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3 years ago

What is the value of k used to find the coordinates of a point that partitions a segment into a ratio of 5:3. Please Explain.

Mathematics

1 answer:

Dafna11 [192]3 years ago

4 0

Answer:

The value of k is 5/8

Step-by-step explanation:

The value of k is found by dividing the numerator of the original ratio, 5, by the sum of the numerator and denominator of the ratio

When finding a point, P, to partition a line segment AB into the ratio a/b, we find a ratio c = a / (a + b)

According to this formula we find the value of k.

k = a/(a+b)

where a = 5

b = 3

Now plug the values in the formula:

k = 5/(5+3)

k = 5/8 ....

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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:

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

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2 years ago

I need help with a MathsWatch question!

KIM [24]

To find the area of a circle, you do π × diameter (in this case 10). They have told you to use 3.142 as π, so you do 3.142 × 10 = 31.42. Because it's a semi-circle, you need to halve 31.42 to get 16.21, which is the answer

6 0

3 years ago

Read 2 more answers

Write an equation of the line passing through the point (3, -1) and parallel to the line y=2/3x - 5. Show work

alex41 [277]

Answer:

The answer is: y = 2/3x - 3

Step-by-step explanation:

Given point: (3, -1)

Given equation: y = 2/3x - 5, which is in the form y = mx + b where m is the slope and b is the y intercept.

Parallel lines have the same slope. Use the point slope form of the equation with the point (3, -1) and substitute:

y - y1 = m(x - x1)

y - (-1) = 2/3(x - 3)

y + 1 = 2/3x - 6/3

y + 1 = 2/3x - 2

y = 2/3x - 3

Proof:

f(3) = 2/3(3) - 3

= 6/3 - 3

= 2 - 3

= -1, giving the point (3, -1)

Hope this helps! Have an Awesome Day!! :-)

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3 years ago

Ming wrote the table of points below.

borishaifa [10]

Answer:

I am 99.99% sure it is the first one

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