If
C(x) = 13000 + 400x − 3.6x2 + 0.004x3
is the cost function and
p(x) = 1600 − 9x
is the demand function, find the production level that will maximize profit. (Hint: If the profit is maximized, then the marginal revenue equals the marginal cost.)
units
Q 2
Find f.
f '''(x) = cos(x), f(0) = 4, f '(0) = 1, f ''(0) = 9
f(x) =
Q 3
A particle is moving with the given data. Find the position of the particle. a(t) = 2t + 3, s(0) = 9, v(0) = −4 s(t) =
Q 4
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)
f(x) = 6x5 − 7x4 − 6x2
F(x) =
Q 5
Factor the polynomial and use the factored form to find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)
P(x) = x3 + 3x2 − 9x − 27
x =
Answers
1. The production level that will maximize profit is 240 units.2. f(x) = sin(x) + x^3/3 + 4x + C where C is the constant of integration.
2. f(x) = sin(x) + x^3/3 + 4x + 1.
3. s(t) = 3t^2 + 2t + 9.
4. F(x) is the most general antiderivative of f(x).
5. The factorization of P(x) is (x - 3)(x + 3)^2.The zeros of P(x) are -3 and 3.
1. The production level that will maximize profit is 240 units. Given,
C(x) = 13000 + 400x - 3.6x^2 + 0.004x^3 = cost function
p(x) = 1600 - 9x = demand functionProfit = Total revenue - Total cost Let,
P(x) = TR(x) - TC(x)
where P(x) is profit function, TR(x) is total revenue function, and TC(x) is total cost function.
Now,
TR(x) = p(x) * x = (1600 - 9x) * x = 1600x - 9x^2and
TC(x) = C(x) = 13000 + 400x - 3.6x^2 + 0.004x^3
Let's differentiate both TC(x) and TR(x) to find the marginal cost and marginal revenue.
MC(x) = d(TC(x))/dx = 400 - 7.2x + 0.012x^2MR(x) = d(TR(x))/dx = 1600 - 18x
Now, if profit is maximized, then MR(x) = MC(x).1600 - 18x = 400 - 7.2x + 0.012x^21600 - 400 = 10.8x - 0.012x^2
1200 = x(10.8 - 0.012x^2)1200/10.8 = x - 0.00111x^3
111111.111 = 100000x - x^3
0 = x^3 - 100000x + 111111.111
From trial and error method, x = 240 satisfies the above equation.
Therefore, the production level that will maximize profit is 240 units.2. f(x) = sin(x) + x^3/3 + 4x + C where C is the constant of integration.
2. First, find f''(x) and f'''(x).
f''(x) = d/dx[f'(x)]
= d/dx[cos(x)]
= -sin(x)
f'''(x) = d/dx[f''(x)]
= d/dx[-sin(x)]
= -cos(x)Since f(0) = 4, f'(0) = 1, and f''(0) = 9,
f'(x) = f'(0) + integral of f''(x)dx
= 1 - cos(x) + C1
f(x) = f(0) + integral of f'(x)dx
= 4 + integral of (1 - cos(x))dx + C2
= 4 + x - sin(x) + C2
Now,
f(0) = 4, f'(0) = 1, f''(0) = 9
So, 4 + C2 = 4 => C2 = 0and
1 - cos(0) + C1 = 1 => C1 = 1
Therefore,
f(x) = sin(x) + x^3/3 + 4x + 1.
3. The position of the particle is given by the equation,
s(t) = s(0) + v(0)t + 1/2 a(t)t^2Given a(t) = 2t + 3, s(0) = 9, and v(0) = -4
s(t) = 9 - 4t + t^2 + 3t^2/2
s(t) = 3t^2 + 2t + 9.
4. The most general antiderivative of the function is given by,
F(x) = Integral of f(x)dxwhere f(x) = 6x^5 - 7x^4 - 6x^2Now,
F(x) = x^6 - 7x^5/5 - 2x^3 + C where C is the constant of integration.F'(x) = f(x)
= 6x^5 - 7x^4 - 6x^2
So, F(x) is the most general antiderivative of f(x).
5. First, find the factorization of P(x).
P(x) = x^3 + 3x^2 - 9x - 27
= x^2(x + 3) - 9(x + 3)
= (x^2 - 9)(x + 3)
= (x - 3)(x + 3)(x + 3)
Therefore, the factorization of P(x) is (x - 3)(x + 3)^2.The zeros of P(x) are -3 and 3.
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Q1) The production level that will maximize profit is 111 units.
