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4 years ago

What’s the largest common prime number in 8x2y, 24y2, 18xy

Mathematics

1 answer:

Feliz [49]4 years ago

6 0

Answer:

24y2

Step-by-step explanation:

i did a test similar to this question and got the answer correct

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Evaluate the integral, show all steps please!

zalisa [80]

Answer:

$\dfrac{3}{2} \ln |x-4| - \dfrac{1}{2} \ln |x+2| + \text{C}$

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.

Given indefinite integral:

$\displaystyle \int \dfrac{x+5}{(x-4)(x+2)}\:\:\text{d}x$

Take partial fractions of the given fraction by writing out the fraction as an identity:

$\begin{aligned}\dfrac{x+5}{(x-4)(x+2)} & \equiv \dfrac{A}{x-4}+\dfrac{B}{x+2}\\\\\implies \dfrac{x+5}{(x-4)(x+2)} & \equiv \dfrac{A(x+2)}{(x-4)(x+2)}+\dfrac{B(x-4)}{(x-4)(x+2)}\\\\\implies x+5 & \equiv A(x+2)+B(x-4)\end{aligned}$

Calculate the values of A and B using substitution:

$\textsf{when }x=4 \implies 9 = A(6)+B(0) \implies A=\dfrac{3}{2}$

$\textsf{when }x=-2 \implies 3 = A(0)+B(-6) \implies B=-\dfrac{1}{2}$

Substitute the found values of A and B:

$\displaystyle \int \dfrac{x+5}{(x-4)(x+2)}\:\:\text{d}x = \int \dfrac{3}{2(x-4)}-\dfrac{1}{2(x+2)}\:\:\text{d}x$

$\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int ax^n\:\text{d}x=a \int x^n \:\text{d}x$\end{minipage}}$

If the terms are multiplied by constants, take them outside the integral:

$\implies \displaystyle \dfrac{3}{2} \int \dfrac{1}{x-4}- \dfrac{1}{2} \int \dfrac{1}{x+2}\:\:\text{d}x$

$\boxed{\begin{minipage}{5 cm}\underline{Integrating}\\\\$\displaystyle \int \dfrac{f'(x)}{f(x)}\:\text{d}x=\ln |f(x)| \:\:(+\text{C})$\end{minipage}}$

$\implies \dfrac{3}{2} \ln |x-4| - \dfrac{1}{2} \ln |x+2| + \text{C}$

Learn more about integration here:

brainly.com/question/27805589

brainly.com/question/28155016

4 0

2 years ago

If you were to plot (10, -2) and (-3, 8), what two quadrants would you be in?

Rasek [7]

Ten and negative 2 will be in q1 and negative 3 and 8 will be in q2

3 0

4 years ago

How much cardboard will be needed to make the box? 4 feet by 3 feet with a height of 2 feet

sergiy2304 [10]

Answer:

52 ft²

Step-by-step explanation:

When you are calculating the amount of cardboard needed to make a box, you are trying to the the surface area.

The formula for surface area of a rectangular prism is:

SA = 2(lw + hl + wh)

The dimensions for the box are written l X w X h (length times width times height).

We know:

l = 4

w = 3

h = 2

The units for surface area is the unit squared. Feet squared is ft². Be sure the include the units.

Substitute these numbers into the formula. When solving, solve in the BEDMAS order (brackets, exponents, division and multiplication, addition and subtraction).

SA = 2(lw + hl + wh) u²

SA = 2((4*3) + (2*4) + (3*2)) ft² Multiply within each smaller bracket

SA = 2(12 + 8 + 6) ft² Add inside the brackets

SA = 2(26) ft² Multiply

SA = 52 ft² Final answer

Therefore 52 square feet of cardboard will be needed to make the box.

8 0

3 years ago

What is the perimeter of this rectangle?

zubka84 [21]

Perimeter:24 units Horizontal side is 7 units and vertical side is 5 units. You first multiply 7 by 2 and 5 by 2. You will get 14 and 10. Then, you add 14+10. The answer would be 24.

7 0

3 years ago

Read 2 more answers

(GEOMETRY HELP PLS) What is the approximate measure of angle F? Use the law of sines to find the answer.

spayn [35]

You can just use sine.

Sin(F) = opposite/hypotenuse = 28/40.

F = $sin^{-1}$ (28/40)

Plug into your calculator.

44.4

7 0

3 years ago

Read 2 more answers