Answers
Step-by-step explanation:
we know from the laws of motion that in the equation
h = 20t - 1.86t²
the gravitational acceleration is in the factor of the t² term.
h = v0t + 1/2 × g × t²
v0 being the initial velocity (20 m/s).
and we can therefore see, that the gravitational acceleration "a" on Mars is 2×1.86 = 3.72 m/s²
(a)
the velocity v after 2 seconds is (first law of motion)
v = v0 + at = 20 - 3.72×2 = 12.56 m/s
gravity pulling down, so negative acceleration.
(b)
first we need the time when the rock is at 25 m.
25 = 20t - 1.86t²
0 = -1.86t² + 20t - 25
the solution to a quadratic equation is always
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = t
a = -1.86
b = 20
c = -25
t = (-20 ± sqrt(400 - 4×-1.86×-25))/(2×-1.86) =
= (-20 ± sqrt(214))/-3.72
t1 = (-20 + 14.62873884...)/-3.72 =
= 1.443887409... s ≈ 1.44 s
t2 = (-20 - 14.62873884...)/-3.72 =
= 9.308800763... s ≈ 9.31 s
that means, on its way up the rock reached 25m after
1.44 s.
on its way down the rock reached 25 m after
9.31 s.
velocity 0 (the rock came to a stop before falling back down) was after
0 = 20 - 3.72t
3.72t = 20
t = 20/3.72 = 5.376344086... s
that means the rock was falling after this point back to the ground and was gaining speed again.
that accelerating phase until the rock was again at 25 m was
9.308800763... - 5.376344086... = 3.932456677... s
long
the velocity at these points was
v-up = 20 - 3.72×1.443887409... = 14.62873884... m/s ≈
≈ 14.63 m/s
v-down = 0 + 3.72×3.932456677... = 14.62873884... m/s ≈
≈ 14.63 m/s
as expected : the rock did a perfectly symmetric flight path between the two 25 m marks.
so time and speed on both sides had to be identical.
but we have proven it.
Answer:
a) 12.56 m/s
b) up: 14.63 m/s (2 d.p.)
down: -14.63 m/s (2 d.p.)
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{The Constant Acceleration Equations (SUVAT)}\\\\s = displacement in m (meters)\\u = initial velocity in m s$^{-1}$ (meters per second)\\v = final velocity in m s$^{-1}$ (meters per second)\\a = acceleration in m s$^{-2}$ (meters per second per second)\\t = time in s (seconds)\\\\When using SUVAT, assume the object is modeled\\ as a particle and that acceleration is constant.\end{minipage}}[/tex]
The average gravitational acceleration on Mars is 3.721 m/s² (about 38% of that of Earth). The fact that the rock is thrown from the surface of Mars rather than the surface of Earth is of no consequence when using the equations of constant acceleration (SUVAT equations) as long as acceleration is not used in the calculations.
Part (a)Given:
[tex]s=20t-1.86t^2, \quad u=20, \quad t=2[/tex]
[tex]\begin{aligned}\textsf{Using }\: s&=\dfrac{1}{2}(u+v)t\\\\\implies 20(2)-1.86(2)^2 & = \dfrac{1}{2}(20+v)(2)\\\\32.56 & = 20+v\\\\v & = 32.56-20\\\\v & = 12.56\:\: \sf m/s\end{aligned}[/tex]
Therefore, the velocity of the rock after 2 s is 12.56 m/s.
