Answer:
s = height above ground
s = 60 + 20 t - 4.9 t^2 (standard physics equation on earth)
at t = 0
s = 60 (clearly :)
now when does it hit the bleak earth?
That is when s = 0
4.9 t^2 - 20 t -60 = 0
solve quadratic and use the positive t (the negative t was back before you threw it if you had thrown it from the ground)
t = 6.09 or - 2.01
use t = 6.09
now to do the last part there are two obvious ways to get t at the peak
1. look for vertex of parabola
2. look for halfway between t = -2.01 and t = 6.09
I will do it the hard (11) waay by completing the square
4.9 t^2 - 20 t = -(s-60)
t^2 - 4.08 t = -.204 s + 12.2
t^2 - 4.08 t +2.04^2 = -.204 s +12.2 + 4.16
(t-2.04)^2 = -.204(s-80.2)
so
top at 80.2 meters at t = 2.04 s
===============
quick check on time
should be average of 6.09 and -2.01
=4.08 /2 = 2.04 check
Answer: I HOPE THAT MY ANSWER WILL HELP U
Step-by-step explanation:
s = height above ground
s = 60 + 20 t - 4.9 t^2 (standard physics equation on earth)
at t = 0
s = 60 (clearly :)
now when does it hit the bleak earth?
That is when s = 0
4.9 t^2 - 20 t -60 = 0
solve quadratic and use the positive t (the negative t was back before you threw it if you had thrown it from the ground)
t = 6.09 or - 2.01
use t = 6.09
now to do the last part there are two obvious ways to get t at the peak
1. look for vertex of parabola
2. look for halfway between t = -2.01 and t = 6.09
I will do it the hard (11) waay by completing the square
4.9 t^2 - 20 t = -(s-60)
t^2 - 4.08 t = -.204 s + 12.2
t^2 - 4.08 t +2.04^2 = -.204 s +12.2 + 4.16
(t-2.04)^2 = -.204(s-80.2)
so
top at 80.2 meters at t = 2.04 s
===============
quick check on time
should be average of 6.09 and -2.01
=4.08 /2 = 2.04 check
How can I simplify this equation 2y+3(x-4x)
Answer:
2y - 9x
Step-by-step explanation:
2y + 3 ( x - 4x )
First, solve the brackets.
2y + 3x - 12x
Combine like terms.
2y - 9x
Answer:
[tex]\sf 2y-9x[/tex]
Step-by-step explanation:
Hi There Student! Let me help you out on this question.
________________________________________________________
SimplifyingIn this problem, we are given an expression [tex]\longmapsto\pmb{2y+3(x-4x)}[/tex], and asked to simplify it.
↪
First, we can perform the operation inside the parentheses, x-4x:
[tex]\longmapsto\sf 2y+3(-3x)}[/tex].
Now we can multiply 3 times -3x:
[tex]\longmapsto\sf 2y-9x[/tex]
And that is our final answer, because 2y and -9x are not like terms.
Hope that this helped! Have a good day ahead.
Best Wishes!
[tex]\star\bigstar\overline{\overline{\underline{\underline{\textsf {Reach far. Aim high. Dream big.}}}}}\bigstar\star[/tex]
◆◈-Greetings!-◈◆
-______________________________
DO NOT PUT A WRONG ANSWER OR ELSE I WILL START TO REPORT YOU!!! MAKE SURE THAT YOU SHOW ALL THE STEPS OR SOLUTIONS AND EXPLAIN THE PROBLEM.
Consider a ‘Witch of Agnesi’ curve, defined:
x^2 y + 4y = 8
Find:
a) dy/dx as a function of x, using implicit differentiation. Then, verify your result by finding y explicitly and differentiating.
b) The equation of the tangent line to the graph when x = 2.
The answers are as follow:
a) y'= -2x/y
b) y' = -4/y
Why do we use implicit differentiation?
The technique of implicit differentiation allows you to find the derivative of y with respect to x without having to solve the given equation for y.
