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iren [92.7K]
3 years ago
8

Suppose a toy rocket is launched vertically upward from the top of a building with an initial velocity of 128 feet per second. i

f air resistance is ignored, the rocket's h height after t seconds is given by the equation h = −16t2 +128t + 100. How long will the rocket's flight last? (to the nearest tenth of a second) A) 7.6 seconds B) 7.9 seconds C) 8.7 seconds D) 9.3 seconds

Mathematics
1 answer:
faltersainse [42]3 years ago
4 0

Answer:

Option C)

t = 8.7 s

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The projectile formula is

h(t) = a*t^2 + v*t + h0

Where,

v = initial vertical velocity of the rocket in feet per second

h0 = initial height of the rocket in feet

h(t) = −16t^2 +128t + 100

If we look at the graph, we can find the point in which the height becomes zero. The value for t at this point will represent the rocket's fight duration

For this problem,

t = 8.717 s

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horsena [70]

P(7,6), Q(1,6), R(4,2)

We have PQ parallel to the x axis. We'll call that the base,

b = 7 - 1 = 6

The altitude is then the y difference h = 6 - 2 = 4

The area is \frac 1 2 bh = \frac 1 2 (6)(4) = 12

Answer: 12 square units


In general we can use the shoelace formula for the area of any polygon given coordinates. We write the points like this:

(7,6), (1,6), (4,2)

(1,6), (4,2), (7,6)

The area is then half the absolute value of the sum of the cross products:

A = \frac 1 2 | 7(6)-6(1) + 1(2)-6(4) + 4(6)-2(7) | = \frac 1 2 |24| = 12


6 0
3 years ago
Read 2 more answers
Gabriel wants to paint the model. How
enyata [817]

Answer:

<h2>The area of the base is 144 square inches.</h2><h2>The area of each triangular face is 66 square inches.</h2><h2>Grabiel needs 408 square inches of paint.</h2>

Step-by-step explanation:

The complete problem is attached.

Notice that the figure is a square pyramid, where its base dimensions are 12 inches by 12 inches, which represents an area of

B=12 \times 12 = 144 \ in^{2}

The slant height of the pyramid is 11 inches, which allow us to find the area of each triangle face

A=\frac{1}{2}bh =\frac{1}{2}(12)(11)= 66 \ in^{2}

But there are four triangle faces, so A_{faces} =4(66)=264 \ in^{2}.

Therefore, the area of each triangular face is 66 square inches.

So, the total surface area would be the sum

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3 years ago
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Answer:

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(q+4/2)^2=3/2+16/4

taking the square root of both side

√(q+4/2)^2=√(3/2+16/4)

Note that the square will cancel the square root then you will take LCM on the right hand side

q+4/2=√6+16/4

q+4/2=√22/4

q= -4/2+-√22/4

q=(-4+_√22/4)

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3 years ago
The sales tax in mike's state is 6%. mike bought a jetta having a sales tax of $820. what was the cost of the vehicle? round to
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3 years ago
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astraxan [27]

Answer:

Mean age = 1271.27

Step-by-step explanation:

No of children = 77

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Mean age = No of children × age at which children first began to combine words

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Mean age = 1271.27

7 0
3 years ago
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