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2 years ago

Find (f +g)(x) where f(x) = x+ 3 and g(x) = x + 4.

Mathematics

1 answer:

zlopas [31]2 years ago

7 0

Answer:

Correct answer is A

Step-by-step explanation:

In pic

Credits: Symbolab)

(Hope this helps can I pls have brainlist (crown)☺️)

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The base of a solid is the region in the first quadrant between the graph of y=x2 and the x -axis for 0≤x≤1 . For the solid, eac

nata0808 [166]

Answer:

The volume of the solid is π/40 cubic units.

Step-by-step explanation:

Please refer to the graph below.

Recall that the area of a semi-circle is given by:

$\displaystyle A=\frac{1}{2}\pi r^2$

The volume of the solid will be the integral from x = 0 to x = 1 of area A. Since the diameter is given by y, then the radius is y/2. Hence, the volume of the solid is:

$\displaystyle V=\int_0^1\frac{1}{2}\pi \left(\frac{y}{2}\right)^2\, dx$

Substitute:

$\displaystyle V=\frac{1}{2}\pi\int_0^1\left(\frac{x^2}{2}\right)^2\, dx$

Simplify:

$\displaystyle V=\frac{1}{2}\pi \int_0^1\frac{x^4}{4}\, dx$

Integrate:

$\displaystyle V=\frac{1}{2}\pi \left[\frac{x^5}{20}\Big|_0^1\right]$

Evaluate:

$\displaystyle V=\frac{\pi}{40}\left((1)^5-\left(0\right)^5\right)=\frac{\pi}{40}\text{ units}^3$

The volume of the solid is π/40 cubic units.

4 0

3 years ago

Find all points on the curve that have the given slope.x = 2cost, y= 8sint, slope =-1

tatuchka [14]

Answer:

$t_{1} = 0.422\pi \pm \pi\cdot i$ , $\forall \,i \in \mathbb{N}_{O}$

$t_{2} = 1.422\pi \pm \pi\cdot i$ , $\forall \,i \in \mathbb{N}_{O}$

Step-by-step explanation:

In the case of parametric equations, the slope of the curve is equal to:

$\frac{dy}{dx} = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }$

Where $\frac{dx}{dt}$ and $\frac{dy}{dt}$ are the first derivatives of $x$ and $y$ regarding $t$ . Let be $x(t) =2\cdot \cos t$ and $y(t) = 8\cdot \sin t$ , their first derivatives are found:

$\frac{dx}{dt} = -2\cdot \sin t$ and $\frac{dy}{dt} = 8\cdot \cos t$

Thus, equation for the slope is:

$\frac{dy}{dx} = -\frac{8\cdot \cos t}{2\cdot \sin t}$

$\frac{dy}{dx} = -\frac{4}{\tan t}$

If $\frac{dy}{dx} = -1$ , then:

$-1 = -\frac{4}{\tan t}$

$\tan t = 4$

Tangent is positive at 1st quadrant and is a function with a periodicity of $\pi$ , the set of solutions are:

$t_{1} = 0.422\pi \pm \pi\cdot i$ , $\forall \,i \in \mathbb{N}_{O}$

$t_{2} = 1.422\pi \pm \pi\cdot i$ , $\forall \,i \in \mathbb{N}_{O}$

7 0

3 years ago

What is x - the square root of -2

Lena [83]

Sqrt(-2), can be written as i * sqrt(2). Thus, our answer is x - i sqrt(2).

4 0

3 years ago

What is 80 divided by 15

elena-s [515]

80/15 simplfies to 5.33 repeating in decimal form.

7 0

4 years ago

Read 2 more answers

The equation shown below involves a perfect square trinomial. 4x2 + 20x + 25 = 7 Which of the following is a step in solving thi

fomenos

4 x^2 + 20 x + 25 = 7
Divide both sides by 4:
x^2 + 5 x + 25/4 = 7/4
Write the left-hand side as a square:
(x + 5/2)^2 = 7/4
Take the square root of both sides:
x + 5/2 = sqrt(7)/2 or x + 5/2 = -sqrt(7)/2
Subtract 5/2 from both sides:
x = sqrt(7)/2 - 5/2 or x + 5/2 = -sqrt(7)/2
Subtract 5/2 from both sides:
Answer: x = sqrt(7)/2 - 5/2 or x = -5/2 - sqrt(7)/2

3 0

4 years ago