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3 years ago

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The smallest of three consecutive integers is added to four times the largest integer; the result so obtained is 15 less than th

ree times the middle integer. Find the integers.

1 answer:

Anton [14]3 years ago

3 0

Answer:

Let the three consecutive integers be x,x+1,x+2

ATQ

x+2(x+2)+15=4(x+1)

=3x+19=4x+4

= x=15

..... Hence. The nos. Are 15,15+1=16 and 15+2=17

Step-by-step explanation:

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Maru [420]

Answer:

32 times is the answer

8 0

3 years ago

Read 2 more answers

A man starts walking north at 2 ft/s from a point P. Five minutes later a woman starts walking south at 3 ft/s from a point 500

Vedmedyk [2.9K]

Answer:

The rate at which both of them are moving apart is 4.9761 ft/sec.

Step-by-step explanation:

Given:

Rate at which the woman is walking, $\frac{d(w)}{dt}$ = 3 ft/sec

Rate at which the man is walking, $\frac{d(m)}{dt}$ = 2 ft/sec

Collective rate of both, $\frac{d(m+w)}{dt}$ = 5 ft/sec

Woman starts walking after 5 mins so we have to consider total time traveled by man as (5+15) min = 20 min

Now,

Distance traveled by man and woman are $m$ and $w$ ft respectively.

⇒ $m=2\ ft/sec=2\times \frac{60}{min} \times 20\ min =2400\ ft$

⇒ $w=3\ ft/sec = 3\times \frac{60}{min} \times 15\ min =2700\ ft$

As we see in the diagram (attachment) that it forms a right angled triangle and we have to calculate $\frac{dh}{dt}$ .

Lets calculate h.

Applying Pythagoras formula.

⇒ $h^2=(m+w)^2+500^2$

⇒ $h=\sqrt{(2400+2700)^2+500^2} = 5124.45$

Now differentiating the Pythagoras formula we can calculate the rate at which both of them are moving apart.

Differentiating with respect to time.

⇒ $h^2=(m+w)^2+500^2$

⇒ $2h\frac{d(h)}{dt}=2(m+w)\frac{d(m+w)}{dt} + \frac{d(500)}{dt}$

⇒ $\frac{d(h)}{dt} =\frac{2(m+w)\frac{d(m+w)}{dt} }{2h}$ ...as $\frac{d(500)}{dt}= 0$

⇒ Plugging the values.

⇒ $\frac{d(h)}{dt} =\frac{2(2400+2700)(5)}{2\times 5124.45}$ ...as $\frac{d(m+w)}{dt} = 5$ ft/sec

⇒ $\frac{d(h)}{dt} =4.9761$ ft/sec

So the rate from which man and woman moving apart is 4.9761 ft/sec.

3 0

3 years ago

A basketball coach will select the members of a five-player team from among 9 players, including John and Peter. If the five pla

vivado [14]

Answer:

Step-by-step explanation:

Given that a basketball coach will select the members of a five-player team from among 9 players, including John and Peter.

Out of nine players five are chosen at random.

The team consists of John and Peter.

Hence we can sort 9 players as I group, John and Peter and II group 7 players.

Now the selection is 2 from I group and remaining 3 from II group.

Hence no of ways of selecting a team that includes both John and Peter= $2C2*7C3$ =35

Total no of ways = $9C5$ =126

= $\frac{2C2*7C3}{9C5}$ = $\frac{35}{126} =\frac{5}{18}$

6 0

3 years ago

I need help please?!!!!!

ozzi

Answer:

8

Step-by-step explanation:

plug in the number 4, it would be 5•4-12

Do 5•4=20

20-12=8

7 0

3 years ago

What is the area of a rectangle if 1 base is 14 in, the 2nd base is 3.5 in and the height is 8 in?

algol13

Check the picture below.

notice, we have three pair of sides, let's add them all up to get the area

$\stackrel{\textit{left and right}}{2(8\cdot 14)}+\stackrel{\textit{front and back}}{2(3.5\cdot 8)}+\stackrel{\textit{top and bottom}}{2(3.5\cdot 14)}\implies 378~in^2$

5 0

3 years ago