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Natasha_Volkova [10]

2 years ago

12

Carl is on the school track team. To prepare for an upcoming race, he plans to run 207 miles total over the next 31 days. Write

an equation to determine how many miles, m, he needs to run per day, assuming he runs the same amount each day.

1 answer:

Mkey [24]2 years ago

8 0

207 divide 31 = 6.7 miles per day
y= days
x= distance
y=6.7

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2 years ago

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Let $f(x) = x^2$ and $g(x) = \sqrt{x}$. Find the area bounded by $f(x)$ and $g(x).$

Anna [14]

Answer:

$\large\boxed{1\dfrac{1}{3}\ u^2}$

Step-by-step explanation:

Let's sketch graphs of functions f(x) and g(x) on one coordinate system (attachment).

Let's calculate the common points:

$x^2=\sqrt{x}\qquad\text{square of both sides}\\\\(x^2)^2=\left(\sqrt{x}\right)^2\\\\x^4=x\qquad\text{subtract}\ x\ \text{from both sides}\\\\x^4-x=0\qquad\text{distribute}\\\\x(x^3-1)=0\iff x=0\ \vee\ x^3-1=0\\\\x^3-1=0\qquad\text{add 1 to both sides}\\\\x^3=1\to x=\sqrt[3]1\to x=1$

The area to be calculated is the area in the interval [0, 1] bounded by the graph g(x) and the axis x minus the area bounded by the graph f(x) and the axis x.

We have integrals:

$\int\limits_{0}^1(\sqrt{x})dx-\int\limits_{0}^1(x^2)dx=(*)\\\\\int(\sqrt{x})dx=\int\left(x^\frac{1}{2}\right)dx=\dfrac{2}{3}x^\frac{3}{2}=\dfrac{2x\sqrt{x}}{3}\\\\\int(x^2)dx=\dfrac{1}{3}x^3\\\\(*)=\left(\dfrac{2x\sqrt{x}}{2}\right]^1_0-\left(\dfrac{1}{3}x^3\right]^1_0=\dfrac{2(1)\sqrt{1}}{2}-\dfrac{2(0)\sqrt{0}}{2}-\left(\dfrac{1}{3}(1)^3-\dfrac{1}{3}(0)^3\right)\\\\=\dfrac{2(1)(1)}{2}-\dfrac{2(0)(0)}{2}-\dfrac{1}{3}(1)}+\dfrac{1}{3}(0)=2-0-\dfrac{1}{3}+0=1\dfrac{1}{3}$

6 0

2 years ago

How do I find the area. Please explain

olganol [36]

All you have to do is multiply it then you get the answer

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2 years ago

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ryzh [129]

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Function 1:

The starting point is (0,0.5)

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As x increases, y decreases

Step-by-step explanation:

In order to find the starting point, we need to plug in x=0.

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$y=3(0.5)^0\\\\y=3(1)\\\\y=3$

As we plug in increasing numbers into function#1, the y-value increases

As we plug in increasing numbers into function #2, the y-value is decreasing

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2 years ago

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nasty-shy [4]

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2 years ago