Q2) \(f(x) = sin(x) + x - cos(x) + x + 4\)
Q3) \(s(t) = (t³/3) + (3t²/2) - 4t + 9\)
Q4) \(F(x) = x⁶ - (7/5)x⁵ - 2x³ + C1\)
Q5) The zeros of the polynomial are: x = -3, 3
Q1) We are given the following equations:
\(C(x) = 13000 + 400x − 3.6x2 + 0.004x\)
\(3p(x) = 1600 − 9x\)
Given profit function:
\(π(x) = R(x) - C(x)\) where R(x) = p(x)*x is the revenue function
\(π(x) = x(1600-9x) - (13000 + 400x − 3.6x² + 0.004x³)\)
Taking the first derivative to maximize the profit
\(π'(x) = 1600 - 18x - (400 - 7.2x + 0.012x²)\)
\(π'(x) = 0\)
⇒ \(1600 - 18x = 400 - 7.2x + 0.012x²\)
Solving for x, we get: x = 111.11 ≈ 111 units (approx)
Hence, the production level that will maximize profit is 111 units.
Q2) We have been given: f '''(x) = cos(x), f(0) = 4, f '(0) = 1, f ''(0) = 9
Taking the antiderivative of f '''(x) with respect to x, we get:
\(f''(x) = sin(x) + C1\)
Differentiating f''(x) with respect to x, we get:
\(f'(x) = -cos(x) + C1x + C2\)
Differentiating f'(x) with respect to x, we get:
\(f(x) = sin(x) + C1x - cos(x) + C2x + C3\)
We know that f(0) = 4, f'(0) = 1 and f''(0) = 9
Putting the given values, we get: C1 = 1, C2 = 1, C3 = 4
Hence, \(f(x) = sin(x) + x - cos(x) + x + 4\)
Q3) We have been given: a(t) = 2t + 3, s(0) = 9, v(0) = −4
Using the initial conditions, we get: \(v(t) = ∫a(t)dt = t² + 3t + C1\)
Using the initial conditions, we get: C1 = -4
Hence, \(v(t) = t² + 3t - 4\)
Using the initial conditions, we get: \(s(t) = ∫v(t)dt = (t³/3) + (3t²/2) - 4t + C2\)
Using the initial conditions, we get: C2 = 9
Hence, s(t) = (t³/3) + (3t²/2) - 4t + 9
Q4) We need to find the antiderivative of \(f(x) = 6x⁵ - 7x⁴ - 6x²\)
Taking the antiderivative, we get: \(F(x) = (6/6)x⁶ - (7/5)x⁵ - (6/3)x³ + C1\)
Simplifying the above equation, we get: \(F(x) = x⁶ - (7/5)x⁵ - 2x³ + C1\)
Hence, \(F(x) = x⁶ - (7/5)x⁵ - 2x³ + C1\)
Q5) We have been given: \(P(x) = x³ + 3x² − 9x − 27\)
\(P(x) = (x-3)(x² + 6x + 9)\)
\(P(x) = (x-3)(x+3)²\)
Hence, the zeros of the polynomial are: x = -3, 3
Therefore, the answer is (-3, 3).
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Related Questions
which sentence correctly describes a data set that follows a normal distribution with a standard diviation of 4 and a mean of 14
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Answer: A sentence that correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 14 is:
"The data set is approximately normally distributed, with the majority of the data falling within a range of 6 to 22, with a few data points falling outside of this range. The mean of the data set is 14, and the standard deviation is 4."
Step-by-step explanation:
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Step-by-step explanation:
Use the solution method from this example to find a basis for the given subspace. S = span {[1 -1 0 2], [3 -5 4 8], [0 1 -2 -1]} Give the dimension of the basis. v
Answers
Answer:
Step-by-step explanation:
The dimension of the basis is {[1 0 0 2], [-1 1 0 0]}.
To find a basis for the subspace S = span {[1 -1 0 2], [3 -5 4 8], [0 1 -2 -1]}, we can use the same method as in the example. First, we put the vectors in a matrix and row-reduce it:
[1 -1 0 2]
[3 -5 4 8]
[0 1 -2 -1]
R2 - 3R1 -> R2
R3 -> R3 + 2R1
[1 -1 0 2]
[0 -2 4 2]
[0 1 -2 -1]
-1/2R2 -> R2
[1 -1 0 2]
[0 1 -2 -1]
[0 1 -2 -1]
R3 - R2 -> R3
[1 -1 0 2]
[0 1 -2 -1]
[0 0 0 0]
We can see that the last row is all zeros, so we have only two pivots and one free variable. This means that the dimension of the subspace S is 2. To find a basis, we can write the pivots as linear combinations of the original vectors:
[1 -1 0 2] = [1 0 0 2] + [-1 1 0 0]
[0 1 -2 -1] = [0 1 -2 -1]
Therefore, a basis for S is {[1 0 0 2], [-1 1 0 0]}.
