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nadezda [96]
3 years ago
5

**HELP!**

Mathematics
1 answer:
mr_godi [17]3 years ago
3 0
If two figures or lengths are similar, then the ratios of the corresponding lengths are equal.
Thus, 8/32 =5/x
          8x = 160
            x = 20 feet
Therefore, the length of the flag pole was 20 feet long
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What is the value of x is?
Nina [5.8K]

Answer:

96

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Decide if the situation involves a permutation... anyone?
ehidna [41]

Each medal is different and is handed out depending on the outcome of the race/order of the racers, so we're counting the number of permutations. 4 medals are given to 4 runners, so there are

4!=4\cdot3\cdot2\cdot1=24

possible ways to do it.

4 0
3 years ago
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
3 years ago
A conversion factor can be written _________ different ways. How do you select the most appropriate conversion factor?
DochEvi [55]

Answer:

can be written two ways

Step-by-step explanation:

A conversion factor is written based on the equality between the two units

5 0
3 years ago
Read 2 more answers
Factor completely: 2a2 − a − 10
bezimeni [28]
Correct answer is D.

2a^2-a-10
\\2a^2- 5a+4a -10
\\a(2a-5)+2(2a-5)
\\(2a-5)(a+2)
6 0
3 years ago
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