# How did West Africa trade routes affect the cultures of people along the way?

**MATH**

**f'(x)=1+3x−−√,f(4)=25f′(x)=1+3x,f(4)=25 Find ff.**

f'(x)=1+3x−−√f′(x)=1+3x f(x)=∫(1+3x−−√)dxf(x)=∫(1+3x)dx f(x)=x+3(x12+112+1)+cf(x)=x+3(x12+112+1)+c f(x)=x+3(x3232)+cf(x)=x+3(x3232)+c f(x)=x+3(23)x32+cf(x)=x+3(23)x32+c f(x)=x+2×32+cf(x)=x+2×32+c Now let’s find constant c , given f(4)=25…

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**MATH**

**f”'(t)=et+t−4f′′′(t)=et+t-4 Find ff.**

f”'(t)=et+t−4.f′′′(t)=et+t-4. Integrate this once: f”(t)=et+(−13)t−3+C1,f′′(t)=et+(-13)t-3+C1, twice: f'(t)=et+(−12)(−13)t−2+C1t+C2,f′(t)=et+(-12)(-13)t-2+C1t+C2, thrice:

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**MATH**

**f”'(t)=cos(t)f′′′(t)=cos(t) Find ff.**

f”'(t)=cos(t)f′′′(t)=cos(t) f”(t)=∫f”'(t)dtf′′(t)=∫f′′′(t)dt f”(t)=∫cos(t)dtf′′(t)=∫cos(t)dt f”(t)=sin(t)+c1f′′(t)=sin(t)+c1 f'(t)=∫(sin(t)+c1)dtf′(t)=∫(sin(t)+c1)dt f'(t)=−cos(t)+c1t+c2f′(t)=-cos(t)+c1t+c2 f(t)=∫f'(t)dtf(t)=∫f′(t)dt f(t)=∫(−cos(t)+c1t+c2)dtf(t)=∫(-cos(t)+c1t+c2)dt

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**MATH**

**f”(x)=6x+sin(x)f′′(x)=6x+sin(x) Find ff.**

You need to evaluate f, knowing the second derivative, hence, you need to use the following principle, such that: ∫f”(x)dx=f'(x)+c∫f′′(x)dx=f′(x)+c ∫f'(x)dx=f(x)+c∫f′(x)dx=f(x)+c Hence, you need to evaluate…

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**MATH**

**f”(x)=(23)x23f′′(x)=(23)x23 Find ff.**

f”(x)=23x23f′′(x)=23×23 f'(x)=∫23x23dxf′(x)=∫23x23dx f'(x)=23(x23+123+1)+c1f′(x)=23(x23+123+1)+c1 f'(x)=(23)(35)x53+c1f′(x)=(23)(35)x53+c1 f'(x)=25×53+c1f′(x)=25×53+c1 c_1 is constant f(x)=∫(25×53+c1)dxf(x)=∫(25×53+c1)dx…

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**MATH**

**f”(x)=x6−4×4+x+1f′′(x)=x6-4×4+x+1 Find ff.**

f”(x)=x6−4×4+x+1f′′(x)=x6-4×4+x+1 f'(x)=∫f”(x)dxf′(x)=∫f′′(x)dx f'(x)=∫(x6−4×4+x+1)dxf′(x)=∫(x6-4×4+x+1)dx f'(x)=x77−4(x55)+x22+x+c1f′(x)=x77-4(x55)+x22+x+c1 f'(x)=x77−4×55+x22+x+c1f′(x)=x77-4×55+x22+x+c1 f(x)=∫f'(x)dxf(x)=∫f′(x)dx…

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**MATH**

**f”(x)=20×3−12×2+6xf′′(x)=20×3-12×2+6x Find ff.**

f”(x)=20×3−12×2+6xf′′(x)=20×3-12×2+6x f'(x)=∫(20×3−12×2+6x)dxf′(x)=∫(20×3-12×2+6x)dxApplying the sum rule and power yields, f'(x)=20(x44)−12×33+6×22+c1f′(x)=20(x44)-12×33+6×22+c1 f'(x)=5×4−4×3+3×2+c1f′(x)=5×4-4×3+3×2+c1 f(x)=∫f'(x)dxf(x)=∫f′(x)dx…

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**MATH**

**f(x)=4−3(1+x2)−1,F(1)=0f(x)=4-3(1+x2)-1,F(1)=0 Find the antiderivative FF that satisfies the given…**

f(x)=4−3(1+x2)−1f(x)=4-3(1+x2)-1 F=∫(4−3(1+x2)−1)dxF=∫(4-3(1+x2)-1)dx F=∫4dx−∫31+x2dxF=∫4dx-∫31+x2dx F=4x−3arctan(x)+c1F=4x-3arctan(x)+c1 Let’s find constant c_1 , given F(1)=0 F(1)=0=4(1)−3arctan(1)+c1F(1)=0=4(1)-3arctan(1)+c1 0=4−3(π4)+c10=4-3(π4)+c1 c1=3π4−4c1=3π4-4…

