Ask question

Ask question

All categories

3 years ago

11

To get to the park from her house, Rachel walked 4 kilometers due north and then 3 kilometers due west. On the way back, she cut

across a field, taking the shortest
possible route home,
How far did Rachel walk on the round-trip?

1 answer:

Natasha_Volkova [10]3 years ago

4 0

Answer:

12 km

Step-by-step explanation:

Using the Pythagorean Theorem, you know that 3^2 + 4^2 = x^2, so 9 + 16 = x^2, which means that x = the square root of 25, which is 5. Then you add all three lengths of the triangle together to get the round trip. 3 + 4 + 5= 12.

You might be interested in

One pound of candies costs $3.50. How much will we have to pay for 3 lb?

Romashka-Z-Leto [24]

Answer: 10.50 dollars

Step-by-step explanation:

3.50 x 3 = 10.50

8 0

3 years ago

You stand a known distance from the base of the tree, measure the angle of elevation the top of the tree to be 15â—¦ , and then

gogolik [260]

Answer:

The maximum possible error of in measurement of the angle is $d\theta_1 =(14.36p)^o$

Step-by-step explanation:

From the question we are told that

The angle of elevation is $\theta_1 = 15 ^o = \frac{\pi}{12}$

The height of the tree is h

The distance from the base is D

h is mathematically represented as

$h = D tan \theta$ Note : this evaluated using SOHCAHTOA i,e

$tan\theta = \frac{h}{D}$

Generally for small angles the series approximation of $tan \theta \ is$

$tan \theta = \theta + \frac{\theta ^3 }{3}$

So given that $\theta = 15 \ which \ is \ small$

$h = D (\theta + \frac{\theta^3}{3} )$

$dh = D (1 + \theta^2) d\theta$

=> $\frac{dh}{h} = \frac{1 + \theta ^2}{\theta + \frac{\theta^3}{3} } d \theta$

Now from the question the relative error of height should be at most

$\pm p$ %

=> $\frac{dh}{h} = \pm p$

=> $\frac{1 + \theta ^2}{\theta + \frac{\theta^3}{3} } d \theta = \pm p$

=> $d\theta = \pm \frac{\theta + \frac{\theta^3}{3} }{1+ \theta ^2} * \ p$

So for $\theta_1$

$d\theta_1 = \pm \frac{\theta_1 + \frac{\theta^3_1 }{3} }{1+ \theta_1 ^2} * \ p$

substituting values

$d [\frac{\pi}{12} ] = \pm \frac{[\frac{\pi}{12} ] + \frac{[\frac{\pi}{12} ]^3 }{3} }{1+ [\frac{\pi}{12} ] ^2} * \ p$

=> $d\theta_1 = 0.25 p$

Converting to degree

$d\theta_1 = (0.25* 57.29) p$

$d\theta_1 =(14.36p)^o$

4 0

3 years ago

2y + 12 = -3x<br><br> solve pls i have more

frutty [35]

I believe that y=-1.5x-6 is the answer.

6 0

3 years ago

Read 2 more answers

The number of electoral votes each state is assigned is determined by the size of its population every ten years. The chart show

sattari [20]

Answer:

D. $Q_3=47$

Step-by-step explanation:

We have been given a table that represents the the number of electoral votes California was assigned each decade of the past century. We are asked to find the 3rd quartile of our given data.

The number of votes are: 9, 13, 13, 22, 25, 32, 40, 45, 47, 54, 55.

We will use upper quartile formula to solve our given problem.

$Q_3=\frac{3}{4}*(n+1)^{\text{th term}}$ , where, n represents the number of elements in the data set.

We can see that our data set has 11 data points, so upon substituting n=11 in above formula we will get,

$Q_3=\frac{3}{4}*(11+1)^{\text{th term}}$

$Q_3=\frac{3}{4}*(12)^{\text{th term}}$

$Q_3=3*3^{\text{th term}}$

$Q_3=9^{\text{th term}}$

Now let us count 9th term of our data set. Upon counting our data set from left to right we can see that 9th term of our data set is 47, therefore, 3rd quartile of our given data is 47 and option D is the correct choice.

3 0

3 years ago

Read 2 more answers

In order to clear out room for new merchandise, James decided to mark down some of the items for sale in his electronics store.

sergiy2304 [10]

Answer:

a) Which item’s price was reduced by more, and by how many dollars more was it reduced?

The DVD player's price was reduced more by $3.82 than the stereo tuner's price.

b) Round all dollar values to the nearest cent.

Rounding $3.82 dollars to the nearest cents

$1 = 100 cents

$3.82 =

3.82 × 100 cents

= 382 cents

The DVD player's price was reduced by 382 cents more than the stereo tuner's price

Step-by-step explanation:

Lets day the original price of the DVD player was $100

We are told the price was marked down to 36%

36% of $100 = $36

$100 - $36 = $64

We are told the DVD cost $41.60 after the markdown.

Original cost of DVD =

$41.60/$64 × 100 = $65

Lets the original price of the Stereo player was $100

We are told the price was marked down to 22%

22% of $100 = $22

$100 - $22 = $78

We are told the DVD cost $69.42 after the markdown.

Original cost of Stereo =

$69.42/$78 × 100 = $89

DVD = $65 - $41.60 = $23.40 less

Stereo = $89 - 69.42 = $19.58 less

Difference between the DVD and the Stereo is

$23.40 - $19.58 = $3.82

Therefore,the DVD player's price was reduced by $3.82 more than the stereo tuner's price

Rounding $3.82 dollars to the nearest cents

$1 = 100 cents

$3.82 =

3.82 × 100 cents

= 382 cents

8 0

3 years ago

Read 2 more answers