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Amiraneli [1.4K]

3 years ago

6

Before being put out of service, the supersonic jet Concorde made a trip averaging 120 mi/h less than the speed of sound for 0.1

h and 410 mi/h more than the speed of sound for 3.0 h. If the trip covered 3,990 mi, what is the speed of sound?

1 answer:

evablogger [386]3 years ago

8 0

Answer:

894.19 mi/hr

Step-by-step explanation:

Total distance of the trip = 3990 mi

Let the speed of the sound be 'x' miles per hour

Now,

Total distance = Speed × Time

Therefore,

According to the question

3,990 mi = [ ( x - 120 ) × 0.1 ] + [ ( x + 410 ) × 3.0 ]

or

3,990 mi = 0.1x - 12 + 3x + 1230

or

0.1x + 3x = 2772

or

3.1x = 2772

or

x = 894.19 mi/hr

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a ball is thrown with a slingshot at a velocity of 110ft/sec at an angle of 20 degrees above the ground from a height of 4.5 ft.

satela [25.4K]

Answer:

$t=2.47\ s$

Step-by-step explanation:

The equation that models the height of the ball in feet as a function of time is

$h(t) = h_0 + s_0t -16t ^ 2$

Where $h_0$ is the initial height, $s_0$ is the initial velocity and t is the time in seconds.

We know that the initial height is:

$h_0 = 4.5\ ft$

The initial speed is:

$s_0 = 110sin(20\°)\\\\s_0 = 37.62\ ft/s$

So the equation is:

$h (t) = 4.5 + 37.62t -16t ^ 2$

The ball hits the ground when when $h(t) = 0$

So

$4.5 + 37.62t -16t ^ 2 = 0$

We use the quadratic formula to solve the equation for t

For a quadratic equation of the form

$at^2 +bt + c$

The quadratic formula is:

$t=\frac{-b\±\sqrt{b^2 -4ac}}{2a}$

In this case

$a= -16\\\\b=37.62\\\\c=4.5$

Therefore

$t=\frac{-37.62\±\sqrt{(37.62)^2 -4(-16)(4.5)}}{2(-16)}$

$t_1=-0.114\ s\\\\t_2=2.47\ s$

We take the positive solution.

Finally the ball takes 2.47 seconds to touch the ground

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3 years ago

Roxanne bought a 40-inch television that measures 24 inches in height. What is the width of the television?

Natali5045456 [20]

Answer:

The width is 32 inches

Step-by-step explanation:

3 0

3 years ago

Look at the images please help

Wittaler [7]

Answer:

$SA=672\ yd^2$

The net in the attached figure

Step-by-step explanation:

we know that

The surface area of the square pyramid using a net, is equal to the area of a square plus the area of its four lateral triangular faces

so

$SA=16^2+4[\frac{1}{2}(16)(13)]$

$SA=256+416=672\ yd^2$

6 0

3 years ago

The quantity demanded x each month of Russo Espresso Makers is 250 when the unit price p is $138. The quantity demanded each mon

Stells [14]

Answer:

(a) $D(q)=\frac{-1}{25} q+148$

(b) $S(q)=\frac{1}{50}q+58$

(c) $p_{*} =88\\\\q_{*} =1500$

Step-by-step explanation:

(a) For the demand equation D(q) we have

<em>P1: 138 Q1: 250</em>

<em>P2: 108 Q2: 1000</em>

We can find <u><em>m</em></u>, which is the slope of the demand equation,

$m=\frac{p_{2} -p_{1} }{q_{2} -q_{1} }=\frac{108-38}{1000-250} =\frac{-30}{750}=\frac{-1}{25}$

and then we find b, which is the point where the curve intersects the y axis.

We can do it by plugging one point and the slope into the line equation form:

$y=mx+b\\\\D(q)=mq+b\\\\138=\frac{-1}{25}(250) +b\\\\138=-10+b\\\\138+10=b=148$

<em>With b: 148 and m: -1/25 we can write our demand equation D(q)</em>

$D(q)=\frac{-1}{25} q+148$

(b) to find the supply equation S(q) we have

<em>P1: 102 Q1: 2200</em>

<em>P2: 102 Q2: 700</em>

<em></em>

Similarly we find <em>m</em>, and <em>b</em>

$m=\frac{p_{2} -p_{1} }{q_{2} -q_{1} }=\frac{72-102}{700-2200} =\frac{-30}{-1500}=\frac{1}{50}$

$y=mx+b\\\\D(q)=mq+b\\\\72=\frac{1}{50}(700) +b\\\\72=14+b\\\\72-14=b=58\\$

<em>And we can write our Supply equation S(q):</em>

$S(q)=\frac{1}{50}q+58$

(c) Now we may find the equilibrium quantity q* and the equilibrium price p* by writing <em>D(q)=S(q)</em>, which means the demand <u><em>equals</em></u> the supply in equilibrium:

$D(q)=S(q)\\\\\frac{-1}{25}q+148=\frac{1}{50}q+58\\\\$

$148-58=\frac{1q}{50} +\frac{1q}{25} \\\\90= \frac{1q}{50} +\frac{2q}{50}\\\\90=\frac{3q}{50}\\ \\q=1500\\\\$

We plug 1500 as q into any equation, in this case S(q) and we get:

$S(q)=\frac{1}{50}q+58\\\\S(1500)=\frac{1}{50}(1500)+58\\\\S(1500)=30+58\\\\S(1500)=88$

Which is the equilibrium price p*.

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3 years ago

Trampoline Park has an admission fee, plus an hourly fee of $4.50. What is the initial value?

anzhelika [568]

Answer:

c?

Step-by-step explanation:

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3 years ago