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Find the slope of the line passing through the points (4, 4) and (4, - 4) .
Answers
Answer:
Slope = undefinedStep-by-step explanation:
We know that:
Slope Formula = y₂ - y₁/x₂ - x₁Solution:
y₂ - y₁/x₂ - x₁ = -4 - 4/4 - 4=> -8/0 = undefinedSince the slope of the line is un-defined, the line is vertical. Please look at my graph to understand better.
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
i odnt know use ur fingers or a calculator
Step-by-step explanation:
show that the function f(x) = [infinity] x n n! n = 0 is a solution of the differential equation f ′(x) = f(x).
Answers
This equation holds true for any value of x, which means that f(x) = ∑(n=0)(∞) xn/n! is indeed a solution of the differential equation f′(x) = f(x).
To show that the function f(x) = ∑(n=0)(∞) xn/n! is a solution of the differential equation f′(x) = f(x), we need to demonstrate that f′(x) = f(x) holds true for this function.
Let's first compute the derivative of f(x) using the power series representation:
f(x) = ∑(n=0)(∞) xn/n!
f'(x) = ∑(n=1)(∞) nxn-1/n!
Now we can substitute f(x) and f'(x) into the differential equation:
f′(x) = f(x)
∑(n=1)(∞) nxn-1/n! = ∑(n=0)(∞) xn/n!
We can rewrite the left-hand side of this equation by shifting the index of summation by 1:
∑(n=1)(∞) nxn-1/n! = ∑(n=0)(∞) (n+1)xn/n!
We can also factor out an x from each term in the series:
∑(n=0)(∞) (n+1)xn/n! = x∑(n=0)(∞) xn/n!
Now we can see that the right-hand side of this equation is just f(x) multiplied by x, so we can substitute f(x) = ∑(n=0)(∞) xn/n! to get:
x ∑(n=0)(∞) xn/n! = ∑(n=0)(∞) xn/n!
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To show that the function f(x) = ∑(n=0 to infinity) xn/n! is a solution to the differential equation f′(x) = f(x), we need to show that f′(x) = f(x).
First, we find the derivative of f(x):
f′(x) = d/dx [ ∑(n=0 to infinity) xn/n! ]
= ∑(n=1 to infinity) xn-1/n! · d/dx (x)
= ∑(n=1 to infinity) xn-1/n!
Now, we need to show that f′(x) = f(x):
f′(x) = f(x)
∑(n=1 to infinity) xn-1/n! = ∑(n=0 to infinity) xn/n!
To do this, we can write out the first few terms of each series:
f′(x) = ∑(n=1 to infinity) xn-1/n! = x^0/0! + x^1/1! + x^2/2! + x^3/3! + ...
f(x) = ∑(n=0 to infinity) xn/n! = x^0/0! + x^1/1! + x^2/2! + x^3/3! + ...
Notice that the only difference between the two series is the first term. In the f′(x) series, the first term is x^0/0! = 1, while in the f(x) series, the first term is also x^0/0! = 1. Therefore, the two series are identical, and we have shown that f′(x) = f(x).
Therefore, f(x) = ∑(n=0 to infinity) xn/n! is indeed a solution to the differential equation f′(x) = f(x).
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What is the solution set for the exponential inequality (1/2)^2x+1 <4?
Answers
Answer: x < 12
-------------------------------------------------------------------------------------------------------
Answer:
[-3/2, infinity)
Step-by-step explanation:
Which of the following is not a fundamental identity? A. cot θ = cos θ/sinθ. B. sec θ = 1/cosθ. C. sec^2 + 1 = tan^2θ. D. 1 + cot^2θ = csc^2θ.
Answers
A fundamental identity is an equation that relates the values of the trigonometric functions for a given angle. The equation cot θ = cos θ/sinθ is an example of a fundamental identity.
