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WITCHER [35]
2 years ago
7

Rui is a professional deep water free diver.

Mathematics
2 answers:
Vladimir [108]2 years ago
5 0
The correct question is 
<span>Rui is a professional deep water free diver. His altitude (in meters relative to sea level), xxx seconds after diving, is modeled by: d(x)=1/2x^2 -10x What is the lowest altitude Rui will reach?

we have that
</span>d(x)=(1/2)x² -10x

we know that
the function is quadratic (a parabola) 
so
<span>the lowest altitude (depth) is the vertex
</span>
using a graph tool
see the attached figure

the vertex is the point  (10,-50)
that means
His altitude (in meters relative to sea level), 10 seconds after diving is 50 meters under the sea level

therefore
the answer is
<span>the lowest altitude is 50 meters under the sea level</span>

Black_prince [1.1K]2 years ago
5 0

Answer:

its -50 meters

Step-by-step explanation:

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Mr. Cruz fills a 3-gallon water cooler for a family picnic. He brings plastic cups that each hold 12 fluid ounces of water. How
oksian1 [2.3K]

One gallon is equivalent to 128 fluid ounces

3 gallons is equivalent to 3*128 fluid ounces

= 384 fluid ounces

One plastic cup can hold 12 guide ounces

So cups needed will be 384/12

32 cups

8 0
1 year ago
Consider the initial value problem: 2ty′=8y, y(−1)=1. Find the value of the constant C and the exponent r so that y=Ctr is the s
VikaD [51]

The correct question is:

Consider the initial value problem

2ty' = 8y, y(-1) = 1

(a) Find the value of the constant C and the exponent r such that y = Ct^r is the solution of this initial value problem.

b) Determine the largest interval of the form a < t < b on which the existence and uniqueness theorem for first order linear differential equations guarantees the existence of a unique solution.

c) What is the actual interval of existence for the solution obtained in part (a) ?

Step-by-step explanation:

Given the differential equation

2ty' = 8y

a) We need to find the value of the constant C and r, such that y = Ct^r is a solution to the differential equation together with the initial condition y(-1) = 1.

Since Ct^r is a solution to the initial value problem, it means that y = Ct^r satisfies the said problem. That is

2tdy/dt - 8y = 0

Implies

2td(Ct^r)/dt - 8(Ct^r) = 0

2tCrt^(r - 1) - 8Ct^r = 0

2Crt^r - 8Ct^r = 0

(2r - 8)Ct^r = 0

But Ct^r ≠ 0

=> 2r - 8 = 0 or r = 8/2 = 4

Now, we have r = 4, which implies that

y = Ct^4

Applying the initial condition y(-1) = 1, we put y = 1 when t = -1

1 = C(-1)^4

C = 1

So, y = t^4

b) Let y = F(x,y)................(1)

Suppose F(x, y) is continuous on some region, R = {(x, y) : x_0 − δ < x < x_0 + δ, y_0 −ę < y < y_0 + ę} containing the point (x_0, y_0). Then there exists a number δ1 (possibly smaller than δ) so that a solution y = f(x) to (1) is defined for x_0 − δ1 < x < x_0 + δ1.

Now, suppose that both F(x, y)

and ∂F/∂y are continuous functions defined on a region R. Then there exists a number δ2

(possibly smaller than δ1) so that the solution y = f(x) to (1) is

the unique solution to (1) for x_0 − δ2 < x < x_0 + δ2.

c) Firstly, we write the differential equation 2ty' = 8y in standard form as

y' - (4/t)y = 0

0 is always continuous, but -4/t has discontinuity at t = 0

So, the solution to differential equation exists everywhere, apart from t = 0.

The interval is (-infinity, 0) n (0, infinity)

n - means intersection.

7 0
2 years ago
NEED HELP!!!! Based on this part of the soliloquy, which best describes Hamlet’s perception of life?
ANEK [815]
<span>He believes that life is full of pain and suffering.</span>
7 0
2 years ago
Read 2 more answers
One of the greatest assets of a secretary is often his/her ability on the keyboard of a computer. Mrs. Garcia has been recognize
GalinKa [24]
Y=70x
If she types at a consistent speed for 49 minutes she will have typed 3,430 words.
7 0
2 years ago
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Hikers came across a part of a redwood stump. If the length of the chord is 8 feet, what was the diameter of the tree?
erastova [34]
So in the problem, the length of the chord there is the circumference of the tree. So in order to get the diameter of the tree, we must use the formula in getting the circumference of a circle that is stated as follows. 

C = 2pi *Radius

so first we need the get the radius of the tree which represent by this formula:

Radius = C /2pi = 8/6.2832 = 1.2732 ft 
Diameter = 2*radius = 2 * 1.27 32 = 2.5465 feet 

In summary, the diameter of the tree is 2.565 feet. 


7 0
2 years ago
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