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**MATH**

**f(x)=5×4−2×5,F(0)=4f(x)=5×4-2×5,F(0)=4 Find the antiderivative FF that satisfies the given…**

You need to evaluate the antiderivative F,under the given condition, such that: ∫f(x)dx=F(x)+c∫f(x)dx=F(x)+c Hence, you need to evaluate the indefinite integral of function f(x), such that:

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**MATH**

**f(x)=2+x21+x2f(x)=2+x21+x2 Find the most general antiderivative of the function. (Check…**

You need to evaluate the most general antiderivative, using the following rule, such that: ∫f(x)dx=F(x)+c∫f(x)dx=F(x)+c ∫2+x21+x2dx=∫1+x21+x2dx+∫11+x2dx∫2+x21+x2dx=∫1+x21+x2dx+∫11+x2dx

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**MATH**

**f(x)=x5−x3+2xx4f(x)=x5-x3+2xx4 Find the most general antiderivative of the function.**

You need to evaluate the most general antiderivative, using the following rule, such that: ∫f(x)dx=F(x)+c∫f(x)dx=F(x)+c

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**MATH**

**f(x)=2x−−√+6cos(x)f(x)=2x+6cos(x) Find the most general antiderivative of the function. (Check…**

You need to evaluate the most general antiderivative, using the following rule, such that: ∫f(x)dx=F(x)+c∫f(x)dx=F(x)+c ∫(2x−−√+6cosx)dx=∫2x−−√dx+∫6cosxdx∫(2x+6cosx)dx=∫2xdx+∫6cosxdx

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**MATH**

Integrating f gives (both integrals are well-known) 5ex−3sinh(x)+C,5ex-3sinh(x)+C, where CC is any constant. This is the answer. Checking by differentiation:…

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**MATH**

∫f(t)dt=∫sin(t)+2sinh(t)dt=∫sin(t)dt+2∫sinh(t)dt∫f(t)dt=∫sin(t)+2sinh(t)dt=∫sin(t)dt+2∫sinh(t)dtWe note that the derivative of cosh(t)=sinh(t)⇒ddxcosh(t)=sinh(t)⇒ddxsinh(t)=cosh(t)cosh(t)=sinh(t)⇒ddxcosh(t)=sinh(t)⇒ddxsinh(t)=cosh(t)This means that

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**MATH**

**h(θ)=2sin(θ)−sec2(θ)h(θ)=2sin(θ)-sec2(θ) Find the most general antiderivative of the function.**

The most general antiderivative H(θ)H(θ) of the function h(θ)h(θ) can be found using the following relation: ∫h(θ)dθ=H(θ)+c∫h(θ)dθ=H(θ)+c

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**MATH**

**r(θ)=sec(θ)tan(θ)−2eθr(θ)=sec(θ)tan(θ)-2eθ Find the most general antiderivative of the…**

The most general antiderivative R(θ)R(θ) of the function r(θ)r(θ) can be found using the following relation: ∫r(θ)dθ=R(θ)+c∫r(θ)dθ=R(θ)+c

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**MATH**

**g(t)=1+t+t2t√g(t)=1+t+t2t Find the most general antiderivative of the function.**

The most general antiderivative G(t) of the function g(t) can be found using the following relation: ∫g(t)dt=G(t)+c∫g(t)dt=G(t)+c

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**MATH**

**f(t)=3t4−t3+6t2t4f(t)=3t4-t3+6t2t4 Find the most general antiderivative of the function….**

The most general antiderivative F(t) of the function f(t) can be found using the following relation: ∫f(t)dt=F(t)+c∫f(t)dt=F(t)+c

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**MATH**

**f(x)=15−2xf(x)=15-2x Find the most general antiderivative of the function. (Check your answer…**

f(x)=15−2xf(x)=15-2x To determine the most general antiderivative of this function, take the integral of it. F(x)=∫f(x)dx=∫(15−2x)dxF(x)=∫f(x)dx=∫(15-2x)dx Then, apply the integral formula ∫cdu=cu+C∫cdu=cu+C and

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**MATH**

**f(x)=x2−−√3+xx−−√f(x)=x23+xx Find the most general antiderivative of the function….**

f(x)=x2−−√3+xx−−√f(x)=x23+xx To determine the most general antiderivative of this function, take the integral of f(x). F(x)=∫f(x)dx=∫(x2−−√3+xx−−√)dxF(x)=∫f(x)dx=∫(x23+xx)dx Express the radicals in…