Part (b)Find the time when the height of the rock is 25 m:
[tex]\begin{aligned}20t-1.86t^2 & = s\\\implies 20t-1.86t^2 & = 25\\1.86t^2-20t+25 & = 0\end{aligned}[/tex]
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore:
[tex]a=1.86, \quad b=-20, \quad c=25[/tex]
[tex]\implies t=\dfrac{-(-20) \pm \sqrt{(-20)^2-4(1.86)(25)} }{2(1.86)}[/tex]
[tex]\implies t=\dfrac{20 \pm \sqrt{214}}{3.72}[/tex]
[tex]\implies t=9.308800763..., 1.443887409...[/tex]
Therefore, the height of the rock is 25 m when:
t = 9.31 s (2 d.p.)t = 1.44 s (2 d.p.)To find the velocity (v) of the rock at these times, substitute the found values of t into the equation, along with s = 25 and u 20 m/s:
[tex]\begin{aligned}\textsf{Using }\: s&=\dfrac{1}{2}(u+v)t\\\\\implies v & = \dfrac{2s}{t}-u\\\\v & = \dfrac{2(25)}{t}-20\\\\v & = \dfrac{50}{t}-20\\\\\end{aligned}[/tex]
When t = 1.443887409...s
[tex]\implies v=\dfrac{50}{1.443887409...}-20=14.63\:\: \sf m/s \: \:(2\:d.p.)[/tex]
When t = 9.308800763...s
[tex]\implies v=\dfrac{50}{9.308800763...}-20=-14.63\:\: \sf m/s \: \:(2\:d.p.)[/tex]
Therefore, the velocity of the rock when its height is 25 m is:
up: 14.63 m/s (2 d.p.)down: -14.63 m/s (2 d.p.)Learn more about constant acceleration equations here:
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Related Questions
19 ft
4 ft
l
Find l.
l = √ [?] ft
Answers
Answer :LF is the abbreviation for linear feet Sq ft is the abbreviation for square feet L – lenght (e.g. room length) W – width (e.g. room width)
Liters to Cubic Feet formula. ft³ =. L * 0.035315. Show working Show result in exponential format More information: Cubic Feet.
Step-by-step explanation:
2^2 + 9^2 = L^2
4 + 81 = L^2
85 = L^2
L = square root of 85
Paula finished the race at 2:14 p.m Beatrice finished the race 22 minutes earlier what time did Beatrice finish the race a 1:54 p.m b 1:48 p.m. c 1:58 p.m. d 1:52 p.m. e none of these f I don't know yet
Answers
Answer: d: 1:52pm
Step-by-step explanation: Since Beatrice finished 22 minutes earlier, we subtract 22 minutes from 2:14. 2:14 - 14 is 2:00. 22-14 is 8. 2:00 - 8 is 1:52.
Find the critical value zα/2 that corresponds to the confidence level 84%.
Answers
The critical value z_α/2 that corresponds to the confidence level 84% is; 1.41
How to find the critical value?We want to find the two tail critical values.
This means that at an 84% confidence level, we want to get the probability of not rejecting the null value to be equal to a = 100% - 84% = 16%.
Now, z - scores refers to a numerical measurement that describes a value's relationship to the mean of a group of values and is gotten from normal distribution. Z-score is measured in terms of standard deviations from the mean.
However, under a normal distribution, we want a/2% = 16%/2 = 8% to be located right in the higher tail and lower tail.
From the above, it denotes that the critical value closest to 0.92 will give you the two tail 84% confidence interval. Utilizing a normal distribution table figure online to find the z score gives;
z = 1.41
Thus, we can conclude from this calculation that he critical value z_α/2 that corresponds to the confidence level 84% is; 1.41
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Two cyclists start at the same point and travel in opposite directions. One cyclist travels 5 faster than the other. If the two cyclists are 74 miles apart after 2 hours, what is the rate of each cyclist?
Answers
The rate of the slower cyclist is 16 mph while the rate of the faster cyclist is 21 mph.
How to calculate the rate of speed?let us assume the following;
x = rate of slower cyclist
x + 5 = rate of faster cyclist
We know that formula for distance is;
distance = travel time*rate
Thus;
2x + 2(x + 5) = 74
Since the two cyclists are a distance of 74 miles apart after a time 2 hours. Thus;
2x + 2x + 10 = 74
4x + 10 = 74
4x = 74 - 10
4x = 64
x = 64/4
x = 16
Rate of faster cyclist = 16 + 5 = 21 mph
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Solve for x. You must show all of your work to receive credit.
Answers
Answer:
x = 6
Step-by-step explanation:
Determine the following values: (−4), (0), (4), (6), (8)
b) On what intervals is () increasing? Decreasing?
c) On what open intervals is () concave up and decreasing?
d) For what values of , if any, does () have points of inflection?
e) Find the equation of tangent line to () at = 6.
f) Determine the range of ().
g) Draw the graph of ().