Given:
x²y+4y=8
On differentiation
applying product rule
2xy+ x²y' = 0
2xy = - x²y'
2y = -xy'
y'= -2x/y
b) equation of the tangent line to the graph when x = 2.
y' = -4/y
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Y=3x-7 complete the missing value in the solution to the equation (1,
Answer: (1, -4) or y = -4
Step-by-step explanation:
Given:
y = 3x - 7
Plug in the value of 1 for x - given to us by "(1, ?)
y = 3x - 7
y = 3(1) - 7
Multiply:
y = 3 - 7
Subtract:
y = -4
y = -4
Which of the following slopes of a line pass through points (1, -3) and (0, 2)?
m=5
m = -5
m = undefined
None of these choices are correct.
The slope of the line that passes through (1, -3) and (0, 2) is: B. m = -5.
What is the Slope of a Line?Slope (m) = rise / run = change in y / change in x.
Given the points, (1, -3) and (0, 2):
Slope (m) = (-3 - 2)/(1 - 0)
Slope (m) = -5/1
Slope (m) = -5
Therefore, the slope of the line is: B. m = -5.
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sketch the graph of y =sine3x
The graph of [tex]\mathbf{y=\sin{3x}}[/tex] is given by,
Here given the function is [tex]y=\sin{3x}[/tex]
when [tex]x=0\Rightarrow y=\sin{3\times 0}=\sin0=0[/tex], then it passes through the origin (0,0).
When [tex]x=\frac{\pi}{6}\Rightarrow y=\sin{3\times\frac{\pi}{6}}=\sin\frac{\pi}{2}=1[/tex]
Since we know that, [tex]-1\leq\sin{x}\leq1,\forall x[/tex], then the function has maximum height at [tex]x=\frac{\pi}{6}[/tex].
Again when [tex]x=\frac{\pi}{3}\Rightarrow y=\sin{(3\times\frac{\pi}{3})}=\sin\pi=0[/tex], again the function is 0.
So clearly the function is the Oscillating function with a maximum value of the function as 1 and a minimum value of the function as -1.
Range of the oscilaltion of the function = 1-(-1) = 1+1 = 2
Using graphing calculator we get the graph of function [tex]y=\sin3x[/tex],
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For what value of b does (one-twelfth) superscript negative 2 b baseline times 12 superscript negative 2 b 2 baseline = 12?
There is no solution for b.
The rule for operations done in exponents are
(a) [tex]a^m*a^n=a^{m+n}[/tex]
(b) [tex]a^m/a^n=a^{m-n}[/tex]
(c)[tex](1/a)^m=a^{-m}[/tex]
Given the expression (one-twelfth) superscript negative 2 b baseline times 12 superscript negative 2 b+2 baseline = 12
the expression (one-twelfth) superscript negative 2 b simplifies that [tex](1/12)^{-2b}[/tex]
12 superscript negative 2b+ 2 simplifies that [tex]12^{-2b+2}[/tex]
so the final expression (one-twelfth) superscript negative 2 b baseline times 12 superscript negative 2 b+2 baseline = 12 will be
[tex](1/12)^{-2b}[/tex] * [tex]12^{-2b+2}[/tex] =12
⇒[tex]12^{-(-2b)}\\[/tex] * [tex]12^{-2b+2}[/tex] =12
⇒[tex]12^{2b[/tex] * [tex]12^{-2b+2}[/tex] =12
⇒[tex]12^{2b-2b+2}[/tex]=12¹
equating the exponts of the both sides
⇒2b-2b+2=1
⇒2=1 (not accepted because un-logic condition)
Therefore there is no solution.
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distribute 5x(3x+7)
help asap
Answer:
The Answer is 50 or 50x
Answer: 15x^2+35x ✅
Step-by-step explanation:
Hii, do you need to distribute [tex]\boldsymbol{5x(3x+7)}[/tex]? No problem! (:
How to Distribute?We can solve problems like this one by using what is known as the "distributive property". What it says is: If you have a term that comes before the parentheses, you multiply it times every single term in the parentheses. Let me show you what I mean...
[tex]\twoheadrightarrow\sf 5x(3x+7)[/tex]
[tex]\bullet[/tex] Multiply 5x tmes 3x and 7 - you will obtain
[tex]\twoheadrightarrow\sf 15x^2+35x[/tex] (if we multiply x times x we obtain x²)
Voila! There's our solution, cheers! (:
--
Hope that this helped! Best wishes.