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**MATH**

**f(x)=3x−−√−2x−−√3f(x)=3x-2×3 Find the most general antiderivative of the function. (Check…**

The most general antiderivative F(x) of the function f(x) can be found using the following relation: ∫f(x)dx=F(x)+c∫f(x)dx=F(x)+c ∫(3x−−√−2x−−√3)dx=∫(3x−−√)dx−∫(2x−−√3)dx∫(3x-2×3)dx=∫(3x)dx-∫(2×3)dx…

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**MATH**

**f(x)=e2f(x)=e2 Find the most general antiderivative of the function. (Check your answer by…**

e2e2 isn’t depend on x, so its antiderivative is x⋅e2.x⋅e2. The general antiderivative is x⋅e2+C,x⋅e2+C, where C is any constant. Let’s check: (x⋅e2+C)’=x’⋅e2+C’=1⋅e2+0=e2.(x⋅e2+C)′=x′⋅e2+C′=1⋅e2+0=e2.

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**MATH**

**f(x)=2–√f(x)=2 Find the most general antiderivative of the function. (Check your answer by…**

The answer is F(x)=x⋅2–√+C,F(x)=x⋅2+C, where C is any constant. Let’s check: F'(x)=(x⋅2–√+C)’=x’⋅2–√+0=1⋅2–√=2–√,F′(x)=(x⋅2+C)′=x′⋅2+0=1⋅2=2,QED.

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**MATH**

**f(x)=x3.4−2×2√−1f(x)=x3.4-2×2-1 Find the most general antiderivative of the function….**

The most general antiderivative F(x) of the function f(x) can be found using the following relation: ∫f(x)dx=F(x)+c∫f(x)dx=F(x)+c

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**MATH**

**f(x)=7×25+8x−45f(x)=7×25+8x-45 Find the most general antiderivative of the function.**

The most general antiderivative F(x) of the function f(x) can be found using the following relation: ∫f(x)dx=F(x)+c∫f(x)dx=F(x)+c ∫(7×25+8x−45)dx=∫(7×25)dx+∫(8x−45)dx∫(7×25+8x-45)dx=∫(7×25)dx+∫(8x-45)dx…

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**MATH**

**f(x)=x(2−x)2f(x)=x(2-x)2 Find the most general antiderivative of the function. (Check your answer…**

You need to evaluate the most general antiderivative, using the following rule, such that: ∫f(x)dx=F(x)+c∫f(x)dx=F(x)+c First, you need to open the brackets, such that:

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**MATH**

**f(x)=(x+1)(2x−1)f(x)=(x+1)(2x-1) Find the most general antiderivative of the function. (Check your…**

First, you need to open the brackets, such that: f(x)=(x+1)(2x−1)=2×2+x−1f(x)=(x+1)(2x-1)=2×2+x-1 You need to evaluate the most antiderivative of the function, such that: ∫f(x)dx=F(x)+c∫f(x)dx=F(x)+c

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**MATH**

**f(x)=8×9−3×6+12x3f(x)=8×9-3×6+12×3 Find the most general antiderivative of the function. (Check…**

You need to evaluate the most antiderivative of the function, such that: ∫f(x)dx=F(x)+c∫f(x)dx=F(x)+c ∫(8×9−3×6+12×3)dx=∫8x9dx−∫3x6dx+∫12x3dx∫(8×9-3×6+12×3)dx=∫8x9dx-∫3x6dx+∫12x3dx

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**MATH**

f(x)=12+34×2−45x3f(x)=12+34×2-45×3 To determine the most general antiderivative of this function, take the integral of f(x). F(x)=∫f(x)dx=∫(12+34×2−45×3)dxF(x)=∫f(x)dx=∫(12+34×2-45×3)dx Then, apply the integral formula

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**MATH**

**f(x)=(12)x2−2x+6f(x)=(12)x2-2x+6 Find the most general antiderivative of the function. (Check your…**

You need to evaluate the most antiderivative of the function, such that: ∫f(x)dx=F(x)+c∫f(x)dx=F(x)+c ∫((12)x2−2x+6)dx=∫(12)x2dx−∫2xdx+∫6dx∫((12)x2-2x+6)dx=∫(12)x2dx-∫2xdx+∫6dx

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**MATH**

**f(x)=x−3f(x)=x-3 Find the most general antiderivative of the function. (Check your answer by…**

f(x)=x−3f(x)=x-3 To find the general antiderivative of this function, we take its integral. F(x)=∫f(x)dx=∫(x−3)dxF(x)=∫f(x)dx=∫(x-3)dx Take the integral of each term. =∫xdx−∫3dx=∫xdx-∫3dx For the first…

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**PERSEPOLIS: THE STORY OF A CHILDHOOD**

**In Persepolis: The Story of a Childhood, how does Marjane Satrapi challenge the myth that Iran is…**

In Persepolis: The Story of a Childhood, Marjane Satrapi challenges Western audiences’ preconceived notions of Iran as a country of fundamentalists and terrorists in the introduction, through the…