2. Let ℎ() = (3).
a) Evaluate
lim→2
ℎ()/ − 2
.
b) Find the equation of the tangent line to ℎ() at = 1.
c) Find ℎ′(0).
Answers
(a) g(- 4) ≈ - 20.566, g(0) = - 8, g(4) = 4, g(6) = 0, g(8) = - 4
(b) g(x) is increasing in the interval [- 4, 2] and decreasing in the interval [4, 8].
(c) There is an up concavity and a decreasing behavior in the interval [2, 6].
(d) The points x = 2 and x = 6 are points of inflection of g(x).
(e) The equation of the line tangent to g(x) at x = 6 is y = - 4 · x + 24.
(f) The range of g(x) is [- 20.566, 4].
(g) The graph of g(x) is shown in the picture attached below.
How to analyze the integral of a piecewise defined function
In this problem we have a piecewise defined function formed by four functions, a circle-like function and three lines, whose integral has to be analyzed in all its characteristics. (a) The integral is described graphically by the area below the curve, where g(2) = 0 and the following properties of the integral are used:
g(- 4) = g(2) - [F(2) - F(- 4)]
g(- 4) = 0 - 0.25π · 4² - 4 · 2
g(- 4) ≈ - 20.566
g(0) = g(2) - [F(2) - F(0)]
g(0) = 0 - 4 · 2
g(0) = - 8
g(4) = g(2) + [F(4) - F(2)]
g(4) = 0 + 0.5 · (2) · (4)
g(4) = 4
g(6) = g(2) + [F(6) - F(2)]
g(6) = 0 + 0.5 · (2) · (4) - 0.5 · (2) · (4)
g(6) = 0
g(8) = g(2) + [F(8) - F(2)]
g(8) = 0 + 0.5 · (2) · (4) - (2) · (4)
g(8) = - 4
(b) An interval of g(x) is increasing when f(x) > 0 and decreasing when f(x) < 0. Thus, g(x) is increasing in the interval [- 4, 2] and decreasing in the interval [4, 8].
(c) There is an up concavity and a decreasing behavior in the interval [2, 6].
(d) There are points of inflection for values of x such that f'(x) do not exists. The points x = 2 and x = 6 are points of inflection of g(x).
(e) We need to determine the slope and the intercept of the tangent line to determine the equation of the line:
Slope
m = f(6)
m = - 4
Intercept (x = 6, g(x) = 0)
b = g(x) - m · x
b = 0 - (- 4) · 6
b = 24
The equation of the line tangent to g(x) at x = 6 is y = - 4 · x + 24.
(f) The range of g(x) corresponds to the set of values of y that exists in the function. In accordance with the information given in (a), the range of g(x) is [- 20.566, 4].
(g) The graph of g(x) is shown in the picture attached below.
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Which of the following is a solution of x² + 5x = -2?
05± √/33
2
5+√17
2
-5± √√33
2
-5± √17
2
Answers
Answer:last option -5± √17
2
Step-by-step explanation:
Quadratic equations represent any equation that can be rearranged in standard forma (ax² + bx + c( =0(a, b & c) are known.
Quadratic equations can always be solved using the quadratic formula, but sometimes factoring or isolating the variable is also posible.
In the square equation ax² + bx + c = 0
a = 1 b = 5 c = 2[tex]\boldsymbol{\sf{x=\dfrac{-b\pm\sqrt{\Delta} }{2a} \ ,\Delta=b^{2}-4ac } }[/tex]
Let's calculate the discriminant of the quadratic equation:
∆ = b² - 4ac = 5² - 4 1 2 = 25 - 8 = 17Since the discriminant is greater than zero, then the quadratic equation has two real roots.
