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Kaylis [27]
3 years ago
15

A 5 foot tall person walks away from a 12 foot tall lamppost at a constant rate of 4 feet per second. What is the rate that the

tip of the shadow moves away from the lamppost when the person is 9 feet away from the pole?
Mathematics
1 answer:
erastovalidia [21]3 years ago
4 0

Solution :

Given :

The height of the person is 5 foot.

The height of the lamppost is 12 foot.

Speed of the person away from the lamppost = 4 ft/s

Let the distance of the tip of the shadow of the perosn to the pole at t seconds after the person started walking away from the pole be d(t).

By similarity of the triangles, we see that

$\frac{12}{d}=\frac{5}{x}$  .................(i)

Here x is the distance from the person to the tip of the shadow. As it is given the speed of the person is 4 ft/s, then the distance of the person from the pole 4t. So we have,

x = d - 4t  .............(ii)

Putting (ii) in (i) and solving for d is

d(t) = 6.85 t

So now if we derive d(t), we will get the wanted rate of the tip of the shadow.

∴ d'(t) = 6.85 ft/s

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A new scooter is valued at $15 000.
aksik [14]

here

p= 15000

r=15%

t= 3 yrs

now

depreciation = p(1-r/100)^t

= 15000(1-15/100)^3

=9211.875

=9212 or 9211.88

4 0
3 years ago
Suppose the average tread-life of a certain brand of tire is 42,000 miles and that this mileage follows the exponential probabil
Ahat [919]

Answer: The probability that a randomly selected tire will have a tread-life of less than 65,000 miles is 0.7872 .

Step-by-step explanation:

The cumulative distribution function for exponential distribution is :-

P(X\leq x)=1-e^{\frac{-x}{\lambda}}, where \lambda is the mean of the distribution.

As per given , we have

Average tread-life of a certain brand of tire :  \lambda=\text{42,000 miles }

Now , the probability that a randomly selected tire will have a tread-life of less than 65,000 miles will be :

P(X\leq 65000)=1-e^{\frac{-65000}{42000}}\\\\=1-e^{-1.54761}\\\\=1-0.212755853158\\\\=0.787244146842\approx0.7872

Hence , the probability that a randomly selected tire will have a tread-life of less than 65,000 miles is 0.7872 .

8 0
3 years ago
What is 6,224 in scientific notation
meriva

Answer:

6.224  x 10^3 Hope this helped out :)

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the  

10 .If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

then you end up getting  6.224  x 10^3

4 0
3 years ago
7.3 homework help me
olga_2 [115]

Answer:

1. Yes

∆RST ~ ∆WSX

by SAS

2. Yes

∆ABC ~ ∆PQR

by SSS

3. Yes

∆STU ~ ∆JPM

by SAS

4. Yes

∆DJK ~ ∆PZR

by SAS

5. Yes

∆RTU ~ ∆STL

by SAS

5. Yes

∆JKL ~ ∆XYW

by SAS

6. No

7. Yes

∆BEF ~ ∆NML

by SAS

8. Yes

∆GHI ~ ∆QRS

by SSS

9. x=22

10. x=12

Step-by-step explanation:

1. RS/WS=ST/SX and m<RST=m<WSX

2. AB/PQ=8/6=4/3

BC/QR=AC/PR=12/9=4/3

AB/PQ=BC/QR=AC/PR

3. ST/JP=10/15=2/3

SU/JM=14/21=2/3

ST/JP=2/3=SU/JM

and m<TSU=70°=m<PJM

4. DK/PR=8/4=2

JK/ZR=18/9=2

DK/PR=2=JK/ZR

and m<DKJ=65°=m<PRZ

5. RT/ST=UT/LT

and m<RTU=m<STL

6. KL/YW=20/18=10/9

JL/XW=36/24=3/2

KL/YW=10/9≠3/2=JL/XW

7. BF/NL=24/16=3/2

BE/NM=39/26=3/2

BF/NL=3/2=BE/NM

and m<EBF=m<MNL

8. GH/QR=32/20=8/5

HI/RS=40/25=8/5

GI/QS=24/15=8/5

GH/QR=HI/RS=GI/QS=8/5

9. x/33=18/27

Simplifying the fraction on the right side of the equation:

x/33=2/3

Solving for x: Multiplying both sides of the equation by 33:

33(x/33)=33(2/3)

x=11(2)

x=22

10. x/16=9/12

Simplifying the fraction on the right side of the equation:

x/16=3/4

Solving for x: Multiplying both sides of the equation by 16:

16(x/16)=16(3/4)

x=4(3)

x=12

4 0
3 years ago
This question is realy hard so helpp
LUCKY_DIMON [66]

Answer:

Algebrically the result can be written as -

9 {x}^{2}  + 24x + 16

Step-by-step explanation:

Let the number be 'x'.

  1. When multiplied by 3 , algebrically it is written as "3x".
  2. When 4 is added to 3x , algebrically it is written as "3x + 4".
  3. When (3x + 4) is squared completely , algebrically it is written as - {(3x + 4)}^{2}  = 9 {x}^{2}  + 24x + 16
8 0
2 years ago
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