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3 years ago

PLS HELP ASAP NO TROLLS!

Mathematics

1 answer:

galben [10]3 years ago

7 0

Prop Q because the line opposite is the biggest making it the widest angle

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Gas is escaping from a spherical balloon at the rate of 12 ft3/hr. At what rate (in feet per hour) is the radius of the balloon

bija089 [108]

Answer:

This is the rate at which the radius of the balloon is changing when the volume is 300 $ft^3$ $\frac{dr}{dt}=-\frac{3}{225^{\frac{2}{3}}\pi ^{\frac{1}{3}}} \:\frac{ft}{h} \approx -0.05537 \:\frac{ft}{h}$

Step-by-step explanation:

Let $r$ be the radius and $V$ the volume.

We know that the gas is escaping from a spherical balloon at the rate of $\frac{dV}{dt}=-12\:\frac{ft^3}{h}$ because the volume is decreasing, and we want to find $\frac{dr}{dt}$

The two variables are related by the equation

$V=\frac{4}{3}\pi r^3$

taking the derivative of the equation, we get

$\frac{d}{dt}V=\frac{d}{dt}(\frac{4}{3}\pi r^3)\\\\\frac{dV}{dt}=\frac{4}{3}\pi (3r^2)\frac{dr}{dt} \\\\\frac{dV}{dt}=4\pi r^2 \frac{dr}{dt}$

With the help of the formula for the volume of a sphere and the information given, we find $r$

$V=\frac{4}{3}\pi r^3\\\\300=\frac{4}{3}\pi r^3\\\\r^3=\frac{225}{\pi }\\\\r=\sqrt[3]{\frac{225}{\pi }}$

Substitute the values we know and solve for $\frac{dr}{dt}$

$\frac{dV}{dt}=4\pi r^2 \frac{dr}{dt}\\\\\frac{dr}{dt}=\frac{\frac{dV}{dt}}{4\pi r^2} \\\\\frac{dr}{dt}=-\frac{12}{4\pi (\sqrt[3]{\frac{225}{\pi }})^2} \\\\\frac{dr}{dt}=-\frac{3}{\pi \left(\sqrt[3]{\frac{225}{\pi }}\right)^2}\\\\\frac{dr}{dt}=-\frac{3}{\pi \frac{225^{\frac{2}{3}}}{\pi ^{\frac{2}{3}}}}\\\\\frac{dr}{dt}=-\frac{3}{225^{\frac{2}{3}}\pi ^{\frac{1}{3}}} \approx -0.05537 \:\frac{ft}{h}$

7 0

4 years ago

Use the discriminant, b2 - 4ac, to determine which equation has complex solutions.

ruslelena [56]

Using the discriminant, the quadratic equation that has complex solutions is given by:

x² + 2x + 5 = 0.

<h3>What is the discriminant of a quadratic equation and how does it influence the solutions?</h3>

A quadratic equation is modeled by:

y = ax² + bx + c

The discriminant is:

$\Delta = b^2 - 4ac$

The solutions are as follows:

If $\mathbf{\Delta > 0}$ , it has 2 real solutions.

If $\mathbf{\Delta = 0}$ , it has 1 real solutions.

If $\mathbf{\Delta < 0}$ , it has 2 complex solutions.

In this problem, we want a negative discriminant, hence the equation is:

x² + 2x + 5 = 0.

As the coefficients are a = 1, b = 2, c = 5, hence:

$\Delta = 2^2 - 4(1)(5) = 4 - 20 = -16$

More can be learned about the discriminant of quadratic functions at brainly.com/question/19776811

#SPJ1

3 0

2 years ago

If you work for 10 hours you make 80$ how many do you make an hour

Valentin [98]

Answer:

Step-by-step explanation:

7 0

3 years ago

Find the perimeter of ABC with vertices A (1,1), B (7,1), and C (1,9)

Effectus [21]

Answer:

24 unit

Step-by-step explanation:

Given,

The vertices of the triangle ABC are,

A (1,1), B (7,1), and C (1,9),

By the distance formula,

$AB=\sqrt{(7-1)^2+(1-1)^2}=\sqrt{6^2}=6\text{ unit}$

$BC=\sqrt{(1-7)^2+(9-1)^2}=\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10\text{ unit}$

$CA=\sqrt{(1-1)^2+(1-9)^2}=\sqrt{8^2}=8\text{ unit}$

Thus, the perimeter of the triangle ABC = AB + BC + CA = 6 + 10 + 8 = 24 unit

4 0

3 years ago

Time spent using e-mail per session is normally distributed, with mu equals 11 minutes and sigma equals 3 minutes. Assume that

liq [111]

Answer:

a) 0.259

b) 0.297

c) 0.497

Step-by-step explanation:

To solve this problem, it is important to know the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$