola [76]4 years ago

8 0

$3.99 rounded to 4$ X 2=$8 for 25 for. oz

$6.99 rounded to $7 X 2 =$14 for 90 fl. oz

so $6.99 is cheaper

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Tems11 [23]

Factor out the 3y²
3y²(3y-5)

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4 years ago

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Evaluate the following integral (Calculus 2) Please provide step by step explanation!

Step2247 [10]

Answer:

$\displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x=-\dfrac{2}{x+1}+\text{C}$

Step-by-step explanation:

Fundamental Theorem of Calculus

$\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))$

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given integral:

$\displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x$

Factor the denominator:

$\begin{aligned}\implies x^2+2x+1 & = x^2+x+x+1\\& = x(x+1)+1(x+1)\\& = (x+1)(x+1)\\& = (x+1)^2\end{aligned}$

$\implies \displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x=\int \dfrac{2}{(x+1)^2}\:\:\text{d}x$

$\textsf{Apply exponent rule} \quad \dfrac{1}{a^n}=a^{-n}$

$\implies \displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x=\int 2(x+1)^{-2}\:\:\text{d}x$

$\boxed{\begin{minipage}{4 cm}\underline{Integrating $ax^n$}\\\\$\displaystyle \int ax^n\:\text{d}x=\dfrac{ax^{n+1}}{n+1}+\text{C}$\end{minipage}}$

Use Integration by Substitution:

$\textsf{Let }u=(x+1) \implies \dfrac{\text{d}u}{\text{d}x}=1 \implies \text{d}x=\text{d}u}$

Therefore:

$\begin{aligned}\displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x & = \int 2(x+1)^{-2}\:\:\text{d}x\\\\& = \int 2u^{-2}\:\:\text{d}u\\\\& = \dfrac{2}{-1}u^{-2+1}+\text{C}\\\\& = -2u^{-1}+\text{C}\\\\& = -\dfrac{2}{u}+\text{C}\\\\& = -\dfrac{2}{x+1}+\text{C}\end{aligned}$

Learn more about integration here:

brainly.com/question/27988986

brainly.com/question/27805589

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2 years ago

There is a pyramid which is 5.95cm and a base of 5.1 what is the surface area?

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3 years ago

Solve the system of equations -x-2y=0 and -x+y=6 by combining the equations

Elden [556K]

Answer:

x=-4 and y=10

Step-by-step explanation:

Use the second equation to make y=x+6

sub y=x+6 into the first equation

-x-2*(x+6)=0

-x-2x-12=0

-3x-12=0

3x=-12

x=-4

Now sub x=-4 into the second equation

-(-4)+y=6

y=6+4

y=10

3 0

3 years ago

A person 6ft tall stands 10ft from point P directly beneath a lantern hanging 30 ft above the ground. The lantern start to fall,

xxMikexx [17]

Answer:

$\frac{dL}{dt}=30 \frac{ft}{s}$

Step-by-step explanation:

In order to solve this it is always a good idea to start by drawing a diagram of the situation (See attached picture).

From the diagram we can see that we are dealing with similar triangles. We can use similar triangles to build an equation that relates the length of the shadow with the height of the lamp, so we get:

$\frac{L}{6}=\frac{10+L}{h}$

the height of the lamp can be found by subtracting the $16t^{2}$ distance the lamp falls in a given time t from the original 30ft the lamp was located at.