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3 years ago

What is the area of the figure? How do you find it?

Mathematics

1 answer:

Anika [276]3 years ago

7 0

The area of a square is just side times side. So 3 * 3 = 9.

There are 4 half-circles which is the same as 2 full circles. Area of a circle is pi * the radius squared or $A = \pi r^{2}$ .

So we do 2(pi * (1.5)²) >> 2(2.25pi) = 4.5pi.

Now we add our two areas together. So the area of the whole thing is represented by the equation 4.5pi + 9. Plug this into a calculator to get your accurate measurement.

4.5pi + 9 ≈ 23.137 m²

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Answer:

0.008 °C

Explanation:

<u>1) Write the changes in the temperature of the city over the 4 days in an easy way to read.</u>

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1.34 °C

- 5 / 7 °C

- 0.75 °C

4/9 ° C

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<u>2) Write the expression to show the average daily change in temperature.</u>

The average of a set of data is calculated with the expression:

Average = (sum of the data) / amount of data

Hence, you need to add the four change of temperature data and divide by 4.

The expression is:

Average = [ 1.34 °C + (- 5 / 7 °C) + ( - 0.75 °C) + 4/9 ° C ] / 4

<u>3) Write the steps to solve the expression:</u>

You can choose between adding fractions or adding the decimal forms of the numbers.

If you choose adding decimals, keep the complete decimals in your calculator, to avoid the accumulation of errors due to rounding. Round only the final result.

These are the steps.

<u>a. Find the decimal forms of the fractions:</u>

- 5/7 ≈ 0.71428

4 /9 ≈ 0.44444

1.34°C + (- 0.71428 °C) + (-0.75 °C) + 0.44444 °C ≈ 0.32019 °C

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<u>c. Divide the sum by the number of data (4)</u>

0.32019 °C / 4 ≈ 0.080004 °C

<u>4. Round to the nearest hundredth</u>

The place of the hundreth is the second after the decimal point, which is 8 in this case:

0.080004 °C ≈ 0.08 °C

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3 years ago

<img src="https://tex.z-dn.net/?f=4%20%20%20%7B%7D%5E%7Bx%20%7D%20%20%2B%206%20%7B%7D%5E%7Bx%7D%20%3D%209%20%7B%7D%5E%7Bx%7D%20%

Nookie1986 [14]

So, the value of x is 1.19

The question is an exponential equation

<h3>What is an exponential equation?</h3>

An exponential equation is a mathematical expression between two quantities in which one variable is raised to a power of the other variable.

Since $4^{x} + 6^{x} = 9^{x}$ ,

Dividing through by 4ˣ, we have

$\frac{4^{x} }{4^{x} } + \frac{6^{x} }{4^{x} } = \frac{9^{x} }{4^{x} } \\1 + (\frac{6}{4})^{x} } = (\frac{9}{4})^{x} } \\1 + (\frac{3}{2})^{x} } = (\frac{3^{2} }{2^{2} })^{x} } \\1 + (\frac{3}{2})^{x} } = (\frac{3}{2})^{2x} }$

Let y = (3/2)ˣ

So,

1 + y = y²

y² - y - 1 = 0

Using the quadratic formula to find y,

$y = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}$

where a = 1 b = -1 and c = -1

Substituting the values of the variables into the equation, we have

$y = \frac{-(-1) +/- \sqrt{(-1)^{2} - 4\times 1 \times (-1)} }{2\times 1}\\= \frac{1 +/- \sqrt{1 + 4} }{2}\\= \frac{1 +/- \sqrt{5} }{2}\\= \frac{1 - \sqrt{5} }{2} or \frac{1 + \sqrt{5} }{2}\\= \frac{1 - 2.236}{2} or \frac{1 + 2.236}{2}\\= \frac{- 1.236}{2} or \frac{3.236}{2}\\= -0.618 or 1.618$

Since y = (3/2)ˣ

Takung logarithm of both sides, we have

㏒y = ㏒(3/2)ˣ

㏒y = x㏒(3/2)

x = ㏒y/㏒(3/2)

x = ㏒y/㏒1.5

Since we do not have logarithm of a negative number, we use y = 1.618.

So, x = ㏒y/㏒1.5

x = ㏒1.618/㏒1.5

x = 0.2090/0.1761

x = 1.19

So, the value of x is 1.19

Learn more about exponential equation here:

brainly.com/question/11832081

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