12 more than 8.2 times n

An airplane makes a 400-mile trip against a head wind in 4 hours. The return trip takes 2.5 hours, the wind now being a tall win

tangare [24]

Answer:

$v_p=130\ miles/h$

$v_w=30\ miles/h$

Step-by-step explanation:

Lets call $v_p$ the the still-air speed of the plane and $v_w$ the speed of the wind. On the first part the speed of the plane relative to the ground will be $v_1=v_p-v_w$ , and on the second part it will be $v_2=v_p+v_w$ .

We know that the distance d=400 miles on the first and second parts are the same, so by the definition of velocity we will have:

$v_1=\frac{d}{t1}$

$v_2=\frac{d}{t2}$

Or:

$v_p-v_w=\frac{d}{t1}$

$v_p+v_w=\frac{d}{t2}$

Adding both equations:

$(v_p-v_w)+(v_p+v_w)=2v_p=\frac{d}{t1}+\frac{d}{t2}$

$v_p=\frac{1}{2}(\frac{d}{t1}+\frac{d}{t2})$

Which for our values is:

$v_p=\frac{1}{2}(\frac{400\ miles}{4h}+\frac{400\ miles}{2.5h})=130\ miles/h$

If instead of adding, we substact, we would have:

$(v_p+v_w)-(v_p-v_w)=2v_w=\frac{d}{t2}-\frac{d}{t1}$

$v_w=\frac{1}{2}(\frac{d}{t2}-\frac{d}{t1})$

Which for our values is:

$v_w=\frac{1}{2}(\frac{400\ miles}{2.5h}-\frac{400\ miles}{4h})=30\ miles/h$

6 0

4 years ago

4x^2+19x+19=0 to the nearest tenth

zzz [600]

Answer:

the answer is

Step-by-step explanation:

7 0

3 years ago

The line segment joining the points a (3,2) and b (5,1) is divided at the point p in the ratio 1:2 and p lies on the line 2x-18y

kumpel [21]

your answer would be 2x-18y+k=0

8 0

3 years ago

The results of a survey are shown in the pie chart below and the survey 28 students say their favorite dessert is ice cream how

Rainbow [258]

Answer:

12 students.

Step-by-step explanation:

The complete question would be:

If ice cream is the last dessert, then we can solve for how many percent of the students like ice cream. If we add the 4 desserts percent, it should be equal to 100%

Pie : 15%

Candy : 23%

Cake : 27%

Pie% + Candy% + cake% + ice cream% = 100%

15% + 23% + 27% + Ice cream% = 100%

65% + Ice cream% = 100%

Ice cream% = 100% - 65%

Ice cream % = 35%

Percent is a way of saying how many out of a 100. Before we can tell how many students like pie, we need to figure out how many students were surveyed.

It says here that 35% of them like ice cream and among the students, 28 students like ice cream. This means that 28 is 35% of a number, which will be the number of students surveyed.

So as a fraction:

$35\% = \dfrac{35}{100}$

We need to find a ratio that is proportional to that, with 28 as the part of the whole.

$\dfrac{35}{100} = \dfrac{28}{x}\\\\Cross-multiply\\\\35x = 28(100)\\\\35x = 2800\\\\Divide\;both\;sides\;by\;35\\\\\dfrac{35x}{35} = \dfrac{2800}{35}\\\\x=80$

So that is the number of students survey. Now to look for how may people like pie, we find what is 15% of 80. So we find the part of the whole this time:

$\dfrac{15}{100}=\dfrac{x}{80}\\\\15(80)=100x\\\\1200 = 100x\\\\\dfrac{1200}{100}=\dfrac{100x}{100}\\\\12 = x$

4 0

3 years ago

Lucas and William are playing a video game and they have scored a total of 20,000 points. Lucas scored 1000 more than Williams.

const2013 [10]

Answer:

Hey there!

The system can be written as

l+w=20000

w+1000=l

Let me know if this helps :)

8 0

3 years ago