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3 years ago

Find the distance between the two points S(–5, –2) and T(–3, 4).

Mathematics

1 answer:

Oxana [17]3 years ago

7 0

Answer:

(2,6)

Step-by-step explanation:

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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

C6.1 PA1 short term decision Artisan Metalworks has a bottleneck in their production that occurs within the engraving department

laila [671]

Answer: $4850

Step-by-step explanation:

The other information related to the question is:

Direct materials = $3.50

Direct labor = $1.10

Variable overhead = $0.45

Fixed overhead = $2.80

Total = $7.85

Based on the information given in the question, the increase in the profit will be calculated as the contribution from the 3000 extra units minus the worker's salary.

Contribution from 3000 units will be:

= (Selling price - Direct materials - Direct labor - Variable overhead) × 3000

= ($25 - $3.50 - $1.10 - $0.45) × 3000

= $19.95 × 3000

= $59850

Increase on Profit:

= $59850 - $55000

= $4850

5 0

3 years ago

What is √25x2y2/√xy in simplest form? assume x>0 and y>0. (I guessed and it's ,5√xy)

VikaD [51]

Answer:

25 sqrt(x y^3)

Step-by-step explanation:

6 0

3 years ago

Mindy can a drive a total of 375 miles on a full tank of gas, which is 25 gallons. Based on this information, what is the consta

stepan [7]

Answer:

Step-by-step explanation:

$\frac{25}{375} = \frac{1}{x}$

Cross multiply to get 25x = 375

Divide each side by 25 to get x = 15

5 0

2 years ago

Emily is making bracelets for herself and 6 of her friends she needs 1/5 of a yard of string to make each bracelet. How much str

frosja888 [35]

10 feet of string to make all the bracelets.

4 0

3 years ago

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