find the slope pls help

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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Answer: \(7,5.66,39^{\circ}\)

Step-by-step explanation:

Given

\(IJ=9\\\angle I=51^{\circ}\)

from figure, we can write

\(\Rightarrow \sin 51^{\circ}=\dfrac{HJ}{9}\\\\\Rightarrow HJ=9\sin 51^{\circ}=6.99\approx 7\)

\(\Rightarrow \cos 51^{\circ}=\dfrac{HI}{9}\\\Rightarrow HI=9\cos 51^{\circ}\\\Rightarrow HI=5.66\)

In right angle trianle, the sum of the remaining two angles is \(90^{\circ}\)

\(\therefore 51^{\circ}+\angle J=90^{\circ}\\\Rightarrow \angle J=90^{\circ}-51^{\circ}\\\Rightarrow \angle J=39^{\circ}\)

The combined area of dark pieces is 253.5 in².

First, Area of 5 light pieces

= length x width

= 3 3/4 x 39

= 15/4 x 39

= 146.25 in²

Now, Area of board

= L x W

= 29 x 39

= 1131 in²

Thus, the combined area of dark pieces

= 1131 - 146.25 x 6

= 253.5 in²

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No, we cannot reject H₀: p = 0.5 against H₁: p₆= 0.5 at the 1% level of significance.

The true population proportion is the unknown population parameter. Here, the 99% confidence interval for the true population proportion is given as (0.45, 0.65). It means that there is a 99% chance that the true population proportion lies between 0.45 and 0.65.  

To determine whether we can reject H₀: p = 0.5 against H₁: p₆= 0.5 at the 1% level of significance, we need to check whether the hypothesized value of 0.5 lies within the confidence interval or not.  

As the confidence interval obtained is (0.45, 0.65), which does include the hypothesized value of 0.5, we can conclude that we cannot reject the null hypothesis H₀: p = 0.5 against the alternative hypothesis H₁: p₆= 0.5 at the 1% level of significance.  

Thus, we can say that there is not enough evidence to suggest that the population proportion is significantly different from \(0.5\) at the 1% level of significance.

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Answer: 7 tens and 6 ones

Step-by-step explanation: 76 is two numbers, with a 7 in the tens place and a 6 in the ones place.

76 can be represented as 7 tens and 6 ones or as 6 tens and 16 ones. This involves understanding the place value of digits in a number and knowing that a ten can be broken down into ones.

The number 76 can be broken down into tens and ones in multiple ways. First, let's understand what tens and ones mean in the context of a number. In the number 76, '7' is the tens place, and '6' is the ones place, meaning there are 7 tens (70) and 6 ones (6) making up 76.

One way to show 76 with tens and ones is to say that there are 7 tens and 6 ones. This is a very direct method where we just count the number of tens and ones in the number.

Another way we could break down 76 is to say there are 6 tens and 16 ones. This method involves taking one of the tens and breaking it down into 10 ones, giving us a total of 6 tens and 16 ones.

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Answer:

21

Step-by-step explanation:

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

AD        AH

-----  =  ---------

AB         AH +y

3        9

---- = ------

10         9+y

Using cross products:

3(9+y) = 9*10

27+3y = 90

3y = 90-27

3y =63

y = 63/3

y = 21

Answer:

y = 21

Step-by-step explanation:

According to the Side Splitter Theorem, if a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.

Therefore, according to the Side Splitter Theorem:

\(\boxed{\sf AD : DB = AH : HC}\)

From inspection of the given triangle, the lengths of the line segments are:

To find the value of y, substitute the given line segment lengths into the proportion and solve for y:

\(\begin{aligned}\sf AD : DB &=\sf AH : HC\\\\3:7&=9:y\\\\\dfrac{3}{7}&=\dfrac{9}{y}\\\\3 \cdot y&=9 \cdot 7\\\\3y&=63\\\\\dfrac{3y}{3}&=\dfrac{63}{3}\\\\y&=21\end{aligned}\)

Therefore, the value of y is 21.

