You go to a store to pick up milk and cereal. You see that the milk costs $4

Mathematics

2 answers:

PolarNik [594]3 years ago

4 0

Use the estimate but that should be more than the exact price

Sholpan [36]3 years ago

4 0

Answer: your answer is a

Step-by-step explanation: it honestly depends on what money you have but because it is an odd number i would say to just estimate

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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

Prove: If n is a positiveinteger and n2 is<br> divisible by 3, then n is divisible by3.

notka56 [123]

Answer:

If $n^2$ is divisible by 3, the n is also divisible by 3.

Step-by-step explanation:

We will prove this with the help of contrapositive that is we prove that if n is not divisible by 3, then, $n^2$ is not divisible by 3.

Let n not be divisible by 3. Then $\frac{n}{3}$ can be written in the form of fraction $\frac{x}{y}$ , where x and y are co-prime to each other or in other words the fraction is in lowest form.