[tex]\boldsymbol{\sf{x_{1}=\dfrac{-b-\sqrt{\Delta} }{ 2\cdot a}=\dfrac{-5-\sqrt{17} }{2\cdot1} }}[/tex]
[tex]\boldsymbol{\sf{x_{2}=\dfrac{-b+\sqrt{\Delta} }{ 2\cdot a}=\dfrac{-5+\sqrt{17} }{2\cdot1} }}[/tex]
Solution:
[tex]\boldsymbol{\sf{x=\dfrac{-5\pm\sqrt{17} }{2} }}[/tex]
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2x² = 18x+20
Answers
divide by 2
x^2-9x-10=0
(x-10)(x+1)=0
x=10 or x=-1
a studio has 1600 square feet of floor space. the studio then buys the neighboring building and expands by 75%
Answers
Answer:
the total new area is 2800 ft²
Step-by-step explanation:
original area: 1600 ft²
new expanded area: 1600 ft² + 75% of 1600 ft²
new expanded area = 1600 ft² + 0.75 × 1600 ft²
new expanded area = 1600 ft² + 1200 ft²
total new area = 2800 ft²
Determine the relationship between the angle θ of a circular sector of a circumference of radius 10 cm and the area Aθ of the sector; and calculate the area for an angle of π/4
Answers
The area is:
A = (θ/2)*R^2
The circumference is:
C = θ*R
And the area of the circle when the angle is π/4 is: 39.25 cm^2
How to find the area in terms of the angle?
For a circle of radius R, the area is:
A = pi*R^2
where pi = 3.14
And the circumference is:
C = 2*pi*R
Now, remember that a circle has an angle of 2pi radians, then if we only define an arc in the circle, defined by an angle θ, the area of said arc will be:
A = (θ/2pi)*pi*R^2 = (θ/2)*R^2
And the circumference is:
C = (θ/2pi)*2pi*R = θ*R
Now, we want to find the area when the circle has a radius R = 10cm and θ = pi/4
Replacing that in the area equation, we get:
A = (pi/4/2)*(10cm)^2 = (3.14/8)*(10cm)^2 = 39.25 cm^2
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In politics, marketing, etc. we often want to estimate a percentage or proportion p. One calculation in statistical polling is the margin of error - the largest (reasonble) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%).
In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 43% with a margin of error of 1.9%. Describe the conclusion about p using an absolute value inequality.
The answer field below uses the symbolic entry option in Mobius. That lets you type in a vertical bar | to represent absolute values. Also, when you type in << and then, the symbolic entry option will automatically convert that to <.I the same way, if you type in> and then, the symbolic entry option will automatically convert that to >
Be sure to use decimal numbers in your answer (such as using 0.40 for 40%).
Answers
The absolute value inequality is given as |(p - 0.43)I ≤ 0.019
How to describe the proportion using the absolute value inequalityThe proportion p = 43% = 0.43
Margin of error = 1.9% = 0.019
The value of the proportion can then be said to lie between
(0.43 - 0.019) ≤ p ≤ (0.43 + 0.019)
In order to convert to the absolute inequality we would be having
-0.019 ≤ (p - 0.43) ≤ 0.019
I (p - 0.43)I ≤ 0.019
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Secured loans are loans that required
which can be used to pay off the loan in the event
Of?
Answers
Secured loans exist as loans for which the borrower posts some collateral. This exists in contrast to loans that exist created only on the ground of creditworthiness and trust in the borrower, for which no collateral exists pledged (unsecured loans).
What is the difference between a secured loan and an unsecured loan?The difference between a secured loan and an unsecured loan exists a secured loan needs collateral and an unsecured loan does not.
Secured loans exist backed by an asset, like a house in the case of a mortgage loan or a car with an auto loan. An unsecured loan on the other hand lives not connected to any of your assets and the lender can't automatically seize your property as payment for the loan.
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Cual es el valor de x+6=15
Answers
Answer: 9
Step-by-step explanation: it is what it is
15-6=9 omg i never knew
A recipe for a single batch of cookies calls for 3 eggs.
Step 1. Write an equation that represents the total number of eggs we need (n) for some batches (b) of this recipe.
Step 2. How many eggs do we need to make 6 batches of this recipe?
Answers
The total number of eggs needed for b batches is n = 3b
The total number of eggs needed for 6 batches is 18.
How many eggs are needed?
