X2+8x=-1 complete the square

A spherical balloon is inflated so that its volume is increasing at the rate of 3 ft3/min. How fast is the diameter of the ballo

beks73 [17]

When an spherical balloon volume is increasing at the rate of $3ft^3/min$ then the diameter of the balloon is increasing $\frac{3}{2\pi }ft /min$

How can we find the rate of change of balloon's diameter ?

The volume of a spherical balloon is $v=\frac{4}{3} \pi r^3$

In form of diameter we can write as

$v=\frac{4}{3} \pi (\frac{D}{2} )^3\\=\frac{1}{6} \pi D^3$

Now we will differentiate both sides wrt to $t$ we get

$\frac{dv}{dt} =\frac{1}{6} \pi 3D^2 \frac{dD}{dt} \\\frac{dD}{dt} =\frac{2}{\pi D^2} \frac{dv}{dt} \\\\when r=1\\D=2ft$

Given in the question $\frac{dv}{dt} =3ft^3/min$

thus when we substitute the values we get

$\frac{dD}{dt} =\frac{2}{\pi *2^2} (3)\\\frac{dD}{dt}=\frac{3}{2\pi } ft/min$

Learn more about the differentiation here:

brainly.com/question/28046488

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3 0

2 years ago

How many feet are in a mile

stiks02 [169]

1mile=5280 feet that is the correct answer

5 0

2 years ago

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Let’s assume that, over the years, a paper and pencil test of anxiety yields a mean score of 35 for all incoming college freshme

vovangra [49]

Answer:

|t| = 2.235 > 2.093

we rejected null hypothesis.

It is not coming from population

Step-by-step explanation:

Step:-1

Let’s assume that, over the years, a paper and pencil test of anxiety yields a mean score of 35 for all incoming college freshmen.

μ = 35

small sample size n =20

mean of the sample x⁻ = 30

standard deviation of (S) = 10

Null hypothesis :- The difference between x⁻ and μ is not significant

Alternative hypothesis:- The difference between x⁻ and μ is significant

that is μ ≠ 35

Level of significance :-∝ =0.05

The test statistic:-

$t = \frac{x^{-} - population mean}{\frac{S}{\sqrt{n} } }$

substitute all values in above equation

μ = 35 ,n =20

mean of the sample x⁻ = 30

standard deviation of (S) = 10

$t = \frac{30 - 35}{\frac{10}{\sqrt{20} } }$

t= -2.235

|t| = 2.235

The degrees of freedom γ =n-1 =20-1 =19

By tabulated value of 't' for 19 degrees of freedom at 5% level of significance.= 2.093 for two tailed test.(see attached diagram below)

conclusion:-

|t| = 2.235 > 2.093

we rejected null hypothesis.

It is not coming from population

8 0

3 years ago

Which of the following inequalities is best represented by this graph?

Nataly [62]

For this case, the first thing to do is find the equation of the line correctly and then see which of the inequalities represents the shaded region.
We have then:
5x - y = 2
For x = 0
5 (0) - y = 2
-y = 2
y = -2
For y = 0
5x - 0 = 2
5x = 2
x = 2/5 = 0.4
Therefore the line is:
5x - y = 2
Then, we see that for the point (0, 0)
5x - y ≥ 2
5 (0) - (0) ≥ 2
0 ≥ 2
The inequality is not met, which is correct because this point is not part of the shaded region.
Answer:
The inequality that best is represented by the graph if:
5x - y ≥ 2

5 0

3 years ago

What is the question mark 7×5=35. 5=?

satela [25.4K]

The question mark is 1

7 0

3 years ago

Read 2 more answers