[tex]\it Reach\quad far.\:Aim\quad high. \,Dream\quad big.[/tex]
[tex]\bigstar\underbrace[/tex]
--
PLease simplify this!!!
show all work!
The simplified form of the given expression is [tex]\frac{27}{4x^{12} y^{8} }[/tex].
The given expression is [tex]\frac{4(3x^{2} y^{4} )^{3} }{(2x^{3} y^{5} )^{4} }[/tex].
What are exponents?Exponentiation is a mathematical operation, written as bⁿ, involving two numbers, the base b and the exponent or power n, and pronounced as "b raised to the power of n".
We need to simplify the given expression.
Now, [tex]\frac{4(3^{3}x^{6} y^{12} )}{2^{4} x^{12}y^{20} }[/tex]
⇒[tex]\frac{108x^{6}y^{12} }{16x^{12} y^{20} }[/tex]
⇒[tex]\frac{27}{4x^{12} y^{8} }[/tex]
Therefore, the simplified form of the given expression is [tex]\frac{27}{4x^{12} y^{8} }[/tex].
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Philip ran out of time while taking a multiple-choice test and plans to guess the last 4 questions. Each question has 5 possible choices, one of which is correct. Let X=X=X, equal the number of answers Philip correctly guesses in the last 444 questions. Assume that the results of his guesses are independent.
What is the probability that he answers exactly 1 question correctly in the last 4 questions?
Using the binomial distribution, it is found that there is a 0.4096 = 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.Considering that there are 4 questions, and each has 5 choices, the parameters are given as follows:
n = 4, p = 1/5 = 0.2.
The probability that he answers exactly 1 question correctly in the last 4 questions is P(X = 1), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{4,1}.(0.2)^{1}.(0.8)^{3} = 0.4096[/tex]
0.4096 = 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.
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Find the equation of the tangent line to the curve:
y = ( 1 + 2x)
at the point (2, 25).
Answer:
the first answer y = 20x - 15
Step-by-step explanation:
since the correct tangent line must share the same point with the originated function, only a line function that delivers y = 25 for x = 2 can be correct.
only the first answer option provides this (20×2 - 15 = 25).
so, we know, this line goes through the given point, but does it have the correct slope for the tangent ?
the correct slope we get from the first derivative of the original function.
f(x) = (1 + 2x)² = 1 + 4x + 4x²
f'(x) = 4 + 8x
for x = 2 we get the tangent slope at that point as
4 + 8×2 = 20
and the provided line is again
y = 20x - 15
with the slope being the factor of x (20).
so, it fits, and indeed, answer 1 is correct.
Assume that a procedure yeilds a binomial with n trial and the probability of success for one trial is p. Use the given values of n and p to find the mean and standard deviation. Also, use the range rule of thumb to find the minimum usual value mean -2standard deviation and the maximum usual value mean + 2 standard deviation n=1490,p=2/5
The value of minimum usual value is, [tex]\mu-2\sigma=-119.2[/tex]
The value of maximum usual value is, [tex]\mu+2\sigma=1311.2[/tex]
Given the values of the parameters of Binomial Distribution are,
Total number of trials (n) = 1490
probability of success in one trial is (p) = 2/5
The probability of failure in on trial is given by,
[tex]q=1-p=1-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}[/tex]
For Binomial distribution we know that,
Mean [tex](\mu)=np=1490\times\frac{2}{5}=596[/tex]
and Standard Deviation [tex](\sigma)=\sqrt{npq}=\sqrt{1490\times\frac{2}{5}\times\frac{3}{5}}=357.6[/tex]
Now, calculating the required measurement we get,
The minimum usual value is given by,
Mean -2 Standard Deviation [tex]=\mu-2\sigma=596-2\times357.6=-119.2[/tex]
The maximum usual value is given by,
Mean + 2 Standard Deviation [tex]=\mu+2\sigma=596+2\times357.6=1311.2[/tex]
Hence the minimum and maximum usual values are -119.2 and 1311.2 respectively.
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the answer to this asap please!