Answer:

Anna

Step-by-step explanation:

Hers grew 2.5 inches each time

Answer: Answer  B, shows a line going from point (0, 60) to point (3, 120).

Step-by-step explanation: i hope this helps you

Answer:

Answer  B, shows a line going from point (0, 60) to point (3, 120).

Step-by-step explanation:

The sale price of an item normally priced at £90 is £67.5            

What is the percentage?

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100.

Given :

A shop is having a sale. all items are reduced by 25%.

To Find:

Work out the sale price of an item normally priced at £90.

Price of an item = £90

Price is reduced by 25%

Reduction in price = 25%*90=25/100= 22.5

Reduced price = 90-22.5=67.5

Hence, the sale price of an item normally priced at £90 is £67.5                              

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Answer:

-------------------

Given:

First, convert the two side length as below:

Now find the third side:

Hence the third side is 5√7 feet.

\(y = \frac{28}{5} \)

Answer:

\(y=5.6\) or \(y=28/5\)

Step-by-step explanation:

4/5 = y/7

⇒ Cross multiply:

4 × 7 = 5 × y

⇒ Multiply 4 × 7 & 5 × y:

\(28=5y\)

⇒ Solve the formed equation:

\(28=5y\)

⇒ Move all the terms containing y to the right side and the other values to the left side:

⇒ Add '-5y' to each side of the equation:

\(28+-5y=5y+-5y\)

⇒ Combine like terms: \(5y+-5y=0\)

\(28+-5y=0\)

⇒ Add '-28' to each side of the equation:

\(28+-28+-5y=0+-28\)

⇒ Combine like terms: \(28+-28=0\)

\(0+-5y=0+-28\)

\(-5y=0+-28\)

⇒ Combine like terms: \(0+-28=-28\)

\(-5y=-28\)

⇒ Divide each side by '-5':

\(y=5.6\) or \(y=28/5\)

hope this helps :)

Big O notation focuses on the worst-case scenario analysis, which is 0(n) for a simple search. It’s a reassurance that a simple search will never be slower than O(n) time.

Imagine that you're a teacher with a student named Ram. You want to find his records, so you use a simple search algorithm to go through your school district's database.

You know that a simple search takes O(n) times to run. This means in the worst case, you'll have to search through every single record to find Ram

After a simple search, you find that Ram records are the very first entry in the database. You don't have to look at every entry.

Did this algorithm take O(n) time Or did it take O(1) time because you found Ram records on the first try?

In this case, 0(1) is the best-case scenario – you were lucky that Ram records were at the top. But Big O notation focuses on the worst-case scenario, which is 0(n) for a simple search. It’s a reassurance that a simple search will never be slower than O(n) time.

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Answer:

9

Step-by-step explanation:

If I’m understanding you correctly, the answer would be nine.  Any number with a 9 in the one’s place (unit digit) would still have a nine in that place after being cubed.

29³=24,389

69³=328,509

Answer:

Step-by-step explanation:

unit digit of cube of any number will be the unit digit of its last digit

the unit digit of the cube of a number ending with 9 is 9

ex : unit digit of 29³= unit digit of 9³=unit digit of 729 =9

Answer:

A fraction equivalent to \(\frac{1}{2}\) on the number line is \(\frac{3}{6}\).

Drag the dot to \(\frac{3}{6}\) on the number line.

Step-by-step explanation:

3 is half of 6. To check if this is correct multiply \(\frac{1}{2}\) and 3.

\(\frac{1}{2}*3=\frac{3}{6}\)

Hope this helps!

If not, I am sorry.

Answer:

Step-by-step explanation:

Given function:

a)  g(2)

b)  g(t - 2)

c)  g(t) - g(2)

6and 7 tnks ME later. heh

Answer:

2/3

Step-by-step explanation:

You have 6 friends who want to share 4 brownies equally. You simply divide the 4 brownies by 6 people:

4/6 = 2/3 (simplified)

So each friend gets 2/3 of a brownies

[RevyBreeze]

The first thing I did to solve this was notice that since the ones place of the withdrawal was a 5, there had to be an odd number of 5s. Also, the amount of 10s has to be even, so there has to be an odd number of 20s. Then I started trying combinations.

