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If an egg is thrown up and off the roof of a 100 foot building with an initial upward velocity of 10 feet per second, how long u

Deffense [45]

The equation of the height as a function of time for this case is given by:
h (t) = - 16t ^ 2 + 10t + 100
By the time the egg hits the ground we have:
-16t ^ 2 + 10t + 100 = 0
We look for the roots of the polynomial:
t1 = -2.2069555463432966
t2 = 2.8319555463432966
As it is about time, we use the positive root:
t = 2.83 s
Answer:
it hits the ground at:
t = 2.83 s

8 0

4 years ago

Sebastian saved money in his piggy bank. He kept track on how much money he saved at the end of each week on the line graph belo

Luba_88 [7]

Answer:

$90

Step-by-step explanation:

Look at the number 7 on the bottom right of the graph. That means at the end of 7 weeks. Now look vertically up from there until you see a point directly above 7 weeks. Look to the left of that point, and you see that the point directly above 7 weeks is at the level of $90. That means that at the end of 7 weeks, he had $90.

4 0

4 years ago

Read 2 more answers

3. A mysterious metal medallion has a mass of 3,088 grams. Water is poured into a graduated glass container with a 10-by-10 cm s

velikii [3]

Answer:

Initial volume:

10*10*53 = 5300 cm³

Increased volume:

10*10*54.6 = 5460 cm³

Volume of the medallion:

5460 - 5300 = 160 cm³

Density = mass / volume

Density is:

3.088/160 = 19.3 g / cm³

6 0

3 years ago

A long-jumper lifts off 3 m after starting his run, and lands 6 m later. When he is 8 m from the start line, he is 5 cm above th

Alexeev081 [22]

Answer:

The equation of the parabola that models the path of the long jumper through the air is $y = -x^{2} +12$ × $x-27$

Step-by-step explanation:

Mathematically, we know that parabolas are second-order polynomials and every second-order polynomials, also known as quadratic functions, can be constructed by knowing three different points of the curve. The standard form of the parabola is:

$y = a$ × $x^{2} +b$ × $+ C$

Where:

x - Horizontal distance from the start line, measured in meters.

y - Height of the long jumper, measured in meters.

a,b,c - Polynomial constants, measured in $\frac{1}{m}$ , dimensionless and meters, respectively.

If we know that $(x_{1},y_{1}) = (3\,m, 0\,m), (x_{2},y_{2}) = (8\,m, 0.05\,m)$ and $(x_{3}, y_{3}) = (9\,m, 0\,m),$ this system of linear equations is presented below:

$9\cdot a + 3\cdot b + c = 0 (Eq. 1)81\cdot a + 9\cdot b + c = 0 (Eq. 2)64\cdot a + 8\cdot b + c = 0.05 (Eq. 3)$

The coefficients of the polynomial are, respectively:

$a = -\frac{1}{100}, b = \frac{3}{25}, c = -\frac{27}{100}$

The equation of the parabola that models the path of the long jumper through the air is $y' = -\frac{1}{100}\cdot x^{2}+\frac{3}{25}\cdot x -\frac{27}{100}.$