answer.
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
Anastaziya
1 month ago
6

a falling object travels a distance given by the formula d=5t + 16t^2 ft, where t is measured in seconds. how long will it take

for the object to traveled 74 ft?
Mathematics
2 answers:
lawyer [12.5K]1 month ago
8 0

Answer:

The time required for the object to travel 74 feet is:

t=2\ seconds

Detailed breakdown:

The distance covered by a falling object in time t is described by the equation:

d=5t+16t^2

Now, we wish to calculate the time t necessary for the object to move 74 feet.

In other words, we need to determine t when d=74 ft.

That is:

16t^2+5t=74\\\\16t^2+5t-74=0

Any quadratic equation of the form:

ax^2+bx+c=0

can be resolved using the quadratic formula:

x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}

In our scenario:

a=16\,\ b=5\ and\ c=-74

Now, substituting these values into the formula gives us:

t=-2.313\ and\ t=2

Since the time cannot be negative.

Thus, we conclude:

t=2

zzz [12.3K]1 month ago
8 0

It is provided that

d=5t+16t^{2}

We need to determine t when d equals 74

Thus, 74=5t+16t^{2} or

16t^{2}+5t-74 = 0

16t^{2}+37t-32t-74 = 0

t(16t + 37) - 2(16t + 37) = 0

(t - 2)(16t + 37) = 0

t - 2 = 0 or 16t + 37 = 0

t cannot be negative.

Thus, t equals 2

Therefore, it will require 2 seconds for the object to cover 74 feet.










You might be interested in
Two planes A and B can each fly through still air at 550 mph. The distance from Paris to Los Angeles is 5000 miles. Wind blows f
PIT_PIT [12445]

Answer:2688.63 miles

Step-by-step explanation:

Given

The distance from Paris to Los Angeles d=5000 miles

Wind traveling at 100 mph from Los Angeles to Paris

The velocity of the plane through still air is v=550 mph

Relative velocity of Plane A is v_a=550-100 =450 mph since Plane A is heading against the wind

Relative velocity of Plane B is v_b=550+100=650 mph

Plane A departs at noon

Distance covered by Plane A in 1 hour =450\times 1=450 miles

The total separation distance between the planes is 5000-450=4550 miles

Assuming they meet after t hours

Distance covered by Plane B in that time frame =v_b\times t=650\times t

Distance traveled by Plane A in t hours is =v_a\times t=450 t

The total distance equals 4550 miles

4550=650t+450t

t=\frac{4550}{1100}

t=4.13 hr

Distance traveled by B is =650\times 4.136=2688.63 miles

thus, they meet at a point 2688.63 miles away from Los Angeles.

5 0
1 month ago
What is 65, 124 rounded to the nearest thousand
AnnZ [12381]
65,000. I'm quite certain because a 1 wouldn't be sufficient to shift the 5 higher.
7 0
22 days ago
Read 2 more answers
At the bank, Brent exchanges $50 in bills for 50 one-dollar coins. The total mass of the coins is 405 grams. ESTIMATE the mass o
Svet_ta [12734]
To determine the answer, you need to divide 405 by 50 to discover the weight of a single coin. The calculation should appear like this:
\frac{405}{50}
= 8.1
The precise weight is 8.1 grams, but if you are looking for an estimate, the conclusion should be
Approximately 8 grams for a one-dollar coin
4 0
1 month ago
Read 2 more answers
Two airplanes are flying to the same airport. Their positions are shown in the graph. Write a system of linear equations that re
zzz [12365]
To formulate the system, it's necessary to consider the slope of each line along with at least one point from each line. The two lines will connect each plane's location to their destination airport. It's important to note that the airport's coordinates represent the intersection of these two lines, corresponding to the solution of the system. First, the slope of the line from airplane one to the airport is: m = 2; this can be observed by plotting the two points. From airplane 1's location, the rise is 8 units while the run is 4 units to reach the airport, making the slope 8 divided by 4 = 2. We then insert the slope and point (2,4) into the point-slope form: y - 4 = 2(x - 4), which can be rearranged to standard form 2x - y = 0. For airplane two, the slope to the airport is obtained by observing the vertical decrease of 3 and a horizontal increase of 9 as we move from the airport to airplane 2. We then substitute the slope and the point (15,9) into the point-slope form: y - 9 = -1/3(x - 15), which can be rearranged to the standard form: x + 3y = 42. Consequently, the system of equations is: 2x - y = 0 and x + 3y = 42. Multiplying the first equation by 3 produces a system of: 6x - 3y = 0 and x + 3y = 42. Adding these equations results in the equation 7x = 42. Thus, x = 6, and by substituting this value back into 2x - y = 0, we determine y = 12. Thus, we demonstrate that the airport's coordinates do indeed comprise the solution to our system.
6 0
22 days ago
the diameter of a cylindrical box of CDs is 5 inches. The height of the box is 4 inches. Whuch measurement is closest to the tot
Svet_ta [12734]
To calculate the area, simply multiply 5 by 4, resulting in 20.
5 0
21 day ago
Read 2 more answers
Other questions:
  • Which graph matches the equation y+6=3/4(x+4)​
    5·2 answers
  • Suppose the clean water of a stream flows into Lake Alpha, then into Lake Beta, and then further downstream. The in and out flow
    14·1 answer
  • Happy is four times as old as Grumpy. The sum of their age is 100. How old are Happy and<br> Grumpy?
    15·2 answers
  • The average rate of the first part of Yi’s walk on a park loop was 4 miles per hour. She then met up with a friend and the two w
    5·2 answers
  • Using the info given, solve for the missing value of the right triangle. Round each angle to the nearest degree, each length to
    12·1 answer
  • PLEASE HELP A barrel in Jim's yard contains 60 gallons of water. Water leaks out of the barrel at a rate of 1 gallon every 10 mi
    12·1 answer
  • Triangle ABC is a right triangle and sin(53o) = StartFraction 4 Over x EndFraction. Solve for x and round to the nearest whole n
    12·1 answer
  • Mr. Barth is painting an arrow on the school parking lot. He draws the edges between the following points on the coordinate plan
    6·1 answer
  • Libby sold $60 worth of vegetables at the farmer's market. Jess sold 3/4ths of what Libby sold. Stephanie sold 1/3rd of what Jes
    10·2 answers
  • a car travels 1.2 miles from point a to point b. the car then turns at point b and travels 1.8 miles to point c before heading b
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!