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2 years ago

Solve for x. -7/8x = -5

Mathematics

1 answer:

Serhud [2]2 years ago

8 0

Answer:4.375 Maybe?

Step-by-step explanation:

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Find integra of xlnxdx

Mademuasel [1]

Answer:

$\dfrac{1}{2}x^2\ln x - \dfrac{1}{4}x^2+\text{C}$

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.

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

Increase the power by 1, then divide by the new power.

Given indefinite integral:

$\displaystyle \int x \ln x \:\: \text{d}x$

To integrate the given integral, use Integration by Parts:

$\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}$

$\text{Let }u=\ln x \implies \dfrac{\text{d}u}{\text{d}x}=\dfrac{1}{x}$

$\text{Let }\dfrac{\text{d}v}{\text{d}x}=x \implies v=\dfrac{1}{2}x^2$

Therefore:

$\begin{aligned}\displaystyle \int u \dfrac{dv}{dx}\:dx & =uv-\int v\: \dfrac{du}{dx}\:dx\\\\\implies \displaystyle \int x \ln x\:\:\text{d}x & = \ln x \cdot \dfrac{1}{2}x^2-\int \dfrac{1}{2}x^2 \cdot \dfrac{1}{x}\:\:dx\\\\& = \dfrac{1}{2}x^2\ln x -\int \dfrac{1}{2}x\:\:dx\\\\& = \dfrac{1}{2}x^2\ln x - \dfrac{1}{4}x^2+\text{C}\end{aligned}$

Learn more about integration here:

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5 0

2 years ago

an electrician has $120 to spend on interior light fixtures. The wholesale price for a 13-watt low-energy lamp is $4. The price

JulsSmile [24]

X = low-energy lamp
y = high-energy lamp

1) 4x + 5y

2) 120= 4x + 5y

8 0

3 years ago

Read 2 more answers

Karen has 4h storyboiks. Karen's storybook collection is 2/3 of what Mary's collection is. How many storybooks do they have in a

Dafna11 [192]

In order to find out the answer , you just need to count :
Let's say that mary's collection is symbolized by x

2/3 x = 4h

x = 3/2 . 4h

x = 6h

The storybooks they have in total would be : 6h + 4h = 10 h

hope this helps

6 0

3 years ago

At a clearance sale,Jill got 70% off a silver bracelet.If she paid the cashier $27 ,what was the original price of the bracelet

mart [117]

Answer:

$38.57

Step-by-step explanation:

Make a proportion.

$\frac{27}{x} = \frac{70}{100}$

Cross multiply.

27 times 100 = 2700

2700 divided by 70 = 38.57142857

Round the result to the hundredths place.

38.57142857 ≈ 38.57

**Hope this helps!

4 0

2 years ago

Solve the equation x2 18x + 21 = -3x to the nearest tenth.

Bumek [7]

Answer:

1x=-29

2x=-1

Step-by-step explanation:

i hope its useful.

7 0

2 years ago