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Anna35 [415]
3 years ago
7

Delete this question please. I don't know how to delete this question.

Mathematics
1 answer:
Serhud [2]3 years ago
8 0
I don’t think you can delete questions
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NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)=−4.9t2+121t
Alenkasestr [34]

NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by

h(t)=-4.9t^2+121t+283

The sea level is represented by h = 0, therefore, to find the corresponding time when h splashes into the ocean we have to solve for t the following equation:

h(t)=0\implies-4.9t^2+121t+283=0

Using the quadratic formula, the solution for our problem is

\begin{gathered} t=\frac{-(121)\pm\sqrt{(121)^2-4(-4.9)(283)}}{2(-4.9)} \\ =\frac{121\pm142.083778...}{9.8} \\ =\frac{121+142.083778...}{9.8} \\ =26.8452834694... \end{gathered}

The rocket splashes after 26.845 seconds.

The maximum of this function happens at the root of the derivative. Differentiating our function, we have

h^{\prime}(t)=-9.8t+121

The root is

-9.8t+121=0\implies t=\frac{121}{9.8}=12.347

Then, the maximum height is

h(12.347)=1029.99

1029.99 meters above sea level.

6 0
1 year ago
What complex number is represented by the polar coordinates (4, -pi/4)
nexus9112 [7]

Answer:

\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}

Step-by-step explanation:

A complex number is defined as z = a + bi. Since the complex number also represents right triangle whenever forms a vector at (a,b). Hence, a = rcosθ and b = rsinθ where r is radius (sometimes is written as <em>|z|).</em>

Substitute a = rcosθ and b = rsinθ in which the equation be z = rcosθ + irsinθ.

Factor r-term and we finally have z = r(cosθ + isinθ). How fortunately, the polar coordinate is defined as (r, θ) coordinate and therefore we can say that r = 4 and θ = -π/4. Substitute the values in the equation.

\displaystyle \large{z=4[\cos (-\frac{\pi}{4}) + i\sin (-\frac{\pi}{4})]}

Evaluate the values. Keep in mind that both cos(-π/4) is cos(-45°) which is √2/2 and sin(-π/4) is sin(-45°) which is -√2/2 as accorded to unit circle.

\displaystyle \large{z=4\left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2}}{2}i \right)}\\\\\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}

Hence, the complex number that has polar coordinate of (4,-45°) is \displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}

3 0
2 years ago
For the given graph shown , select the statement that best represents the given system of equations.
svetlana [45]
The answer should be A
please let me know if this is wrong
3 0
3 years ago
The display gives the result of performing a quadratic regression on a data set where the inputs are speeds in miles per hour an
alina1380 [7]
Y = a x² + b x + c
y = 0.0473809524 · 20² + 2.221428571 · 20 - 0.005952381 = 
= 18.95236 + 44.42875 - 0.05952381 = 63.374978 ≈ 63.4
Answer: C ) 63.4 ft.
7 0
3 years ago
10 1/2 divided by 3/8
gladu [14]
(10 1/2)/(3/8)
= (21/2)/(3/8) Convert to improper
= (21/2)*(8/3) Multiply by reciprocal of second
=(7/1)*(4/1) Cross reduce
=28 Multiply
5 0
3 years ago
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