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3 years ago

How far can light travel in 7 minutes?

Mathematics

2 answers:

Yanka [14]3 years ago

8 0

Answer:

92 million miles

Step-by-step explanation:

hope this helps

sorry if it is wrong

plz mark brainliest

11Alexandr11 [23.1K]3 years ago

4 0

Answer: 78120000 miles

Step-by-step explanation:

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A circular playground for a daycare center is to be covered with square tiles that are 9 inches on each side. The circle has a d

nydimaria [60]

Answer:

9 boxes

Step-by-step explanation:

$Area=\pi r^{2}$

Since 1 ft= 12 inches then with diameter of 12 ft, radius becomes 6 ft and converted to inches it's 6*12=72 in

$Area=\pi\times 72^{2}=16286.01632 in^{2}$

Area of 1 tile= 9*9=81

Number of tiles= $\frac {16286.01632
}{81}=201.0619298
\202 tiles$

Number of boxes= 202/25=8.08 boxes hence 9 boxes

5 0

3 years ago

Read 2 more answers

There are 135 people in a sport centre. 73 people use the gym. 59 people use the swimming pool. 31 people use the track. 19 peop

wlad13 [49]

Answer:

Probability that the person doesn't use any facility = 0.0889

Step-by-step explanation:

Total number of people in a sports center = 135

Number of people using gym 'G' = 73

Number of people using swimming pool 'P' = 59

Number of people using track 'T' = 31

Number of people using gym and pool (G∩P) = 19

Number of people using pool and track (P∩T) = 9

Number of people using gym and track (G∩T) = 16

Number of people using all three facilities (G∩P∩T) = 4

Therefore, from the rule of compound probability,

P(GUPUT) = P(G) + P(P) + P(T) - P(G∩P) - P(G∩T) - P(P∩T) + p(G∩P∩T)

We know probability of an event = $\frac{\text{Favorable event}}{\text{Total outcomes}}$

We will plug in the values of probabilities of each event in the formula.

P(GUPUT) = $\frac{73}{135}+\frac{59}{135}+\frac{31}{135}-\frac{19}{135}-\frac{9}{135}-\frac{16}{135}+\frac{4}{135}$

= $\frac{1}{135}(73+59+31-19-9-16+4)$

= $\frac{123}{135}$

And probability that a person doesn't use any facility = 1 - P(GUPUT)

= 1 - $\frac{123}{135}$

= $\frac{135-123}{135}$

= $\frac{12}{135}$

= $\frac{4}{45}$ ≈ 0.0889

7 0

4 years ago

Read 2 more answers

Find an equation of the tangent plane to the given parametric surface at the specified point.

Neko [114]

Answer:

Equation of tangent plane to given parametric equation is:

$\frac{\sqrt{3}}{2}x-\frac{1}{2}y+z=\frac{\pi}{3}$

Step-by-step explanation:

Given equation

$r(u, v)=u cos (v)\hat{i}+u sin (v)\hat{j}+v\hat{k}$ ---(1)

Normal vector tangent to plane is:

$\hat{n} = \hat{r_{u}} \times \hat{r_{v}}\\r_{u}=\frac{\partial r}{\partial u}\\r_{v}=\frac{\partial r}{\partial v}$

$\frac{\partial r}{\partial u} =cos(v)\hat{i}+sin(v)\hat{j}\\\frac{\partial r}{\partial v}=-usin(v)\hat{i}+u cos(v)\hat{j}+\hat{k}$

Normal vector tangent to plane is given by:

$r_{u} \times r_{v} =det\left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\cos(v)&sin(v)&0\\-usin(v)&ucos(v)&1\end{array}\right]$

Expanding with first row

$\hat{n} = \hat{i} \begin{vmatrix} sin(v)&0\\ucos(v) &1\end{vmatrix}- \hat{j} \begin{vmatrix} cos(v)&0\\-usin(v) &1\end{vmatrix}+\hat{k} \begin{vmatrix} cos(v)&sin(v)\\-usin(v) &ucos(v)\end{vmatrix}\\\hat{n}=sin(v)\hat{i}-cos(v)\hat{j}+u(cos^{2}v+sin^{2}v)\hat{k}\\\hat{n}=sin(v)\hat{i}-cos(v)\hat{j}+u\hat{k}\\$

at u=5, v =π/3

$=\frac{\sqrt{3} }{2}\hat{i}-\frac{1}{2}\hat{j}+\hat{k}$ ---(2)

at u=5, v =π/3 (1) becomes,

$r(5, \frac{\pi}{3})=5 cos (\frac{\pi}{3})\hat{i}+5sin (\frac{\pi}{3})\hat{j}+\frac{\pi}{3}\hat{k}$

$r(5, \frac{\pi}{3})=5(\frac{1}{2})\hat{i}+5 (\frac{\sqrt{3}}{2})\hat{j}+\frac{\pi}{3}\hat{k}$

$r(5, \frac{\pi}{3})=\frac{5}{2}\hat{i}+(\frac{5\sqrt{3}}{2})\hat{j}+\frac{\pi}{3}\hat{k}$

From above eq coordinates of r₀ can be found as:

$r_{o}=(\frac{5}{2},\frac{5\sqrt{3}}{2},\frac{\pi}{3})$

From (2) coordinates of normal vector can be found as

$n=(\frac{\sqrt{3} }{2},-\frac{1}{2},1)$

Equation of tangent line can be found as:

$(\hat{r}-\hat{r_{o}}).\hat{n}=0\\((x-\frac{5}{2})\hat{i}+(y-\frac{5\sqrt{3}}{2})\hat{j}+(z-\frac{\pi}{3})\hat{k})(\frac{\sqrt{3} }{2}\hat{i}-\frac{1}{2}\hat{j}+\hat{k})=0\\\frac{\sqrt{3}}{2}x-\frac{5\sqrt{3}}{4}-\frac{1}{2}y+\frac{5\sqrt{3}}{4}+z-\frac{\pi}{3}=0\\\frac{\sqrt{3}}{2}x-\frac{1}{2}y+z=\frac{\pi}{3}$

5 0

3 years ago

If a data set has only 1 outlier which value will always change when the outlier is excluded

blagie [28]

The median may stay the same.

The range will always change.

I dont think the last 2 will always change.

7 0

3 years ago

Jan,Mya, and sara ran a total of 64 miles last week. Jan and Mya ran the same number of miles. Sarah ran 8 less miles than Maya.

BaLLatris [955]

<span> Jan, Maya and Sarah run a total of 64 miles per week
How many miles did Sarah run if she ran less than 8 miles compare to Maya and Jan
Jan and Maya = x
Sarah = x
Total miles = 64

=> 64 = x + x + x-8
=> 64 = 3x – 8
=> 72 = 3x
=> x = 24
Since Jan and Maya ran the same miles, they ran 24 miles each
Since Sarah is 8 less than Maya’s and Jan’s ran each
=> x – 8
=> 24 -8
=> 16
Sarah ran 16 miles in a week.

</span>

7 0

3 years ago