3(x-4)=18. Solve the equation

A man starts walking north at 4 ft!s from a point . five minutes later a woman starts walking south at 5 ft!s from a point 500 f

damaskus [11]

Answer:

ds/dt = 6.98 ft/s

Step-by-step explanation:

- The speed of man due north Vm = 3 ft/s

- The speed of woman due south Vw = 4 ft/s

- Woman starts walking 5 mins later than man

Find:

At what rate are the people moving apart 15 min after the woman starts walking?

Solution:

- The total time for which the man is walking due north from P, is Tm:

Tm = 5 + 15 = 20 mins

- The total distance traveled by man in Tm mins is:

Dm = Tm*Vm

Dm = 20*60*3

Dm = 3,600 ft

- The total time for which the woman is walking due south from 500 ft due east from P, is Tw:

Tw = 15 = 15 mins

- The total distance traveled by man in Tw mins is:

Dw = Tw*Vw

Dw = 15*60*4

Dw = 3,600 ft

- The displacement between man and woman at any instance is (s) which can be related by pythagoras theorem as follows:

s^2 = (dm + dw)^2 + 500^2

Where, dm : Distance travelled by man at any time Tm

dw : Distance travelled by woman at any time Tw

- Differentiate s with respect to t:

2s*ds/dt = 2*(dm + dw)*(Vm + Vw)

s*ds/dt = (dm + dw)*(Vm + Vw)

ds/dt = [ (dm + dw)*(Vm + Vw) ] / s

- Evaluate the rate of separation of man and woman ds/dt by evaluating at instance Tm = 20 mins and Tw = 15 mins. We have:

ds/dt = [ (Dm + Dw)*(Vm + Vw) ] / sqrt ( (Dm + Dw)^2 + 500^2 )

- Plug in the values:

ds/dt = [ (3600 + 3600)*(3 + 4) ] / [sqrt ( (3600 + 3600)^2 + 500^2 )]

ds/dt = 6.98 ft/s

4 0

1 year ago

PLZ HELP MEEEEE!!!!! IN TEST

natima [27]

Plug it in.

y = -1, y1 = 1

x = 3, x1 = 1

-1 - 1 = m( 3 - 1)

-2 = 2m

m = -1

The slope is -1

y = -x +b

-1 = -3 +b

b = 2

The equation is y = -x + 2

Hope this helps.

7 0

4 years ago

Read 2 more answers

A frustum is made by removing a small cone from a similar large cone. Work out the volume of the frustum, below. Give your answe

AlekseyPX

Answer:

Step-by-step explanation:

volume of cone=1/3 πr²h

volume of frustum=vol of larger cone-vol of smaller cone=1/3πR²H-1/3πr²h

=1/3π(R²H-r²h)

=1/3π(4.5²×9-3²×6)

=1/3π×9×3(4.5×1.5-2)

=9π(6.75-2)

=9π×4.75

=42.75π cm³

3 0

3 years ago

Helpppp plzzz...plz give steps

uysha [10]

Answer:

Volume of hemisphere =

$\frac{2}{3} \pi \: r {}^{3}$

Given volume =

$18\pi \: cube$

$\frac{2}{3} \times \frac{22}{7} \: {r}^{3} = 18 \times \frac{22}{7}$

So pi is there on both the sides so it will be cut from both LHS and RHS

$\frac{2}{3} \times r {}^{3} = 18$

$2 \times r {}^{3 } = 18 \times 3$

$2 \times r {}^{3} = 54$

$r {}^{3} = \frac{54}{2}$

$r {}^{3} = 27$

$r = 3$

Therefore value of r=3 inches

If you are helped with my answer pls tag me brianliest I really want it... Plzz

THANK YOU

3 0

3 years ago

Read 2 more answers

A segment with endpoints A (4, 2) and C (1, 5) is partitioned by a point B such that AB and BC form a 1:3 ratio. Find B.

Furkat [3]

The coordinates of point B that divides the line in the ratio 1:3 is: ( C )(3.25, 2.75)

<h3>What is a line segment?</h3>

A line segment is formed by joining two points by a straight line.

Analysis:

The coordinates of point B(x,y) are gotten by the formula

x = $\frac{px2 + qx1}{p+q}$

y = $\frac{py2 + qy1}{p + q}$

where, x1 and y1 are coordinates of A and x2 and y2 are coordinates of B

are the values of the ratio p:q.

x1 = 4, x2 = 1 y1 = 5, y2 = 2, p = 1, q = 3

x = $\frac{(1 x 1) + (3 x 4)}{1 + 3}$ = 3.25

y = $\frac{(1 x 5) + ( 3 x 2)}{1+3}$ = 2.75

coordinates of B are ( 3.25, 2.75)

In conclusion, the coordinates of point B are (3.25, 2.75)

Learn more about line segment : brainly.com/question/2437195

#SPJ1

4 0

2 years ago