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2 years ago

Add. express your answer in simplest form. 1/12 + 5/12

Mathematics

2 answers:

coldgirl [10]2 years ago

8 0

Answer:

The answer is 1/2

EleoNora [17]2 years ago

8 0

Answer:

1/2

Step-by-step explanation:

$\frac{1}{12}+\frac{5}{12} = \frac{6}{12}\\ \\ \frac{6}{12} = \frac{1}{2}$ They are both equivalent fractions. If you divide the numerator and denominator both by 6, you get 1/2.

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Eric has 1 5/9 cups of yogurt to make smoothies.Each smoothie uses 1/3 of a cup of yogurt.What is the maximum number of smoothie

Vedmedyk [2.9K]

Maximum number of smoothies that Erica can make with the yogurt is 5

<h3><u>Solution:</u></h3>

Given that Eric has $1\frac{5}{9}$ cups of yogurt to make smoothie

Each smoothie uses $\frac{1}{3}$ of a cup of yogurt

To find: maximum number of smoothies that Erica can make with the yogurt

Let 'n' be the number of smoothies that Erica can make with the available yogurt

number of smoothies that Erica can make with the yogurt is calculated by divinding the total available cups of yogurt by cups of yogurt needed for one smoothie

<em><u>Therefore we get:</u></em>

$n=\frac{\text { total available cups of yogurt }}{\text { cups of yogurt needed for one smoothie }}$

total available cups of yogurt = $1\frac{5}{9} = \frac{9 \times 1 +5}{9} = \frac{14}{9}$

cups of yogurt needed for one smoothie = $\frac{1}{3}$

Substituting the values in above formula we get,

$\begin{aligned}&n=\frac{\frac{14}{9}}{\frac{1}{3}}\\\\&n=\frac{14}{9} \times \frac{3}{1}=\frac{14}{3}=4.66 \approx 5\end{aligned}$

Thus maximum number of smoothies that Erica can make with the yogurt is 5

4 0

3 years ago

Integrala x la a treia ori ln la a doua dx va rog

Studentka2010 [4]

I don't speak Romanian, but the closest translation for this suggests you're trying to compute

$\displaystyle \int x^3 \ln(x)^2 \, dx$

Integrate by parts:

$\displaystyle \int x^3 \ln(x)^2 \, dx = uv - \int v \, du$

where

u = ln(x)² ⇒ du = 2 ln(x)/x dx

dv = x³ dx ⇒ v = 1/4 x⁴

$\implies \displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac12 \int x^3 \ln(x) \, dx$

Integrate by parts again:

$\displaystyle \int x^3 \ln(x) \, dx = u'v' - \int v' du'$

where

u' = ln(x) ⇒ du' = dx/x

dv' = x³ dx ⇒ v' = 1/4 x⁴

$\implies \displaystyle \int x^3 \ln(x) \, dx = \frac14 x^4 \ln(x) - \frac14 \int x^3 \, dx$

So, we have

$\displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac12 \left(\frac14 x^4 \ln(x) - \frac14 \int x^3 \, dx \right)$

$\displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac18 x^4 \ln(x) + \frac18 \int x^3 \, dx$

$\displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac18 x^4 \ln(x) + \frac18 \left(\frac14 x^4\right) + C$

$\displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac18 x^4 \ln(x) + \frac1{32} x^4 + C$

$\boxed{\displaystyle \int x^3 \ln(x)^2 \, dx = \frac1{32} x^4 \left(8\ln(x)^2 - 4\ln(x) + 1\right) + C}$

3 0

2 years ago

How do I solve this?

Harrizon [31]

Multiply 5x200x0.75 and then convert your answer to yards :)

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3 years ago

What is the unit rate if there are 258 purple polka-dot pencils in 3 purple polka-dot purses?

stiks02 [169]

Unit rate means one. So the best way to solve this is using a proportion over one. If there are 258 pencils in 3 purses 258/3 then how many are in one purses x/1. Cross multiply next. 258/3 * x/1. You get 3x and 258. To get the x alone, divide both sides by three. Your answer is 86 pencils in one purse.

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3 years ago

What quadratic function f whose only zero is -6

Mrrafil [7]

Answer:

y=(x+6)^2

Step-by-step explanation:

Bc, the root has to be only -6

there fore x=-6

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3 years ago