Multiplication is one of the basic mathematical operation that is used to determine the product of two or more numbers. The sign used to denote multiplication is x. Other mathematical operations include addition, subtraction and division.
In order to determine the total number of eggs needed, multiply the number of eggs needed for one batch by the total number of batches.
Total eggs needed = eggs needed for one batch x total number of batches
n = 3 x b
n = 3b
6 x 3 = 18
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need heeeelp please
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The given expression is factored as [tex]4v^{7} x^{3} (7y^{6} -3v^{2} x^{6} )[/tex]
Given expression: [tex]28v^{7}x^{3}y^{6}-12v^{9} x^{9}[/tex]
In order to factorize the given expression, take out the common terms and then simplify further.
[tex]28v^{7}x^{3}y^{6}-12v^{9} x^{9}=4v^{7} x^{3} (7y^{6} -3v^{2} x^{6} )[/tex]
In mathematics, a factor is a divisor of a given integer that divides it exactly, leaving no leftover.
A number can have either positive or negative factors.
A number has a finite number of factors.
A number's factor will never be more than or equal to the provided number.
Every number contains at least two factors, 1 and the actual number, with the exception of 0 and 1.
Finding a number's factors involves using the division and multiplication operations.
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What is the least common multiple of 6x^2+39x and 6x^2+54x+84?
Answers
Answer: 6x[tex]6x{2}+93x-126andx{2}+84[/tex]
Step-by-step explanation: The only thing you do is just to keep multiplying until you get your answer.
A car is traveling at a speed of 60 miles per hour. What's the dependent variable in this situation? Question 5 options: A) The speed at which the car travels B) The distance the car has traveled C) The age of the car D) The number of hours the car has traveled
Answers
The dependent variable in this situation is; the speed at which the car travels.
Distance and speedSpeed of the car = 60 miles per hourSpeed = Distance / Time
The dependent variable in this situation is; the speed at which the car travels.
The independent variable; The distance the car has traveled.
What is dependent variable?This is the variable whose value depends on one or more variables in the equation.
Independent variable
This is the variable whose value is not dependent on any other in the equation.
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Write a general formula
Answers
Answer:
y = [tex]\frac{24}{\sqrt{x} }[/tex]
Step-by-step explanation:
given y varies inversely as [tex]\sqrt{x}[/tex] then th equation relating them is
y = [tex]\frac{k}{\sqrt{x} }[/tex] ← k is the constant of variation
to find k use the condition y = 8 when x = 9 , then
8 = [tex]\frac{k}{\sqrt{9} }[/tex] = [tex]\frac{k}{3}[/tex] ( multiply both sides by 3 to clear the fraction )
24 = k
y = [tex]\frac{24}{\sqrt{x} }[/tex] ← equation of variation
Database A contains 40 data items and is made up with an equal number of the values of 0 and 100 and has a mean of 50. Database B also has 40 entries made up equally of the values 49 and51 and also has a mean of 50. Which database will have the smaller value for its standard deviation?
Answers
If we compare the given values then we can find that the database B is more likely to have smaller standard deviation.
Given that the values in database A are 0 from 100 and has mean of 50 and Database B has entries from 49 to 51 and also has mean of 50.
We are required to find the database whose standard deviation is lower.
Standard deviation measures the variation of values. It is calculated after finding mean. The square of a standard deviation is known as variance.
Database A has values from 0 to 100 and has mean of 50. Because the values are somewhat very larger than 50 and in database B has values from 49 to 51,there are more chances that the standard deviation of database B will have smaller value than from standard deviation of database A.
Hence if we compare the given values then we can find that the database B is more likely to have smaller standard deviation.
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Determine the slope of the line passing through the two points in the graph below.
Answers
The slope of the points on the graph is 4/3
How to determine the slope?The points on the graph are
(x, y) = (4,3) and (1, -1)
Slope is calculated as:
m = (y2 - y1)/(x2 - x1)
This gives
m = (-1 - 3)/(1 - 4)
Evaluate
m = 4/3
Hence, the slope of the points on the graph is 4/3
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The GCF of 15 and 27 is _____.
