All categories

4 years ago

HELP

2 answers:

7 0

I believe the answer is the ship is traveling at 21.25 MPH, started 10.5 miles from lighthouse and after 11 hours will be 244.25 miles from the lighthouse.

Afina-wow [57]4 years ago

7 0

<h2>Answer:</h2>

Ques 1)

After 11 hours, the cruise ship will be 244.25 nautical miles from the lighthouse.

Ques 2)

At the start of the journey, the cruise ship was 10.5 nautical miles from the lighthouse.

Ques 3)

The cruise ship is traveling at a speed of 21.25 nautical miles per hour.

<h2>Step-by-step explanation:</h2>

We are given a table that represents the number of hours and distance from the Lighthouse as:

Time (in hours) Distance from Lighthouse

(nautical miles)

2 53

4 95.5

6 138

10 223

12 265.5

As the speed is uniform hence, we can find the equation that represents the distance in term of the number of hours.

( As the speed is uniform hence, we get a constant slope i.e. we get a equation of a line)

As we know that the equation of a line passing through two points (a,b) and (c,d) is given by:

$y-b=\dfrac{d-b}{b-a}\times (x-a)$

Let (a,b)=(2,53) and (c,d)=(4,95.5)

where y denote the distance from lighthouse and x denotes the number of hours.

Hence, the equation of line is:

$y-53=\dfrac{95.5-53}{4-2}\times (x-2)\\\\\\y-53=21.25(x-2)\\\\y-53=21.25x-42.5\\\\y=21.25-42.5+53\\\\y=21.25x+10.5$

Now when x=11 we have:

$y=21.25\times 11+10.5\\\\\\y=244.25$

Hence,

After 11 hours, the cruise ship will be 244.25 nautical miles from the lighthouse.

Now when x=0 we have:

$y=21.25\times 0+10.5\\\\\\y=10.5$

Hence,

At the start of the journey, the cruise ship was 10.5 nautical miles from the lighthouse.

Now the speed of the cruise ship is equal to the slope of the equation.

We have slope=21.25

Hence,

The cruise ship is traveling at a speed of 21.25 nautical miles per hour.

You might be interested in

2.3.2: Michael Myers predicts that SAT scores predict college graduation rates in a linear fashion. U of M has an average SAT of

AleksAgata [21]

Answer:

$y = \frac{5000r}{3} -50$

Step-by-step explanation:

Represent the SAT score with y and the rate with r.

So, we have:

$(r_1,y_1) = (90\%,1450)$

$(r_2,y_2) = (69.6\%,1110)$

Required

Determine the equation in slope intercept form

First, we calculate the slope

$m =\frac{y_2 - y_1}{r_2 - r_1}$

This gives:

$m =\frac{1110 - 1450}{69.6\% - 90\%}$

$m =\frac{-340}{-20.4\%}$

Convert percentage to decimal

$m =\frac{-340}{-0.204}$

$m =\frac{340}{0.204}$

Multiply by 1000/1000

$m =\frac{340*1000}{0.204*1000}$

$m =\frac{340000}{204}$

$m = \frac{5000}{3}$

The equation is then calculated as:

$y - y_1 = m(r - r_1)$

This gives:

$y - 1450 = \frac{5000}{3}(r - 90\%)$

Open Bracket

$y - 1450 = \frac{5000r}{3} - \frac{5000}{3}*90\%$

Convert percentage to decimal

$y - 1450 = \frac{5000r}{3} - \frac{5000}{3}*0.90$

$y - 1450 = \frac{5000r}{3} - 5000*0.30$

$y - 1450 = \frac{5000r}{3} - 1500$

Make y the subject

$y = \frac{5000r}{3} - 1500+1450$

$y = \frac{5000r}{3} -50$

3 0

3 years ago

the difference between two numbers is 4. three times the smaller number is equal to two times the larger less two. find the numb

Nataliya [291]

The two numbers are 6 and 10

<em><u>Solution:</u></em>

Let "x" be the smaller number

Let "y" be the larger number

Given that difference between two numbers is 4

larger number - smaller number = 4

y - x = 4 ----- eqn 1

Also given that three times the smaller number is equal to two times the larger less two

three times smaller number = 2 times larger number less two

3x = 2y - 2 ---- eqn 2

From eqn 1,

y = 4 + x --- eqn 3

Substitute eqn 3 in eqn 2

3x = 2(4 + x) - 2

3x = 8 + 2x - 2

x = 6

From eqn 3,

y = 4 + 6 = 10

Thus the two numbers are 6 and 10

3 0

3 years ago

The dimensions of a rectangular prism are length is 2 1/4 feet width is 1 foot and height is 1 1/4 feet and the length of the si

miskamm [114]

Answer: A - 30 cubes

B - Volume of prism = feet³

Step-by-step explanation: We are given that the dimensions of the rectangualr prism is,

Length = = feet

Width = 1 foot

Height = = feet

Thus, the volume of the prism = Length × Width × Height

i.e. Volume of the prism = × 1 × = feet³

Now, the side of the cube = foot each.

Volume of the cube = = feet³

5 0

3 years ago

Read 2 more answers

Rewrite 24+84 using theGCF and the distributive property

irina1246 [14]

Answer:gcf is 12 .

12(2+7)

Step-by-step explanation:write gcf first then this ( and then think what is 24 times 12 which is the GCF which is 2 and think what is 84 divide 12 which is 7.Now put 12 ( 2+7)

Hope it helps :)

7 0

3 years ago

What’s is the same as 97.52 divided by 10

Tems11 [23]

You could do 97.52/10. The slash means divided by.

6 0

3 years ago