This identity states that the cotangent of an angle is equal to the cosine of the angle divided by the sine of the angle. The equation sec θ = 1/cosθ is another example of a fundamental identity. This identity states that the secant of an angle is equal to the reciprocal of the cosine of the angle. The equation sec^2 + 1 = tan^2θ is also a fundamental identity. This identity states that the square of the secant of an angle plus one is equal to the square of the tangent of the angle. The equation 1 + cot^2θ = csc^2θ is not a fundamental identity. This equation states that one plus the square of the cotangent of an angle is equal to the square of the cosecant of the angle. This equation is not a fundamental identity because it does not relate the values of the trigonometric functions for a given angle.
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7. Carlos is renovating a house and hires a plumber to install the piping for 4 points
the new bathroom. The plumber charges an initial fee plus an hourly rate
for the number of hours it will take to complete the installation. The
function y = 100 + 35x can be used to model the total cost of the job, in
dollars. What does the slope in the expression of this function represent? *
the initial fee for the installation, $35
the initial fee for the installation, $100
the cost per hour of installation work, $35
the number of hours to complete the installation, x
Answers
Answer:
the cost per hour of installation work, $35
Step-by-step explanation:
y = 35x + 100
the slope of a function is the coefficient of x, therefore, it is 35. $100 is the initial fee, since it ia the y intercept, and $35 is the cost per hour. y is the total amount, and x is the number of hours. Therefore, the only possible answer is the third choice,
Find the surface area of a cylinder with a height of 9 ft and a base of 5 ft.
Use the value of 3.14 for pi, and do not do any rounding
*Be sure to include the correct unit*
Answers
Answer:
326.56 square feet
Step-by-step explanation:
PLS HELP ASAP PLSSS IT DETECTS IF ITS RIGHT OR WRONG HELPPP
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Answer:
ccccccccccccccccccccc
Answer:
y=2x+4
Step-by-step explanation:
If you look at the table y goes up by 2 every time x goes up by 1 and when x is 0 y is 4 so its y=2x+4
Which quadratic equation is equivalent to (x – 4)2 – (x – 4) – 6 = 0?
Answers
Answer:
Step-by-step explanation:
Posible answers are found
if you square (x-4), open pharenthesis -(x-4) and then combine like terms
x^2 +16-8x -x+4-6 =0
x^2 -9x +14 =0
or you can substitute (x-4) with another letter like x-4 =a so
a^2 -a -6 =0
Answer:
u2 – u – 6 = 0 where u = (x – 4)
Step-by-step explanation:
edge 2020
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lua is creating a rectangular prism the base of her prism is shown below she plans to have a height of 7 cubes
what will the volume of the completed figure be?
_______ cubic units
Answers
Answer:
63
Step-by-step explanation:
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A certain car is rated to get 26 miles per gallon. How far can it travel on 12.5 gallons of gas?
Answers
Our car can do 26 miles with one gallon, so, if we have 12.5 gallons, to find how much we can travel we need to make the product of the amount of gallons we have by the amount of milles we can do with one gallon, wich gives us the expression:
\(12.5\times26=325\)So our car can travel 325 miles with 12.5 gallons of gas.
A farmer goes to the market to sell a box of eggs. A clumsy horse steps on the box of eggs and breaks a lot of them. The horse’s rider offers to pay for all of the eggs in the box and asks the farmer how many eggs there were. The farmer does not remember the exact number, but when she took them out of the box two at a time, there was 1 egg left. The same thing happened when she took them out three, four, five and six eggs at a time, but when she took them out 7 at a time, there were no eggs left
Answers
The smallest number of eggs that could have been in the box is 1134
The problem is to find the smallest number of eggs that could have been in the box, given the remainder when taking them out by different numbers. Here are the moves toward tackling it:
Allow n to be the quantity of eggs in the container. Then we have the accompanying arrangement of congruences:
n ≡ 1 (mod 2)
n ≡ 1 (mod 3)
n ≡ 1 (mod 4)
n ≡ 1 (mod 5)
n ≡ 1 (mod 6)
n ≡ 0 (mod 7)
For this problem, we have k = 6 k = 6, a i = {1,1,1,1,1,0} a_i = {1,1,1,1,1,0}, M i = {1260,840,630,504,420,720} M_i = {1260,840,630,504,420,720}, and y i = {−1,−2,−3,-4,-5,-6} y_i = {-1,-2,-3,-4,-5,-6}.
Plugging these values into the formula and simplifying modulo 5040, we get:
n = (−1260 + −1680 + −1890 + −2016 + −2100 + 0) mod 5040
n = (−8946) mod 5040
n = (−3906) mod 5040
n = 1134 mod 5040
Therefore, the smallest number of eggs that could have been in the box is 1134
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Quadrilateral GHIJ is similar to quadrilateral KLMN. Find the measure of side NK. Round your answer to the nearest tenth if necessary. Figures are not drawn to scale.