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**LORD OF THE FLIES**

**How does Jack challenge Ralph? what is Ralph’s response?**

Jack challenges Ralph from the very beginning of the story and, just as the circumstances of the challenge change, Ralph’s response changes as well. At the first meeting when Jack challenges Ralph…

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**HISTORY**

**What were the three most influential events in Julius Caesar’s life?**

The three most influential events in the life of Julius Caesar are difficult to define with precision, as he had a long and storied career as a consul, general, and politician, all areas that could…

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**DANTE’S INFERNO**

**What parts of the Inferno prove the Medieval worldview of the 12th and 13th century, specifically…**

The synthetic ideas of the 12th and 13th centuries focused on synthesizing Christianity with reason. Up to this point, reason and faith had been seen as antithetical, as were philosophy and…

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**SCIENCE**

**What are four ways enzymes speed up the rate of a chemical reaction?**

The standard definition of an enzyme is a protein molecule that functions as a biological catalyst, allowing reactions to occur more quickly than they normally would. The reason enzymes are able to…

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**THE BOARDED WINDOW**

**What is the phyical setting to “The Boraded Window”?**

The physical setting for this singularly creepy story is a settlement a few miles outside of Cincinatti, Ohio. The year is 1830. The settlement had been hewn from the “immense and almost unbroken…

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**RELIGION**

**In the Bible, what is the forbidden fruit that Adam and Eve ate?**

According to Genesis, there are two special trees in the Garden of Eden: the tree of Life and the tree of the Knowledge of Good and Evil. In Genesis Chapter 2, God tells Adam and Eve that they may…

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**REFERENCE**

**How to write a 4-page summary on Alfred Binet? It’s for Psychology 101, and I don’t know where to…**

Alfred Binet is quite famous in the field of psychology, particularly in the sub-field of psychometrics, which is an area of study that attempts to quantify every psychological behavior, and…

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**HISTORY**

**How far can Henry Vll be credited for the successful government and administration of England?**

On October 2 1485, Henry Tudor defeated and killed King Richard III at the Battle of Bosworth Field. His coronation as King Henry VII not only established the Tudor dynasty but also brought to an…

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**HISTORY**

**What was the result of the education reform movement in the 19th century?**

There were various changes brought about by the educational reform movement of the 1800s. One of the areas of change involved the efforts of Horace Mann. Horace Mann believed teachers needed to be…

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**FAHRENHEIT 451**

**Describe the two machines used on Mildred.**

Early in the book, Fahrenheit 451, by Ray Bradbury, the protagonist, Guy Montag gets home from work to find that his wife, Mildred has taken an entire bottle of sleeping pills, so he calls in an…

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**THE RANSOM OF RED CHIEF**

**How did the criminals change throughout the story?**

At the beginning of the story, Sam says that “It looked like a good thing, but wait till I tell you.” So, initially, their plan seemed like a winner. Describing this initial state of confidence,…

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**THE LION AND THE JEWEL**

**In The Lion and the Jewel, what names do the villagers call Lakunle? Why was he given those…**

Throughout the play The Lion and the Jewel, Lakunle is an outspoken opponent of traditional Yoruba culture and is an enthusiastic supporter of Western civilization. At the beginning of the play,…

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**ROMEO AND JULIET**

**Why is the use of a sonnet appropriate for a play like Romeo and Juliet?**

In order to answer this question, we must first understand what a sonnet is. A sonnet is defined in the following manner: a poem, properly expressive of a single, complete thought,idea, or…

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**RELIGION**

**Explain the conflicting views that are in the Old Testament, which is a sacred book for both…**

There are a number of conflicting accounts in the Old Testament. The main logic for this is because scholars have accepted that dozens of authors wrote the Old Testament. These authors did not…

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**SCIENCE**

**What are three clues that indicate a chemical change has occurred?**

One big indication that a chemical change has occurred is a color change. Many times a chemical reaction will start as relatively colorless or only lightly colored (often times yellow). During…

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**HISTORY**

**How did West Africa trade routes affect the cultures of people along the way?**

The trans-Saharan trade network that was established between west Africa, Arabia, and Europe had dramatic cultural implications for people along the way. The most profound impact was the…

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**HATCHET**

**In the book Hatchet, where does Brian get his knowledge of the wilderness?**

As he crashes into the lake, Brian has basically no knowledge of the wilderness. He had flown over it previously to visit his father but never spent any significant time in it. The fact that his…

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**SINNERS IN THE HANDS OF AN ANGRY GOD**

**In Edwards’ view, what must sinners do to save themselves?**

This sermon, and others like it, was designed to be a wake up call intended to make people take religion more seriously. Full membership in the puritan church required a conversion experience….

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