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3 years ago

Solve: 1/3a2 - 1/a =1/6a2 The solution is a =

Mathematics

2 answers:

aleksklad [387]3 years ago

8 0

Solve the rational equation by combining expressions and isolating the variable aa.

a≈−0.16641103,1.49400147

Flura [38]3 years ago

4 0

Answer:

a= 1/6 is the correct answer.

Step-by-step explanation:

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Suppose you invest $1400 at interest rate of 4.3% compounded continuously. How much will you have in the account after 7 years?

STatiana [176]

$\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1400\\ r=rate\to 4.3\%\to \frac{4.3}{100}\dotfill &0.043\\ t=years\dotfill &7 \end{cases} \\\\\\ A=1400e^{0.043\cdot 7}\implies A=1400e^{0.301}\implies A\approx 1891.69\implies \stackrel{\textit{rounded up}}{A=1892}$

3 0

2 years ago

Select the correct answer. A new building in the shape of a square pyramid is to be constructed. The slant height will be five t

marysya [2.9K]

From the information given about the square pyramid, the maximum base length of the building is 67.42 cm.

<h3>How do you determine the maximum side length?</h3>

We are given the following details are:

Base = b

Slant height (l) = 5b

The lateral surface area is calculated using:

L = 2bl

So, we have:

L = 2 * b * 5b

Evaluate the product

L = 10b²

The total surface area is calculated using:

T = L + b²

So, we have:

T = 10b² + b²

Evaluate the sum

T = 11b²

Recall that the maximum surface area is 50,000 square feet

So, we have:

11b² = 50000

Divide both sides by 11

b² = 50000/11

Taking the square root of both sides, we have

b = 67.42

Hence, the maximum base length of the building is 67.42 cm

Learn more about square pyramids at:

brainly.com/question/12146629

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8 0

1 year ago

Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis

Tju [1.3M]

The equations representing the circle having a diameter of 12 units and a center lying on y-axis are x² + (y – 3)² = 36, and x² + (y + 8)² = 36, making options 1, and 5 the two choices.

In the question, we are looking for the equations of the circle having a diameter of 12 units and a center lying on y-axis.

The standard form of the equation of a circle is (x - h)² + (y - k)² + r², where (h, k) is the center of the circle, and r is its radius.

A circle having a diameter of 12 units, will have a radius of 12/2 = 6 units. Thus, r = 6.

A circle having the center on the y-axis will have a center as (0, k) as all points on the y-axis have x-coordinate 0.

Thus, the equation of the circle, with a diameter of 12 units and the center lying on the y-axis takes the form:

x² + (y - k)² = 6², or, x² + (y - k)² = 36.

From the given options, the equations x² + (y – 3)² = 36, and x² + (y + 8)² = 36, are of this form.

Thus, the equations representing the circle having a diameter of 12 units and a center lying on y-axis are x² + (y – 3)² = 36, and x² + (y + 8)² = 36, making options 1, and 5 the two choices.

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The provided question is incomplete. The complete question is:

"Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.

x² + (y – 3)² = 36
x² + (y – 5)² = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x² + (y + 8)² = 36."

8 0

1 year ago

For every 14 ice cream cones you buy, you get 2 for free.how many cones will you get if you buy 56 cones

lianna [129]

Divide 56/14=4. That means that there are 4 14ns since you will get 2 for every 14 cones. Thay means that you will get 8 cones for free.

6 0

3 years ago

Of 136 randomly selected adults, 33 were found to have high blood pressure. Construct a 95% confidence interval for the true of

navik [9.2K]

Answer:

The 95% confidence interval of the proportion of all adults that have high blood pressure is 0.17059 < $\hat{p}$ < 0.314695

Step-by-step explanation:

The confidence interval for a proportion is given by the following formula;

$CI=\hat{p}\pm z\times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$

Where:

x = 33

n = 136

$\hat{p}$ = x/n = 33/136 = 0.243

z value for 95% confidence is 1.96

Plugging in the values, we have;

$CI=0.243\pm 1.96\times \sqrt{\frac{0.243(1-0.243)}{136}}$

Which gives;

0.17059 < $\hat{p}$ < 0.314695

Hence the 95% confidence interval of the proportion of all adults that have high blood pressure = 0.17059 < $\hat{p}$ < 0.314695

From the above we have;

23.2 < x < 42.798

Since we are dealing with people, we round down as follows;

23 < x < 42.

4 0

2 years ago