Answers
Answer:
30.2
Step-by-step explanation:
56/13 = ~4.30769
7*4.30769=30.153
round up, 30.2
if she needs to allocate her waking time of 15 hours between these two activities, how much studying is she going to do per day?
Answers
She would be doing 9 hours of studying per day and 6 hours of other activities. This is because 15 hours divided by 9 hours of studying and 6 hours of other activities would equal the same amount of time allocated to each activity.
The amount of studying she is going to do per day is 9 hours, and the amount of other activities she is going to do per day is 6 hours. This means that she will be dedicating roughly 60% of her waking hours to studying and 40% to other activities. This is a good balance between the two activities, and it will ensure that she is able to adequately focus on both her studies and other activities.
This balance will also help her to stay motivated and not become overwhelmed by her studies. Having a set amount of time for both activities will also help her to organize her day and stay on track. It will give her a sense of structure and allow her to plan her day accordingly.
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A number line is shown.
E
F
H
G
+
10
-10 -5
0
15 20
Which two point values create a zero pair?
A points E and F
B points Fand G
cpoints G and H
D points E and H
Answers
Answer:
it's b) F and GStep-by-step explanation:
to understand thisyou need to know about:integeradditionPEMDASlet's solve:-5 and 5 make
if you add them you will get 0
-5+5
=0
therefore
it's bThe perimeter of a rectangular cattle feeding area is 100 meters. The
area is 525 square meters. Find the dimensions of the area.
Answers
when 7 is added to 3 times a number, the sum is multiplied by 2 and 15 is subtracted what is the final answer
Answers
Answer:
2(3x+7) -15
Step-by-step explanation:
Let x = unknown number
7 is added to 3 times a number
3x+7
Multiply the sum by 2
2(3x+7)
Subtract 15
2(3x+7) -15
Answer:
Let the required number be " x "
Now, 7 is added to 3 times a number : (3x + 7)
Next, the sum is multiplied by 2 : 2(3x + 7)
And then, 15 is substracted from it : 2(3x + 7) - 15
2(3x + 7) - 15 is the final answer.Use the quadratics formula to solve 2x² +7+4= 0. Approximate the solutions to the nearest hundredth.
A-3.35, -0.15
B) 1.28, 3.66
C) -5.56, -1.44
D) -2.78,-0.72
Answers
Answer:
Step-by-step explanation:
so you do me and can’t
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second.
y=-16x^2+248x+116
Answers
Answer:
Step-by-step explanation:
The rocket will hit the ground when y = 0. If you use the quadratic equation:
x = (-248±√(2482-4(-16)(116))/(2(-16))
What will come in place of (?) in following series following a certain pattern?
16, 20, 28, 27, 42,?
The answer to this problem is 32. How?
Answers
Answer:
The sequence follows a +2 and -2 pattern.
Step-by-step explanation:
As you can see that the series start with 16 and if you look closely, there's a gap of 12 between the first and the third digit. Similarly, there's a gap of 14 digits between the third and the fourth digit, thus +2.
At the same time the correlation between the second and the fourth digit shows a differnece of 7. Similarly, the fourth and the sixth place (?) should be a deficit of 5 and hence, -2.
These sequence follows a varied sometimes non-recurring patterns just to tingle with you brain.
Cheers.
Write an inequality relating the give side lengths or angle measures. It is possible that there is not enough information to reach a conclusion. Fill in the blank with <,>,= or NC.
Answers
Answer:
Which equation is y = –3x2 – 12x – 2 rewritten in vertex form?
y = –3(x + 2)2 + 10
y = –3(x – 2)2 + 10
y = –3(x + 2)2 – 14
y = –3(x – 2)2 – 2
Step-by-step explanation:
Which equation is y = –3x2 – 12x – 2 rewritten in vertex form?
y = –3(x + 2)2 + 10
y = –3(x – 2)2 + 10
y = –3(x + 2)2 – 14
y = –3(x – 2)2 – 2
When ordinal data measurement produces a large number of tied ranks, we should use the: a. Pearson r. b. Spearman's rank-order. c. Cramér's V. d. Goodman's and Kruskal's Gamma
Answers
When dealing with ordinal data measurement that produces a significant number of tied ranks, it is appropriate to use Spearman's rank-order correlation coefficient.
