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4 years ago

A large spherical balloon

Mathematics

1 answer:

mote1985 [20]4 years ago

3 0

V = (4/3)π*r^3
V' = 4π*r^2*r'
600 cm^3/min = 4π(30 cm)^2*r'

r' = (600 cm^3/min)/(4π(30 cm)^2) = 1/(6π) cm/min

The rate of change of radius is about 0.05305 cm/min.

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A factory can produce 60 TVs in 7 days. How long does it take to finish 400 TVs?<br>

andreev551 [17]

Answer:

57.12, but being precise and accurate, you might wanna put 58.

Step-by-step explanation:

So, there's this guy, his name is calculator.

3 0

4 years ago

An arithmetic sequence has t1 = 3, t2 = 10. Find tn, Sn.

Softa [21]

Answer:

see explanation

Step-by-step explanation:

the n th term of an arithmetic sequence is

$t_{n}$ = $t_{1}$ + (n - 1)d

given $t_{1}$ = 3 and $t_{2}$ = 10, then

$t_{2}$ = 3 + d = 10 ⇒ d = 10 - 3 = 7

$t_{n}$ = 3 + 7(n - 1) = 3 + 7n - 7 = 7n - 4

the sum to n terms of an arithmetic sequence is

$S_{n}$ = $\frac{n}{2}$ [2 $t_{1}$ + (n - 1)d ]

= $\frac{n}{2}$ [(2 × 3) + 7(n - 1) ]

= $\frac{n}{2}$ (6 + 7n - 7 )

= $\frac{n}{2}$ (7n - 1)

= $\frac{7}{2}$ n² - $\frac{1}{2}$ n

7 0

3 years ago

Jerry was comparing the points the bulls socered for different games he recorded 85,85, 86,77, 93 determine the mean median mode

maks197457 [2]

Answers:
Mean - 85.2
Median - 85
Mode - 85

Explanation:
Mean - 77+85+85+86+93=426/5 (the amount of data points given) = 85.2

Median - Organize the data points from least to greatest and eliminate the outermost numbers two at a time (one from both side) until you’re left with one.

Mode - The number that appears the most often in a given data set

3 0

3 years ago

Special right triangle

Karo-lina-s [1.5K]

Answer:

Step-by-step explanation:

6) taking 45 degrees as the reference angle,

the adjacent side is √6

The opposite side is x

The hypotenuse is y

Therefore, we would apply trigonometric ratio.

Tan # = opposite side / adjacent side

Tan 45 = x/√6

1 = x/√6

x = 1 × √6 = √6

Cos # = adjacent side/hypotenuse

Cos 45 = √6/y

Cos 45 expressed in surd form is √2/2. Therefore,

√2/2 = √6/y

y √2 = 2√6

y = (2√6)/√2

5 0

3 years ago

Find, correct to four decimal places, the length of the curve of intersection of the cylinder 16x2 + y2 = 16 and the plane x + y

lubasha [3.4K]

First find a parameterization for the curve of intersection.

Given the equation of a cylinder, a natural choice for a parameterization would be one utilizing cylindrical coordinates. Here,

$16x^2+y^2=16\implies x^2+\left(\dfrac y4\right)^2=1$

which suggests we could use

$\begin{cases}x(t)=\cos t\\y(t)=4\sin t\\z(t)\end{cases}$

with $0\le t\le2\pi$ , and we get $z(t)$ from the equation of the plane,

$x+y+z=12\implies z(t)=12-x(t)-y(t)=12-\cos t-4\sin t$

Now use the arc length formula:

$\displaystyle\ell=\int_0^{2\pi}\sqrt{\left(\dfrac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dz}{\mathrm dt}\right)^2}\,\mathrm dt$

$\displaystyle\ell=\int_0^{2\pi}\sqrt{\sin^2t+16\cos^2t+(\sin t-4\cos t)^2}\,\mathrm dt$

$\displaystyle\ell=\sqrt2\int_0^{2\pi}\sqrt{\sin^2t-4\cos t\sin t+16\cos^2t}\,\mathrm dt\approx\boxed{24.0878}$

4 0

4 years ago