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3 years ago

1/2s+3/4s+1/4s+4 equals?

Mathematics

1 answer:

ryzh [129]3 years ago

5 0

step1) Combine multiplied terms into a single fraction

step 2)Multiply by 1

step 3)Combine multiplied terms into a single fraction

step4) Combine multiplied terms into a single fraction

step5) Multiply by 1

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A bag contains 8 red marbles, 6 white marbles, and 6 blue marbles. find P (red or blue)

vlabodo [156]

I'm assuming you're supposed to find the chance of them drawing red or blue/
So the whole is 20, and red and blue combined is 14.So its 14/20, which is 70%, and as a simplified fraction it is 7/10.

5 0

3 years ago

Recycled CDs, Incorporated, offers a choice of 5 used CDs for $27, with each additional CD costing $5. Write a cost function

notka56 [123]

A function assigns the values. The cost of 6 CDs will be $32.

<h3>What is a Function?</h3>

A function assigns the value of each element of one set to the other specific element of another set.

Given that the Recycled CDs. Incorporated, offers a choice of 5 used CDs for $27, with each additional CD costing $5. Therefore, a cost function for purchasing 5 or more CDs, where x represents the number of CDs over 5 can be written as,

C(x) = $27 + $5(x)

Now, if 6 CDs are purchased then the number of CDs that are more than 5 is 1. therefore, the cost of 6 CDs will be,

C(1) = $27 + $5(1)

= $27 + $5

= $32

Hence, the cost of 6 CDs will be $32.

Learn more about Function here:

brainly.com/question/5245372

#SPJ1

8 0

2 years ago

So,some please help!

Leni [432]

4.6 is the correct answer. Hope I helped:)

5 0

3 years ago

Read 2 more answers

Evaluate the integral, show all steps please!

Aloiza [94]

Answer:

$\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x=\dfrac{x}{9\sqrt{9-x^2}} +\text{C}$

Step-by-step explanation:

<u>Fundamental Theorem of Calculus</u>

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

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 indefinite integral:

$\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x$

Rewrite 9 as 3² and rewrite the 3/2 exponent as square root to the power of 3:

$\implies \displaystyle \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x$

<u>Integration by substitution</u>

<u />

<u /> $\boxed{\textsf{For }\sqrt{a^2-x^2} \textsf{ use the substitution }x=a \sin \theta}$

$\textsf{Let }x=3 \sin \theta$

$\begin{aligned}\implies \sqrt{3^2-x^2} & =\sqrt{3^2-(3 \sin \theta)^2}\\ & = \sqrt{9-9 \sin^2 \theta}\\ & = \sqrt{9(1-\sin^2 \theta)}\\ & = \sqrt{9 \cos^2 \theta}\\ & = 3 \cos \theta\end{aligned}$

Find the derivative of x and rewrite it so that dx is on its own:

$\implies \dfrac{\text{d}x}{\text{d}\theta}=3 \cos \theta$

$\implies \text{d}x=3 \cos \theta\:\:\text{d}\theta$

<u>Substitute</u> everything into the original integral:

$\begin{aligned}\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x & = \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x\\\\& = \int \dfrac{1}{\left(3 \cos \theta\right)^3}\:\:3 \cos \theta\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{\left(3 \cos \theta\right)^2}\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{9 \cos^2 \theta} \:\: \text{d}\theta\end{aligned}$

Take out the constant:

$\implies \displaystyle \dfrac{1}{9} \int \dfrac{1}{\cos^2 \theta}\:\:\text{d}\theta$

$\textsf{Use the trigonometric identity}: \quad\sec^2 \theta=\dfrac{1}{\cos^2 \theta}$

$\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta$

$\boxed{\begin{minipage}{5 cm}\underline{Integrating $\sec^2 kx$}\\\\$\displaystyle \int \sec^2 kx\:\text{d}x=\dfrac{1}{k} \tan kx\:\:(+\text{C})$\end{minipage}}$