Spearman's rank-order correlation coefficient is a nonparametric measure used to assess the strength and direction of the relationship between two variables when the data is measured on an ordinal scale or when there are tied ranks.
Unlike Pearson's correlation coefficient, which requires interval or ratio level data, Spearman's rank-order correlation is based on the ranks of the data points.
When there are tied ranks in the data, it means that multiple individuals or observations share the same rank.
This can happen when the measurements are not precise enough to assign unique ranks to each data point.
In such cases, using Pearson's correlation coefficient, which relies on the exact values of the variables, may not be appropriate.
Spearman's rank-order correlation coefficient handles tied ranks by assigning them average ranks. This approach ensures that the analysis considers the relative ordering of the data points, rather than the specific values.
By using this measure, we can assess the monotonic relationship between the variables, even when tied ranks are present.
Therefore, when faced with ordinal data measurement containing tied ranks, it is advisable to use Spearman's rank-order correlation coefficient to accurately assess the relationship between the variables.
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_____, a variation of the bar chart, is useful for tracking progress toward completing a series of events over time.
Answers
Gantt chart, a variation of the bar chart, is useful for tracking progress toward completing a series of events over time.
A Gantt chart is a project management tool that displays business activities over time. Gantt charts were created in the early 20th century by Henry Gantt to improve project planning, scheduling, and tracking by describing how work is being done compared to planned work. Today, project managers and team members use only one tool to plan projects, allocate resources, and track progress.
It is a bar chart that shows the status of the project, when each task should occur, and how long each task will take to complete. As the project progresses, graphs are shaded to show which tasks have been completed. Using Project Manager's Gantt chart, we can assign tasks to our partners, schedule them, estimate costs, and track progress in a timely manner. Therefore, a Gantt chart can be used to track the progress of completion events over time..
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Find the equation of the line
The line has a slope of 4 and passes through the point (2,-1).
Answers
We know that the line has a slope of 4, and the line passes through the point (2,-1). So, we can use the point-slope form of a line to find the equation of the line.
The point-slope form of a line is given by y - y1 = m(x - x1), where m is the slope of the line, and (x1, y1) is a point on the line.
By substituting the values we know into the point-slope form, we get:
y - (-1) = 4(x - 2)
Simplifying:
y + 1 = 4x - 8
Subtract 1 from both sides:
y = 4x - 9
The equation of the line is y = 4x - 9.
Hope this helped!
(y-(-1))=4*(x-2)
y+1=4x-8
4x-y=9
What is the following product? sqrt10 x sqrt10
Answers
The product of the mathematical expression √10 · √10 is 10 option first 10 is correct.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have given a mathematical expression:
= √10 · √10
As we know,
√a² = a
or
√a×√a = a
By applying the above rule:
= √10×√10
= √10²
= 10
Thus, the product of the mathematical expression √10 · √10 is 10 option first 10 is correct.
Learn more about the arithmetic operation here:
brainly.com/question/20595275
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For what value of c does x^2−2x−c=4 have exactly one real solution?
PLEASE HELP!!!!!!!
Answers
Answer:
-5
Step-by-step explanation:
Moving all terms of the quadratic to one side, we have
\(x^2-2x-(c+4)=0\).
A quadratic has one real solution when the discriminant is equal to 0. In a quadratic \(ax^2+bx+d\), the discriminant is \(\sqrt{b^2-4ad}\).
(The discriminant is more commonly known as \(\sqrt{b^2-4ac}\), but I changed the variable since we already have a \(c\) in the quadratic given.)
In the quadratic above, we have \(a=1\), \(b=-2\), and \(d=-(c+4)\). Plugging this into the formula for the discriminant, we have
\(\sqrt{(-2)^2-4(1)(-(c+4))\).
Using the distributive property to expand and simplifying, the expression becomes
\(\sqrt{4-4(-c-4)}=\sqrt{4+4c+16}\\~~~~~~~~~~~~~~~~~~~~~~=\sqrt{20+4c}\\~~~~~~~~~~~~~~~~~~~~~~=\sqrt{4}\cdot\sqrt{5+c}\\~~~~~~~~~~~~~~~~~~~~~~=2\sqrt{c+5}.\)
Setting the discriminant equal to 0 gives
\(2\sqrt{c+5}=0\).
We can then solve the equation as usual: first, divide by 2 on both sides:
\(\sqrt{c+5}=0\).
Squaring both sides gives
\(c+5=0\),
and subtracting 5 from both sides, we have
\(\boxed{c=-5}.\)