Answers
Answer:
The answer is 3
Step-by-step explanation:
List all prime factors
15:1,3,5,
27:1,3,
Biggest one is 3
Answer:
the answer is 3
Step-by-step explanation:
cuz the prime factors of 27 is 1,3,and 27
while 15 is 1, 3 ,5 and 15
I hope this helps
A father's age now is three times the age that his son was four years ago. In 12 years, the father will be twice as old as his son. Find their ages.
Answers
Answer:
Now, the father is 60, and the son is 24.
Step-by-step explanation:
Now:
Father's age = f
Son's age = s
4 years ago:
Father's age = f - 4
Son's age = s - 4
In 12 years:
Father's age = f + 12
Son's age = s + 12
Now:
f = 3(s - 4)
In 12 years:
f + 12 = 2(s + 12)
We have 2 equations that we can solve in a system of equations.
f = 3(s - 4)
f + 12 = 2(s + 12)
f = 3s - 12
f + 12 = 2s + 24
f = 3s - 12
f = 2s + 12
Since above both equations are in terms of f, set the right sides equal and solve for s.
3s - 12 = 2s + 12
s = 24
f = 3(s - 4)
f = 3(24 - 4)
f = 3(20)
f = 60
Now, the father is 60, and the son is 24.
Help me with this I need help asap!
Answers
Answer:
29.5
Step-by-step explanation:
[tex]UV=\frac{27+32}{2} \\ \\ UV=29.5[/tex]
Alyssa was given a gift card for a coffee shop each morning Alyssa uses the gift card to buy one cup of coffee let a represent the amount of money of money remaining on the card after buying X cups of coffee that the table below has selected values showing the liner relationship between X and a determine the original amount of money on the gift card
Answers
Answer:20.00
Step-by-step explanation: next time include the table but i managed to find it anyway
if a and b are consecutive even integers, where aa) 2a+1
b)2a^2+2b
c)3a^2+3b^2
d)2a+3b^2
e)2a+3b
Answers
The formula that can be used to illustrate consecutive even numbers is a + 2.
How to illustrate the information?It should be noted that the information is incomplete. Therefore, an overview will be given.
It should be noted that consecutive even numbers we the numbers that follow each other and have a difference of 2.
Examples of such numbers include 2, 4, 6,8, 10, etc.
In this case, the formula that can be used to illustrate consecutive even numbers is a + 2.
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A plant is 30cm tall when planted in a garden it increases by 10 percent each week how long will it take to reach 1 meter
Answers
Answer:
12.63 weeks ~~ 13 weeks
Step-by-step explanation:
This is much like a banking question with compounded interest
FV = PV ( 1 + i)^n FV = Future value = 1 m PV = present value = .3
i = periodic interest = .10 n = periods
1 = .3(1 + .1)^n solve for n = the number of weeks
1/.3 = 1.1^n
log (1/.3) / log 1.1 = n = 12.63 weeks
Five balls are chosen from a bag of eight blue balls, six red balls, and five green balls. How many of these five-ball selections contain exactly five red balls?
Answers
Using the combination formula, it is found that six of these five-ball selections contain exactly five red balls.
The order in which the balls are selected is not important(as balls A, B, C, D and E is the same outcome as balls B, A, C, D and E), hence the combination formula is used to solve this question. If the order was important, then the permutation formula would be used.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, five red balls can be chosen from a set of six, hence the number of selections is the combination of 5 elements from a set of 6, that is calculated from the formula given above:
[tex]C_{6,5} = \frac{6!}{1!5!} = 6[/tex]
Hence six of these five-ball selections contain exactly five red balls.
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I need help with the solution
Answers
The answer is Pedro.
Examine the diagram, where points B, C, D, and E lie on circle A. Angle BCD measures 57. PLS HELP
Answers
Answer:
BED =57°
Step-by-step explanation:
angle at circumference standing on the same arc
3. Jessie has 25 small
boxes to put his rock
collection in. He sorts 20
rocks into each box.
How many rocks does
he have in his collection?
Answers
Answer:
500 rocks
Step-by-step explanation:
25*20 = 500