The required work done is 62400 J.
work done to lift a 1500 N object from the ground to the top of a 40 m building if the cable weighs 3 N per m
work done, is define as the product of force and displacement.
since,
work done to lift 1500N to height of 40 m is:
W= FS
= 1500 x 40 = 60000J
now work done for rope
is given by
w = mgΔx(40-x)
w= [tex]\int _0^{40}\left mg(40-x\right)dx[/tex]
w=[tex]3\int _0^{40}\left(40-x\right)dx[/tex]
w= 3[tex][40x-x^2/2]\left \{ {{40} \atop {0}} \right.[/tex]
w= 3[1600-800]
w = 2400
Total work done for lifting 1500N to 40m height
= 6000+2400=62400J
Thus the required work done to lift 1500N weight to 40m is 62400J.
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Which statement illustrates a simulation that could be used to generate samples of people on a game show selecting either door A, door B, or door C?
Answer:
The correct option is;
B. Rolling a die; 1 or 2 represents door A, 3 or 4 represents door B, and 5 or 6 represents door C
Z varies directly as x^3 and inversely as y^3. If z=167 when x = 3 and y=10, find z if X=4 and y=6
Answer is 1832.7
step by step
z=kx^3 / y^3
167=27k/1000
k=16700/27
k=6185.2, then
z=6185.2×4^3/6^3
z=6185.2×64/216
z=1832.7
If a patient is given 3 tablespoons of medication for me for 150 ML bottle how many millimeters of medication remain in the bottle
Answer:
105.6397
ROUNDED ANSWER:
105
which of the following is most likely the next step in the series?
Answer:
errrrrr a not too sure but try
Step-by-step explanation:
i did the test got a 90
What is 4 third written in expanded form
Multiply (Make sure to show work on a separate sheet of paper)
Please use the equation writer that is on top. Look for this sign √ and click on it. That will allow you to write an exponent.
(2x−4)(x−6)
Answer:
[tex]2x^{2}[/tex] - 16x + 14
Step-by-step explanation:
(2x - 4)(x - 6)
= (2x + −4)(x + −6)
= (2x)(x) + (2x)(−6) + (−4)(x) + (−4)(−6)
= [tex]2x^{2}[/tex] − 12x − 4x + 24
= [tex]2x^{2}[/tex] - 16x + 14
Inverse Function: One to one function...Help needed! 15 pts for your help!
Answer:
Step-by-step explanation:
hello :
Could use some help! Brainliest to who answers :)
Answer:
N. The number of people purchasing coffee each day in a coffee shop
Step-by-step explanation:
A fraction of a person could not buy coffee because every person is a whole person. If something is not a person, it's not a person. Therefore, the only numbers you could add to this value are 0 and 1.
The lateral area of a right cone which has a base diameter of 4 units and a height of 10 units is:
Answer:
Step-by-step explanation:
can someone turn the equation 3−2=13 into a word problem. (i already know answer)
The word problem for given equation is : When 3 is multiplied with x and subtracted by 2 multiplied by y , the number obtained is 13. Solve the equation for x =1 .
The complete equation will be 3x - 2y =13
What is an Equation ?When an algebraic expression is equated by an equal sign to a constant or any other algebraic expression , then an equation is formed .
The equation given in the question is
3x-2y =13
When 3 is multiplied with x and subtracted by 2 multiplied by y , the number obtained is 13. Solve the equation for x =1 .
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A circle has a radius of 5 ft, and an arc of length 7 ft is made by the intersection of the circle with a central angle. Which equation gives the measure of the central angle, q? 08- 5 O 0-7+5 O e-7-5
The equation gives the measure of the central angle 7/5 times 3 60/2 π.
What is Central angle?An angle with its vertex at the center of a circle and with sides that are radii of the circle.
radius= 5 feet.
Circumference of circle,
= 2πr
=2*3.14*5
= 31.4 feet.
Arc length = 7.
Then, the part of circle 7 feet arc have
=7/31.4
=0.2229
Also, 0.2229 * 360 = 80.244°
In radian,
80.244° = 1.4 radians
Hence, 7/5 times 360/2 π.
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I WILL MARK 5 STARS! PLSSS FAST! At noon, the temperatures in Portland, Maine and Phoenix, Arizona had opposite values. The temperature in Portland was lower than in Phoenix. What was the temperature in each city? Explain your reasoning.
At noon, the temperatures in Portland, Maine and Phoenix, Arizona had opposite values. is mathematically given as
PoT=-PhT PhT =+PoT What was the temperature in each city?Generally, the equation for the temperature at Portland, Maine is mathematically given as
PoT=-PhT
Since Portland, Maine and Phoenix, Arizona had opposite values. The temperature in Portland was lower than in Phoenix.
In conclusion, the temperature in each city is
PoT=-PhT
PhT =+PoT
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The graphs of exponential functions f and g are shown on the coordinate plane below.
Answer:
-5
Step-by-step explanation:
Since g(x) is f(x) shifted 5 units down, g(x) = f(x) -5. Therefore k = -5
Gabrielle's age is three times Mikhail's age. The sum of their ages is 36. What is Mikhail's age?
Answer:
Gabrielle is 27
Mikhail is 9
Step-by-step explanation:
g = 3m
g + m = 36
since g = 3m we can substitute it in the equation
g + m = 36 as
3m + m = 36
4m = 36
m = 9
3m = 27 which is g
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6. Using the discriminant, determine the value of k that will give 1 solution (i.e. discriminant equals zero) y = kx²-4x + 4
Answer:
k = 1
Step-by-step explanation:
Discriminant
[tex]b^2-4ac\quad\textsf{when }\:ax^2+bx+c=0[/tex]
[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]
[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]
[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]
As we need to determine the value of k that will give one solution, set the discriminant to zero.
Given equation:
[tex]y=kx^2-4x+4[/tex]
Therefore:
a = kb = -4c = 4Substitute these values into the discriminant and solve for k:
[tex]\begin{aligned}b^2-4ac & = 0\\\implies (-4)^2-4(k)(4) & = 0\\16-16k & = 0\\16k & = 16\\\implies k & = 1\end{aligned}[/tex]
The functions f(x) = x^2 – 2 and g(x) = –x^2 + 5 are shown on the graph.
Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?
y > x^2 – 2
y ≥ –x^2 + 5
The set of inequalities do not have a solution.
What is inequality?The relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal. But to compare the values, whether it is less than or greater than, different inequalities are used.
Given:
f(x)= x²-2
g(x) = -x²+5
To derive, y ≤ x² + 5 simply change the equality sign in the function g(x).
To derive y > x² - 2 , following transformation on the function f(x)
Shift the function f(x) down by 2 unitsReflect across the x-axisShift the function g(x) up by 5 unitsChange the equality sign in the function g(x) to greater than.The inequalities of the graphs become
y < x² - 2 and y ≤ x² - 5
From the graph of the above inequalities it can be seen that curves of the inequalities do not intersect.
Hence, the set of inequalities do not have a solution
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ASAP NOW! PLSS! I WILL MARK 5 STARS! PLSSS! thank you!! At noon, the temperatures in Portland, Maine and Phoenix, Arizona had opposite values. The temperature in Portland was lower than in Phoenix. What was the temperature in each city? Explain your reasoning.
Opposite values are those values which on the number line has the same distance between them and zero. The temperature in each city is PoT=-PhT and PhT =+PoT.
What are opposite values?Opposite values are those values which on the number line has the same distance between them and zero. Although the sign on the values may be difference. For example if the first value is 4, then its opposite value is -4.
In general, the temperature equation for Portland, Maine is stated mathematically as
PoT=-PhT
As it is given in the question that the Portland, Maine and Phoenix, Arizona had opposite values. Also, the temperature in Portland is lower than in Phoenix. Therefore, the temperature in each city can be written as,
PoT=-PhT
PhT =+PoT
Hence, the temperature in each city is PoT=-PhT and PhT =+PoT.
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Goods costing $2,300 are purchased on account on July 15 with credit terms of 2/10, n/30. On July 18, a $100 credit memo is received from the supplier for damaged goods. Give the journal entry on July 24 to record payment of the balance due within the discount period using a perpetual inventory system
The journal entry on July 24 to record payment of the balance due is $2156
What is Discount Period ?Discount period is the time period given by the supplier to the consumer for getting discount if the payment is made by the due date.
Debit Credit
Accounts payable (2300-100 ) 2200
Cash (2200 - (2200* 2%)) 2156
Purchase Discount / Merchandise Inventory 44
To record the payment of accounts within discount period
Amount Paid = 2300 - 200 -44 = 2156
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