1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sladkih [1.3K]
3 years ago
6

A fire engine starts pumping water at 9:20 am at the rate of 800 gallons per minute. Another fire engine, pumping at the rate of

1000 gallons per minute, starts at 9:30 am. At what time will the two engines have pumped the same number of gallon
Mathematics
2 answers:
weqwewe [10]3 years ago
6 0

Answer:

At 10:10 am

Step-by-step explanation:

Hi to answer this question we have to write a system of equations:

  • <em>Fire engine 1: 800 m  </em>

Where m: pumping time of the engine

  • <em>Fire engine 2: 1000 (m-10) </em>

Because it starts 10 minute later  

So, putting together both equations:

800m = 1000(m-10)

800m = 1000m - 10000

10000 = 1000m-800m

10000= 200m

10000/200=m

50 =m (50 minutes after the first engine starts)

So, 9:20 am + 50 minutes : 10:10 am .

AleksAgata [21]3 years ago
4 0

Answer:

10:10 AM

Step-by-step explanation:

The first thing is to use an identical time variable for both cases, we will do it as follows:

Let t = number of minutes of pumping time of the first fire engine

Therefore, for the second fire truck it would be:

(t-10) = pumping time of the second fire engine, since it started 10 min after the first engine.

To find the value of t, we equalize the equations of the first engine and the second engine:

We know that the first one would be: 800 * t

And the second: 1000 * (t-10)

Thus

1000 * (t-10) = 800 * t

1000 * t - 10000 = 800t

1000 * t - 800 * t = 10000

200 * t = 10000

t = 10000/200

t = 50 minutes

In other words, 50 minutes after the first engine starts pumping, it equaled the second

To know the time they were matched it would be like this:

9:20 AM +: 50 = 10:10 AM

Therefore, at 10:10 AM both engines were matched.

To check the above we have to:

50 * 800 = 40000

40 * 1000 = 40000

Therefore, in that time, they were equalized.

You might be interested in
Austin Family Furniture purchases recliners directly from the manufacturer for $235.00 each. The recliners are marked up 185% of
Elina [12.6K]
235 times 1.85= 434.75
434.75+ 235=669.75
3 0
3 years ago
What is 2 + 2????????????????????
Bogdan [553]
4 would be your answer lol
3 0
3 years ago
Read 2 more answers
Simplify.<br><br> 5 - {-(-2)}<br><br> A)-3<br> B) 3<br> C)-7<br> D) 7
Fed [463]
<span>5 - {-(-2)}
</span>5 - {+2} (negative + negative = positive)
<span>5 - 2 (negative + positive = negative)
</span>3
5 0
3 years ago
The points (0, 3), (4, 0), (9, 0), (0, 11), and (14, 0) are plotted on the graph. On a coordinate plane, points (0, 3), (4, 0),
Advocard [28]

Answer:

can you take a picture it might make it easier for me

3 0
3 years ago
Read 2 more answers
First question, thanks. I believe there should be 3 answers
zysi [14]

Given: The following functions

A)cos^2\theta=sin^2\theta-1B)sin\theta=\frac{1}{csc\theta}\begin{gathered} C)sec\theta=\frac{1}{cot\theta} \\ D)cot\theta=\frac{cos\theta}{sin\theta} \\ E)1+cot^2\theta=csc^2\theta \end{gathered}

To Determine: The trigonometry identities given in the functions

Solution

Verify each of the given function

\begin{gathered} cos^2\theta=sin^2\theta-1 \\ Note\text{ that} \\ sin^2\theta+cos^2\theta=1 \\ cos^2\theta=1-sin^2\theta \\ Therefore \\ cos^2\theta sin^2\theta-1,NOT\text{ }IDENTITIES \end{gathered}

B

\begin{gathered} sin\theta=\frac{1}{csc\theta} \\ Note\text{ that} \\ csc\theta=\frac{1}{sin\theta} \\ sin\theta\times csc\theta=1 \\ sin\theta=\frac{1}{csc\theta} \\ Therefore \\ sin\theta=\frac{1}{csc\theta},is\text{ an identities} \end{gathered}

C

\begin{gathered} sec\theta=\frac{1}{cot\theta} \\ note\text{ that} \\ cot\theta=\frac{1}{tan\theta} \\ tan\theta cot\theta=1 \\ tan\theta=\frac{1}{cot\theta} \\ Therefore, \\ sec\theta\ne\frac{1}{cot\theta},NOT\text{ IDENTITY} \end{gathered}

D

\begin{gathered} cot\theta=\frac{cos\theta}{sin\theta} \\ Note\text{ that} \\ cot\theta=\frac{1}{tan\theta} \\ cot\theta=1\div tan\theta \\ tan\theta=\frac{sin\theta}{cos\theta} \\ So, \\ cot\theta=1\div\frac{sin\theta}{cos\theta} \\ cot\theta=1\times\frac{cos\theta}{sin\theta} \\ cot\theta=\frac{cos\theta}{sin\theta} \\ Therefore \\ cot\theta=\frac{cos\theta}{sin\theta},is\text{ an Identity} \end{gathered}

E

\begin{gathered} 1+cot^2\theta=csc^2\theta \\ csc^2\theta-cot^2\theta=1 \\ csc^2\theta=\frac{1}{sin^2\theta} \\ cot^2\theta=\frac{cos^2\theta}{sin^2\theta} \\ So, \\ \frac{1}{sin^2\theta}-\frac{cos^2\theta}{sin^2\theta} \\ \frac{1-cos^2\theta}{sin^2\theta} \\ Note, \\ cos^2\theta+sin^2\theta=1 \\ sin^2\theta=1-cos^2\theta \\ So, \\ \frac{1-cos^2\theta}{sin^2\theta}=\frac{sin^2\theta}{sin^2\theta}=1 \\ Therefore \\ 1+cot^2\theta=csc^2\theta,\text{ is an Identity} \end{gathered}

Hence, the following are identities

\begin{gathered} B)sin\theta=\frac{1}{csc\theta} \\ D)cot\theta=\frac{cos\theta}{sin\theta} \\ E)1+cot^2\theta=csc^2\theta \end{gathered}

The marked are the trigonometric identities

3 0
1 year ago
Other questions:
  • A Ferris wheel rotates 9π/8 radians prior to making a stop. The total height of the Ferris wheel is 246 ft. How far around did t
    8·1 answer
  • What is b for the equation y=1/3x+b??
    13·1 answer
  • I'm having trouble getting the answer and working out #4
    5·1 answer
  • Only the mr. William problems please!!
    14·2 answers
  • the markup on a restaurant meal is 250%. a meal cost $7.30 to produce. how much will the customer be charged before tax and tip?
    11·1 answer
  • Semicircles and quarter circles are types of arc lengths. Recall that an arc is simply part of a circle. We learned about the de
    7·1 answer
  • what kind of polygon is included in both a net of a triangular prism and a net of a rectangular prism
    8·2 answers
  • Of 1,050 randomly selected adults, 360 identified themselves as manual laborers, 280 identified themselves as non-manual wage ea
    14·1 answer
  • What is 3/4 +3/5 as a mixed number
    13·2 answers
  • It took Michael six hours to drive 312 miles. If he continues at that rate, how long will it take him to drive 520 miles?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!