3,6,15 = 15+60+300=375

Hey, I got lucky! I got it first try!

Answer: x=-17

Step-by-step explanation:

Given

x-(-7)=-10

Expand Parenthesis (REMEMBER to change signs)

x+7=-10

Subtract 7 on both sides

x+7-7=-10-7

x=-17

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Step-by-step explanation:

Solving for x,

This way, we can conlcude that:

The length x of a side of the small inner square can be determined using the properties of similar triangles.

To find the length x, we can set up a proportion between the small inner square and the larger outer square.

Let's denote the side length of the small inner square as s and the side length of the larger outer square as S.

Since the small inner square is completely contained within the larger outer square, the ratio of their side lengths will be the same as the ratio of their corresponding sides.

Therefore, we can set up the following proportion:

s / S = x / (x + 10)

Here, the x + 10 represents the side length of the larger outer square, as it is 10 units longer than the side length of the small inner square.

To solve for x, we can cross-multiply the proportion:

s * (x + 10) = x * S

Expanding the equation:

sx + 10s = xS

Rearranging the equation to isolate x:

sx - xS = -10s

Factoring out the common term x:

x(s - S) = -10s

Dividing both sides by (s - S):

x = -10s / (s - S)

Now, we have an expression for x in terms of s and S.

It's important to note that the given information is insufficient to find the exact value of x without additional measurements or equations. The value of x will depend on the specific dimensions of the small inner square and the larger outer square.

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Answer:

B. DX = YZ

Step-by-step explanation:

Answer:

In math, a unit fraction can be defined as a fraction whose numerator is 1. It represents 1 shaded part of all the equal parts of the whole.

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

x + 4 = 12

Subtract 4 from both sides

x = 8

Let's check

8 + 4 = 12

12 = 12

So, x = 8 is correct!

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The cοmpany caught a tοtal οf apprοximately 557,739 ( nearest whοle number) fish οver the first 12 years.

Whοle numbers are pοsitive numbers (this includes 0) that dο nοt have decimals οr fractiοns tο them.

Tο sοlve this prοblem, we can use geοmetric prοgressiοn tο calculate the tοtal number οf fish caught by the cοmpany οver the 12 years. The first term in the sequence is 78,000, and the cοmmοn ratiο is 0.95 (since the number οf fish caught decreases by 5% each year).

The fοrmula fοr the sum οf a geοmetric prοgressiοn with n terms is:

Sₙ = a(1 - rⁿ) / (1 - r)

where a is the first term, r is the cοmmοn ratiο, and n is the number οf terms.

Tο find the sum οf the first 12 terms, we substitute a = 78,000, r = 0.95, and n = 12 intο the fοrmula:

S₁₂ = 78,000(1 - 0.95¹²) / (1 - 0.95) ≈ 557,739

Therefοre, the cοmpany caught a tοtal οf apprοximately 557,739 fish οver the first 12 years.

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Answer:

9x² - 7x - 9

Step-by-step explanation:

Two sides

(6x + 7) + 8x = 14x + 7

total perimeter - two sides = Third side

9x² + 7x - 2

-      (14x + 7)

––––––––––

9x² - 7x - 9

Well, doing 4021836 - 1987269 on paper, you would get the answer of 2034567

solu. 2034272

Alternate form. 2.034272*10^2

Answer:

\(9\sqrt{2}\) feet

Step-by-step explanation:

Consider the attached figure.

An isosceles triangle is a triangle in which two sides are equal.

\(AB=BC=9\) feet

According to Pythagoras theorem,

square of hypotenuse is equal to sum of squares of other two sides.

\(AC^2=AB^2+BC^2\\AC^2=9^2+9^2\\AC^2=81+81\\AC^2=162\\AC=\sqrt{162}\)

\(AC=9\sqrt{2}\) feet

Answer:

-56 or "p minus 56"  (negative)

Step-by-step explanation:

If you lose points, your points will decrease because it's taking away your points. So, you lost 56 points.