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3 years ago

Solve the following inequality for c. Write your answer in the simplest form. 1+4(8c-6)<-6c-10-1

Mathematics

2 answers:

Damm [24]3 years ago

7 0

$\frac{x}{y} 6/19\\$ Answer:

c < 6/19

Step-by-step explanation:

velikii [3]3 years ago

7 0

This is the correct answer. Have an amazing day!

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The following integral requires a preliminary step such as long division or a change of variables before using the method of par

shtirl [24]

Division yields

$\dfrac{x^4+7}{x^3+2x} = x-\dfrac{2x^2-7}{x^3+2x}$

Now for partial fractions: you're looking for constants a, b, and c such that

$\dfrac{2x^2-7}{x(x^2+2)} = \dfrac ax + \dfrac{bx+c}{x^2+2}$

$\implies 2x^2 - 7 = a(x^2+2) + (bx+c)x = (a+b)x^2+cx + 2a$

which gives a + b = 2, c = 0, and 2a = -7, so that a = -7/2 and b = 11/2. Then

$\dfrac{2x^2-7}{x(x^2+2)} = -\dfrac7{2x} + \dfrac{11x}{2(x^2+2)}$

Now, in the integral we get

$\displaystyle\int\frac{x^4+7}{x^3+2x}\,\mathrm dx = \int\left(x+\frac7{2x} - \frac{11x}{2(x^2+2)}\right)\,\mathrm dx$

The first two terms are trivial to integrate. For the third, substitute y = x ² + 2 and dy = 2x dx to get

$\displaystyle \int x\,\mathrm dx + \frac72\int\frac{\mathrm dx}x - \frac{11}4 \int\frac{\mathrm dy}y \\\\ =\displaystyle \frac{x^2}2+\frac72\ln|x|-\frac{11}4\ln|y| + C \\\\ =\displaystyle \boxed{\frac{x^2}2 + \frac72\ln|x| - \frac{11}4 \ln(x^2+2) + C}$

7 0

3 years ago

What is the area cause I am having a hard trouble

fomenos

The figure consists of a triangle and two rectangles.

-----------------------------
Top Triangle:
-----------------------------
Height = 22 - 10 - 7 = 5cm
Base = 20 - 5 - 5 - 10cm
Area of triangle = 1/2 x 5 x 10 = 25 cm²

-----------------------------
Middle Rectangle:
-----------------------------
Length = 10cm
Width = 7cm
Area = 10 x 7 = 70 cm²

-----------------------------
Bottom Rectangle:
-----------------------------
Length = 20 cm
Width = 10 cm
Area = 20 x 10 = 200 cm²

-----------------------------
Total Area:
-----------------------------
Area = 25 + 70 + 200 = 295 cm²

-----------------------------
Answer: Area = 295 cm²
-----------------------------

6 0

4 years ago

Sarah wants to fence her garden, as shown below. Determine how much fencing to the nearst foot that

coldgirl [10]

Answer:

431.775 ft

Step-by-step explanation:

So basically we should first find the area of the rectangles which is 28 ft * 15 ft, which you get 420. Next for the semicircle, the diameter is 15 but we need the radius so you divide that by 2 to get 7.5 as the radius. Then u multiply 7.5 * π, or 3.14 to get 23.55. But since its a semicircle, or half a circle we divide 23.55 by 2 which is 11.775. Then we just add the results which is 420 ft and 11.755 ft to get a total area of 431.775 ft.

-Hope this helped!

4 0

4 years ago

Factor the trinomial x^2 - 3x - 40

Elenna [48]

The answer is (x+5)(x-8)
Hope this helps

8 0

4 years ago

Read 2 more answers

What is the value of 4 to the power of 3 divided by 2 to the power of 3

sp2606 [1]

Answer: