(a) Show that a differentiable function f decreases most rapidly at x in the direction opposite the gradient vector, that is, in the direction of −∇f(x). Let θ be the angle between ∇f(x) and unit vector u. Then Du f = |∇f| cos(theta). Since the minimum value of cos(theta) is -1 occurring, for 0 ≤ θ < 2π, when θ = π , the minimum value of Du f is −|∇f|, occurring when the direction of u is the opposite of. The direction of ∇f (assuming ∇f is not zero).
(b) Use the result of part (a) to find the direction in which the function f(x, y) = x^(3)y − x^(2)y^(3) decreases fastest at the point (4, −4)
Answers
(a) As we have shown that the differentiable function f decreases most rapidly at x in the direction opposite the gradient vector, that is, in the direction of −∇f(x).
(b) The direction in which f(x, y) = x³y − x²y³ decreases fastest at (4, -4) is the direction of the unit vector u = <-3/5, 4/5>.
To show that a differentiable function f decreases most rapidly at x in the direction opposite the gradient vector, we first need to define the directional derivative. The directional derivative of f at x in the direction of a unit vector u is denoted by Du f and is given by the dot product of the gradient vector ∇f(x) and u.
Du f = ∇f(x)·u
Now, we want to find the direction in which Du f is minimized. Let θ be the angle between ∇f(x) and u. Using the dot product formula, we have:
Du f = |∇f(x)| cos(θ)
where |∇f(x)| is the magnitude of the gradient vector. Since cos(θ) is maximum when θ = 0 (i.e., when u points in the same direction as ∇f(x)) and minimum when θ = π (i.e., when u points in the opposite direction of ∇f(x)), we can conclude that the direction in which f decreases most rapidly at x is opposite the gradient vector −∇f(x).
Now, let's apply this result to the function f(x, y) = x³y − x²y³ and find the direction in which it decreases fastest at the point (4, −4).
First, we need to find the gradient vector of f:
∇f(x, y) = <3x²y-2xy³, x³-3x²y²>
Evaluating at (4, -4), we have:
∇f(4, -4) = <192, -256>
The magnitude of the gradient vector is |∇f(4, -4)| = √(192² + (-256)²) = 320.
To find the direction of fastest decrease, we need to consider the opposite of the gradient vector:
−∇f(4, -4) = <-192, 256>
To make this a unit vector, we divide by its magnitude:
u = <-192, 256>/320 = <-3/5, 4/5>.
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Related Questions
there are 5 blue chips and 3 yellow chips in a bag. one chip is drawn from the bag. that chip is placed back into the bag. a second chip is then drawn. what is the probability that the two selected chips are of different colors? express your answer as a common fraction.
Answers
The probability that the two selected chips are of different colors is 15/32
How to determine the probabilitiesFrom the question, we have the following parameters that can be used in our computation:
Blue = 5
Yellow = 3
This means that
Total = 5 + 3
Total = 8
The probability of different color is then calculated as
P(Different) = Yellow and Blue or Blue and Yellow
So, we have
P = 3/8 * 5/8 * 2
Evaluate
P = 30/64
Simplify
P = 15/32
Hence, the probability is 15/32
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Evaluate the expression if a = 3, b = 4, and c = 2. Simplify, if possible
Answers
Answer:
you didnt give an expression or picture
Step-by-step explanation:
1 point) find the general solution to y′′′ 8y′′ 20y′=0. in your answer, use c1,c2 and c3 to denote arbitrary constants and x the independent variable.
Answers
The general solution to y′′′ + 8y′′ + 20y′ = 0 is: y(x) = e^(-4x)(c1 cos(2x) + c2 sin(2x)) + c3
How to find the general solution?The characteristic equation of the given third-order linear homogeneous differential equation is:
r^3 + 8r^2 + 20r = 0
Dividing both sides by r gives:
r^2 + 8r + 20 = 0
The roots of this quadratic equation can be found using the quadratic formula:
r = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = 8, and c = 20. Plugging in these values, we get:
r = (-8 ± sqrt(8^2 - 4(1)(20))) / 2(1)
= -4 ± 2i
Since the roots are complex and come in a conjugate pair, the general solution to the differential equation is:
y(x) = e^(-4x)(c1 cos(2x) + c2 sin(2x)) + c3
where c1, c2, and c3 are arbitrary constants.
Therefore, the general solution to y′′′ + 8y′′ + 20y′ = 0 is:
y(x) = e^(-4x)(c1 cos(2x) + c2 sin(2x)) + c3
where c1, c2, and c3 are arbitrary constants.
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please help asap asap asap
Answers
55%×180=99
300%×26=78
12%×700=84
99
84
78
Answer:
Answers are
1. 99,
2. 78
3. 84
We show workings if less than 100% with 0. in front
so question 1 workings look like this.
180 x 0.55 = 99
Question 2 workings look like this
3.00 x 26 or 26 x 3 = gives us 78 which is 300%
Question 3
0.12 x700 = 84
We know 10% is 70 and 1% is 7 = 7+7+70 = 84. Let me know if this helps.
Researchers at Texas A&M studied the effect of using standing height desks on the energy expended by nine elementary school students. In their paper about the study, they reported descriptive statistics for the nine students. These descriptive statistics were expressed as a mean plus or minus a standard deviation. One such descriptive statistic was the weight of students before using the standing desks, which was reported as 27.0±7.9 kilograms.
Q: What is the standard error of the mean?
Answers
The standard error of the mean is 2.63.
What is standard error?The standard error simply means the statistical term that's used to measure the accuracy through which the sample distribution illustrates a population by using the standard deviation.
In this case, the effect of using standing height desks on the energy expended by nine elementary school students was studied.
The standard error will be:
= s /✓n
where
s = standard deviation
n = number of students = 9
= 7.9 / ✓9
= 7.9 / 3
= 2.63
The standard error is 2.63.
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Erin buys a jewelry set for $27. 63. She pays with two $20 bills. How much change, in dollars and cents, does Erin receive?
Answers
By taking a difference, we can see that the change is 12 dollars and 37 cents.
How much change, in dollars and cents, does Erin receive?The change will be the difference between the amount that she pays, and the amount that the jewelry set costs.
She pays with two $20 bills, so she pays with $40, and the cost is $27.63, then the difference (and thus the change) is:
Change = $40 - $27.63
Change = $12.37
So she gets a total change of 12 dollars and 37 cents.
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explain why the gradient points in the direction in which f(x) increases the fastest
Answers
The gradient of a function points in the direction in which the function increases the fastest because it represents the direction of greatest increase of the function.
The gradient of a function is a vector that points in the direction of the steepest increase of the function at a particular point. This means that if we move in the direction of the gradient, the value of the function increases the fastest.
To understand why this is true, let's consider the definition of the gradient. The gradient of a function f(x) is defined as a vector of partial derivatives:
∇f(x) = (∂f/∂x1, ∂f/∂x2, ..., ∂f/∂xn)
Each component of the gradient vector represents the rate of change of the function with respect to the corresponding variable. In other words, the gradient tells us how much the function changes as we move a small distance in each direction.
When we take the norm (or magnitude) of the gradient vector, we get the rate of change of the function in the direction of the gradient. This means that if we move in the direction of the gradient, the value of the function changes the fastest, because this is the direction in which the function is most sensitive to changes in the input variables.
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Find the derivative of each of the following functions. Simplify where possible. (12 marks) a) f(x)= x/(2x−3)^2 b) g(x)=(3x^2 −1)^2 (2x+1)^4 c) h(x)=5x*2^(x ^2+1) d) s(x)= cosx/x
Answers
Derivative of the following functions are:f(x)= x/(2x−3)^2g(x)=(3x^2 −1)^2 (2x+1)^4h(x)=5x*2^(x ^2+1)s(x)= cos
The given function is `f(x)= x/(2x−3)^2`.To find its derivative, we apply the quotient rule of derivative.The quotient rule is as follows,`[f(x)/g(x)]' = [f'(x)*g(x) - f(x)*g'(x)] / g^2(x)`So, applying the quotient rule, we get:`
f'(x) = [x*2(2x-3)*1 - 1*(2x-3)^2*1] / (2x-3)^4`Simplifying,
`f'(x) = [-4x + 9] / (2x-3)^3`Therefore, the derivative of `f(x)` is `[-4x + 9] / (2x-3)^3`.b) The given function is
`g(x)=(3x^2 −1)^2 (2x+1)^4`.To find its derivative, we apply the product rule of derivative. The product rule is as follows,
`(f(x)*g(x))' = f'(x)*g(x) + f(x)*g'(x)`So, applying the product rule, we get:
`g'(x) = 2(3x^2-1)*6x*(2x+1)^4 + 4(3x^2-1)^2*(2x+1)^3*2`Simplifying,
`g'(x) = 12x*(2x+1)^3(3x^2-1) + 8(3x^2-1)^2*(2x+1)^3`Therefore, the derivative of \
`g(x)` is `12x*(2x+1)^3(3x^2-1) + 8(3x^2-1)^2*(2x+1)^3`.c) The given function is
`h(x)=5x*2^(x^2+1)`.To find its derivative, we apply the product rule of derivative. The product rule is as follows,
`(f(x)*g(x))' = f'(x)*g(x) + f(x)*g'(x)`So, applying the product rule, we get:
`h'(x) = 5*2^(x^2+1)*(x*ln2*2x)`Simplifying,
`h'(x) = 10x^2*ln2*2^(x^2+1)`Therefore, the derivative of `h(x)` is `10x^2*ln2*2^(x^2+1)`.d) The given function is `s(x)= cosx/x`.To find its derivative, we apply the quotient rule of derivative.The quotient rule is as follows,
`[f(x)/g(x)]' = [f'(x)*g(x) - f(x)*g'(x)] / g^2(x)`So, applying the quotient rule, we get:
`s'(x) = [x*(-sinx) - cosx*1] / x^2`Simplifying,
`s'(x) = [-sinx - cosx/x]`Therefore, the derivative of `s(x)` is `[-sinx - cosx/x]`.
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f(x) = 4x^2+2x+6 what is the discriminant of f? How many distinct real number zeros does f have?
Answers
Answer:
The discriminant of f is 92, and it has no real zeros
Step-by-step explanation:
The discriminant of a quadratic is \(b^2-4ac\), where the quadratic is in the form \(ax^2+bx+c\). The discriminant of this one is therefore:
\(2^2-4(4)(6)=4-96=-92\)
Since the square root of a negative number is imaginary, this quadratic has no real number zeros. Hope this helps!
A ticket to a dinosaur exhibit costs $7.50. A one-year pass to the exhibit costs $30. When is the one-year pass a better deal?
Answers
Answer:
The one-year pass is a better deal when the tickets are a better deal.
Step-by-step explanation:
Logic
It's just logic!Please help me with the correct answers
Answers
Answer:
13 ft
Step-by-step explanation:
we need to find the square root of 169
√169 = 13
PLEASE HELP ASAP! ITS URGENT! Thank you.
Answers
Let's plug in x = 2.
f(x) = x^2
f(2) = 2^2 ... replace every x with 2
f(2) = 4
----------
Now plug in x = 3.
f(x) = x^2
f(3) = 3^2 ... replace every x with 3
f(3) = 9
-----------
And x = 5 as well.
f(x) = x^2
f(5) = 5^2 .... replace every x with 5
f(5) = 25
-----------
We see that
f(2)+f(3) = 4+9 = 13
which is not equal to f(5) = 25.
So f(2)+f(3) = f(5) is false.
------------
Another way to phrase why it doesn't work is because (2,3,5) isn't a pythagorean triple. The equation 2^2+3^2 = 5^2 is false.
If it said f(3)+f(4) = f(5), then it would be correct because 3^2+4^2 = 5^2 is a true equation.
The driver of the water tanker works for 5% days per week and 9 hours per day on week days except on Saturdays where they work for a ½ day (4,5 hours). The rate per hour was R92.50 and the rate of pay was doubled on Saturdays. Calculate the amount of money that the tanker driver receive per day during week days. 2.2Determine the total number of hours that the driver has worked in March 2022. 2.3 Determine the salary that the tanker driver has received in the month of June 2022 if he worked the entire month including Saturdays.
Answers
Answer:
R18,801 + R3,996 = R22,797 per month.
Step-by-step explanation:
To calculate the amount of money that the tanker driver receives per day during weekdays, we need to consider the number of hours worked on each weekday and the rate per hour. The driver works for 5% days per week, so there are 5 weekdays and 1 half-day on Saturdays.
On weekdays (Monday to Friday), the driver works for 9 hours per day, so the daily pay is:
9 hours x R92.50 per hour = R832.50 per day
On Saturdays, the driver works for a half-day (4.5 hours) and the rate of pay is doubled, so the pay for the half-day is:
4.5 hours x R92.50 per hour x 2 = R832.50
Therefore, the total pay for the 5 weekdays and 1 half-day on Saturday is:
5 x R832.50 + R832.50 = R4,162.50
So, the driver receives R4,162.50 per week for working 5 weekdays and 1 half-day on Saturdays.
To calculate the amount of money that the driver receives per day during weekdays, we divide the weekly pay by the number of weekdays:
R4,162.50 / 5 = R832.50 per day
Therefore, the driver receives R832.50 per day during weekdays.
2.2 To determine the total number of hours that the driver worked in March 2022, we need to know the number of weekdays and Saturdays in March. There are typically 22 weekdays in March, so the driver works for:
22 weekdays x 9 hours per day = 198 hours on weekdays
In addition, there are typically 4 Saturdays in March, so the driver works for:
4 Saturdays x 4.5 hours per half-day x 2 (double pay rate) = 36 hours on Saturdays
Therefore, the total number of hours that the driver worked in March 2022 is:
198 hours on weekdays + 36 hours on Saturdays = 234 hours
2.3 To determine the salary that the tanker driver has received in the month of June 2022 if he worked the entire month, including Saturdays, we need to know the number of weekdays and Saturdays in June. There are typically 22 weekdays in June, so the driver would work for:
22 weekdays x 9 hours per day x R92.50 per hour = R18,801 per month on weekdays
In addition, there are typically 4 Saturdays in June so that the driver would work for:
4 Saturdays x 4.5 hours per half-day x 2 (double pay rate) x R92.50 per hour = R3,996 per month on Saturdays
Therefore, the total salary that the tanker driver would receive in the month of June 2022 if he worked the entire month, including Saturdays would be:
R18,801 + R3,996 = R22,797 per month.
simplify a^3 x b x a^3 x b
Answers
Answer:
\( {a}^{6} {b}^{2} \)
solution
\( {a}^{3} \times b \times {a}^{3} \times b \\ = {a}^{3 + 3} \times {b}^{1 + 1} \\ = {a}^{6} {b}^{2} \)
hope this helps...
Good luck on your assignment..
Answer:
\(a^{6}b^{2}\)
Step-by-step explanation:
\(a^3 \times b \times a^3 \times b\)
If there are no exponents written, then the exponent is 1.
\(a^3 \times b^1 \times a^3 \times b^1\)
When multiplying two powers that have the same base, you can add the exponents.
\(a^{3+3} \times b^{1+1}\)
\(a^{6} \times b^{2}\)
solve for x and set up proportion
Answers
The value of x from the given right triangle is 10 units.
Consider triangle ABC and triangle BDC.
Here, ∠ABC=∠BDC=90°
∠BCD=∠BCA (Reflexive angle)
By AA similarity ΔABC is similar to ΔBDC
We know that, when two triangles are similar their corresponding sides will be in ratio.
Now, x/20 = 5/x
x²=100
x=√100
x=10 units
Therefore, the value of x from the given right triangle is 10 units.
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I just need to know if the answer is B or D
Answers
Step 1. The two functions we have are:
\(\begin{gathered} f(x)=2x^2 \\ g(x)=\sqrt[]{x-2} \end{gathered}\)And we are asked to find the composite function f(g(x)) and the domain.
Step 2. The function that we need to find is:
\(f(g(x))\)To find this, we substitute g(x) into the x value of f(x):
\(f(g(x))=2(\sqrt[]{x-2})^2-1\)Step 3. Simplifying:
The square root and the power of two cancel each other
\(f(g(x))=2(x-2)^{}-1\)Distributing the multiplication by 2:
\(f(g(x))=2x-4-1\)Combining the like terms:
\(f(g(x))=\boxed{2x-5}\)Step 4. Find the domain. The domain is the set of possible values that the x variable can take.
Remember the two original functions:
\(\begin{gathered} f(x)=2x^2 \\ g(x)=\sqrt[]{x-2} \end{gathered}\)for f(x) x can take any value. But for g(x) the square root cannot be a negative number, therefore, x-2 has to be equal to or greater than 0:
\(\begin{gathered} \text{Domain:} \\ x-2\ge0 \end{gathered}\)Solving for x:
\(\begin{gathered} \text{Domain:} \\ x\ge2 \end{gathered}\)This domain also applies to the composite function f(g(x)), and it can be written as follows:
\(D\colon\mleft\lbrace x|x\ge2\mright\rbrace\)Answer: Option four
\(\begin{gathered} f(g(x))=2x-5 \\ D\colon\lbrace x|x\ge2\rbrace \end{gathered}\)Solve the equation using inverse operations. Check your solutions. In your final answer, include all of your work.
Answers
————————
2
,3−3i√3
—————
2
Answer:
-3
Step-by-step explanation:
1/4x^3 = -27/4
divide 1/4 from each side
x^3 = -27
find the cubed root of each equation
x = -3
i think this is right so sorry if not.
cot(x+y)=(cotxcoty-1)/(cotx+coty)
Answers
To prove the given trigonometric identity: \(cot(x+y) = )\frac{(cot(x)cot(y) - 1) }{(cot(x) + cot(y)}\), we can use the definition of cotangent and some trigonometric identities.
Recall that \(cot(x) = \frac{1}{tanx}\) and \(tan(x) = \frac{sin(x)}{cos(x)}\).
First, let's find the\(tan(x+y)\)using the angle sum formula for tangent:
\(tan(x+y)=\frac{(tan(x) + tan(y))}{ (1 - tan(x)tan(y))}\)
Now, substitute cot(x) and cot(y) using the definition of cotangent:
\(tan(x+y) =\frac{ (1/cot(x) + (1/cot(y)}{(1 - (1/cot(x))(1/cot(y))}\)
To simplify the expression, find the common denominator for the numerators:
\(tan(x+y) = \frac{ (cot(x)cot(y) + cot(x) + cot(y)) }{cot(x)cot(y) - 1}\)
Now, take the reciprocal of both sides to get \(cot(x+y)\)
\(cot(x+y) =\frac{ (cot(x)cot(y) - 1)}{ (cot(x) + cot(y))}\)
So, we have proven that \(cot(x+y) = \frac{ (cot(x)cot(y) - 1)}{ (cot(x)cot(y) - 1)}\)
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If Marie were to paint her living room alone, it would take 7 hours. Her sister Gloria could do the job in 8 hours. How long would it take them working together
Answers
Thus, working together, Marie and Gloria would take 56/15 hours, or approximately 3.73 hours, to paint the living room.
Let's analyze the situation using the terms "work rate" and "combined work rate" to determine how long it would take Marie and Gloria to paint the living room together.
Marie's work rate is 1/7, as she can complete the job in 7 hours.
Gloria's work rate is 1/8, as she can finish the task in 8 hours. To find their combined work rate, we simply add their individual work rates: (1/7) + (1/8).
To add these fractions, we need a common denominator, which in this case is 56.
So, we can rewrite the fractions as (8/56) + (7/56). Adding them together, we get a combined work rate of 15/56.
Now that we have their combined work rate, we can find out how long it would take them to complete the job together. To do this, we need to find the reciprocal of their combined work rate, which is 56/15.
Therefore, working together, Marie and Gloria would take 56/15 hours, or approximately 3.73 hours, to paint the living room.
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7. The quadratic function below models the flight of a model rocket, where
the height, h(t) is in metres, and the time, t is in seconds. What is the
rocket's height after 3 seconds?
h(t) = -5t² +42t + 54
Answers
The rocket's height after 3 seconds is 6.3 sec.
The quadratic equation y = -x2 - 12x, where y is the height of the rocket in metres at time x seconds after launch, may be used to describe the trajectory of a model rocket. The rocket's highest point should be noted, along with the time it was at that height.
A rocket's height is a function of time, h(t), where h is measured in metres and t is measured in seconds. 9.8 m/s2 is the rate of change of velocity (d2h dt2 - t). The rocket is catapulted into the air, reaching a speed of 50 m/s at time t0.
To find the rocket's height at t = 2 sec, we just have to substitute 2 into the equation for t and then solve for h:
h = -5*t2 + 30*t + 10
h = -5(2)2 + 30(2) + 10
h = -5(4) + 30(2) + 10
h = -20 + 60 +10
h = 50 m
The height of the rocket 2 seconds after launching it is 50 meters.
To find the x-coordinate of the vertex of a parabola, we use the formula:
\(xvertex = -b / 2a\)
t - 3 = ± √(11)
t = 3 ± √(11)
t = 3 ± 3.3
Solving for t, we get two solutions:
t = 3 - 3.3
t = -0.3 sec
and
t = 3 + 3.3
t = 6.3 sec
Remember that the rocket takes off from an elevated platform (the roof of a building), not from the ground, in order to comprehend the two alternatives we came up with. Even though we have two x-intercepts, only one of them, tground = 6.3 seconds, is related to when the rocket touches down. The other x-intercept, t = -0.3 sec, only has theoretical significance and is therefore irrelevant in our actual situation.
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can somebody help me 4/5 divided by 2/3
Answers
Answer:
8/15
Step-by-step explanation:
Answer: 1 7/8
5/4 x 2/3 = 15/8
Then simplify 15/8 and you get 1 7/8
Hope this helped!
A set of symbols that expresses a mathematical rule is called a ___________.
Answers
Answer:
Formula! Have a nice day!
Answer:
yo bro it formula
Step-by-step explanation:
can i get brainiest if im right
I’ll give you brainliest!!!!! Which ordered pair is a solution to the system of inequalities? y=3x y=9
Answers
Answer:
( 6,10)
Step-by-step explanation:
y>3x y>9
Set them equal to each other
3x >9
Divide by 3
3x/3 >9/3
x > 3
y>9
The only option with x > 3 y>9 is ( 6,10)
Answer:
C
Step-by-step explanation:
Since y > 9 the answer is either C or D
However, since y>3x, the answer must be C
Since 3*6 > 11
A security car is parked 25 ft from a movie theater. Find at what speed the reflection of the security strobe lights is moving along the wall of the movie theater when the reflection is 30 ft from the car. The strobe lights are rotating with the speed 2 revolutions per second.
Answers
Answer:
v=20π ft/s
Step-by-step explanation:
Given:
Distance from the security car to the movie theater, D=25 ft
Distance of the reflection from the car, d=30 ft
Speed of rotation of the strobe lights, 2 rev/s
To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.
We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.
ω=2πf
=> ω=2π(2)
=> ω=4π rad/s
The distance between the security car and the reflection on the wall of the theater is...
r=30-25= 5 ft
The speed of reflection is given as (this is the linear velocity)...
v=ωr
Plug our know values into the equation.
v=ωr
=> v=(4π)(5)
∴ v=20π ft/s
Thus, the problem is solved.
The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.
To solve this problem, we can use the concept of related rates. Let's consider the following variables:
x: Distance between the security car and the movie theater wall
y: Distance between the reflection of the security strobe lights and the security car
θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights
We are given:
x = 25 ft (constant)
y = 30 ft (changing)
θ = 2 revolutions per second (constant)
We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.
Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:
x^2 + y^2 = z^2
Differentiating both sides of the equation with respect to time (t), we get:
2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)
Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.
Plugging in the known values, we have:
2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)
Simplifying the equation, we find:
60(dy/dt) = 120π
Dividing both sides by 60, we get:
dy/dt = 2π ft/s
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Mo buys a house for £120 000
He sells the house for £150 000
Work out the percentage profit that Mo makes.
Answers
Answer:
25%Step-by-step explanation:
The profit = 150 000 - 120 000 = 30 000
………………………………………………………
The profit percentage is :
\(=\frac{30000}{120000} \times 100=0.25 \times 100 = 25 \%\)
What are the solutions to the quadratic equation (5y + 6)2 = 24?
y = StartFraction negative 6 + 2 StartRoot 6 EndRoot Over 5 EndFraction and y = StartFraction negative 6 minus 2 StartRoot 6 EndRoot Over 5 EndFraction
y = StartFraction negative 6 + 2 StartRoot 6 EndRoot Over 5 EndFraction and y = StartFraction 6 minus 2 StartRoot 6 EndRoot Over 5 EndFraction
y = StartFraction negative 4 StartRoot 6 EndRoot Over 5 EndFraction and y = StartFraction negative 8 StartRoot 6 EndRoot Over 5 EndFraction
y = StartFraction 4 StartRoot 6 EndRoot Over 5 EndFraction and y = StartFraction 8 StartRoot 6 EndRoot Over 5 EndFraction
Answers
there are two solutions:
a) y = \(\frac{-6+2\sqrt{6} }{5}\)
b) \(y = \frac{-6-2\sqrt{6} }{5}\)
Answer:
it's A
Step-by-step explanation:
Trust me I got the question right on the quiz
Bill had a $7 coupon for the purchase of any item. He bought a dvd recorder that was on sale forlu
of its original price. After using the coupon, Bill paid $86 for the dvd recorder before taxes. What
was the original price of the dvd recorder?
Answers
Answer:
5 maybe
Step-by-step explanation:
tosha has 8 coins in her pocket. she has a mixture of pennies, nickels, dimes and quarters, but she has no more than 3 of any coin. what is the largest amount of money she could possibly have?
Answers
The largest amount of money she could have is: (3 x 25 cents) + (3 x 10 cents) + (2 x 5 cents) = 75 cents + 30 cents + 10 cents = 115 cents or $1.15.
To find the largest amount of money Tasha could have with 8 coins in her pocket, we need to consider the different combinations of coins she could have. Since she has no more than 3 of any coin, the possibilities are:
- 3 quarters, 2 dimes, 1 nickel, 2 pennies = $0.81
- 3 quarters, 2 dimes, 2 nickels, 1 penny = $0.80
- 3 quarters, 2 nickels, 3 pennies = $0.78
- 3 quarters, 1 dime, 3 nickels, 1 penny = $0.76
- 3 quarters, 1 dime, 2 nickels, 3 pennies = $0.74
- 3 quarters, 1 dime, 1 nickel, 4 pennies = $0.73
- 2 quarters, 3 dimes, 1 nickel, 2 pennies = $0.70
- 2 quarters, 3 dimes, 2 nickels, 1 penny = $0.69
- 2 quarters, 2 dimes, 3 nickels, 1 penny = $0.68
- 2 quarters, 2 dimes, 2 nickels, 2 pennies = $0.67
Therefore, the largest amount of money Tasha could have is $0.81 with 3 quarters, 2 dimes, 1 nickel, and 2 pennies.
To maximize the amount of money Tosha could have with 8 coins and no more than 3 of any coin, she should carry the coins with the highest denominations. In this case, she can have 3 quarters (25 cents each), 3 dimes (10 cents each), and 2 nickels (5 cents each). The largest amount of money she could have is:
(3 x 25 cents) + (3 x 10 cents) + (2 x 5 cents) = 75 cents + 30 cents + 10 cents = 115 cents or $1.15.
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Tawny wrote an expression to represent "the quotient of 82 and a number, decreased by 26." She then evaluated the expression when n = 2. Which statements are true about the expression and its value? Check all that apply.
Answers
Answer:
D, E, G
Step-by-step explanation:
Quotient of 82 and a number=82/n
Decreased by 26
82/n-26
She evaluate the expression when n=2
82/n-26
When n=2
82/2-26
=41-26
=15
Answer
D. The correct expression is 82/n-26
E.The operations include division and subtraction.
G.The value of the expression is 15
Answer:
The correct answer is b,d,e,g
Step-by-step explanation:
Is the number 1 prime? Explain why or why not.
Please explain why.
Answers
1 can only be divided by one other integer except1, hence it is not a prime number.
The reason why 1 is not a prime number.Any natural number higher than 1 that is not the sum of two smaller natural numbers is referred to be a prime number. A composite number is a natural number greater than one that is not prime.
Given this definition, 1 is not a prime number because it can only be divided by one other integer, which is 1 itself.
Based on the explanation above, we can then conclude that 1 is not a prime number.
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