The maximum profit that the considered company can get is 142,400 bucks. That profit is earned when input x (the number of items produced) is 380
How to obtain the maximum value of a function?To find the maximum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.
Putting those values of x in the second rate of function, if results in negative output, then at that point, there is maxima. If the output is positive then its minima and if its 0, then we will have to find the third derivative (if it exists) and so on.
The missing part of question is:
" [tex]C(x)=2000+70x[/tex], [tex]R(x)=830x-x^2[/tex]
A. Determine the maximum profit of the company.
B. Determine the number of items that must be produced and sold to obtain the maximum profit"
The profit is the difference between the revenue and the cost, so we get:
[tex]P(x) = R(x) - C(x) = 760x - x^2 - 2000[/tex]
Finding its first and second rate with respect to x:
[tex]P'(x) = 760 -2x\\P''(x) = -2[/tex]
Equating first rate to 0 to get the critical values:
[tex]P'(x) = 0 \implies 760 = 2x \implies x = 380[/tex]
The second rate is < 0 for any x, x = 380 is minima, and x = 380 being only critical value, it is global maximum.
At x = 380, the profit evaluates to:
[tex]P(x) = 760x - x^2 - 2000\\P(380) = 760(380) - (380)^2 - 2000 = (380)^2 - 2000\\P(380) = 142400[/tex]
Thus, the maximum profit that the considered company can get is 142,400 bucks. That profit is earned when input x (the number of items produced) is 380
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[100 points]
Using mathematically precise language, explain in detail how you would multiply the complex number z1=r1 (cos theta1+isin theta 1) with the complex number z2=r2 (cos theta 2+isin theta 2)
Answer:
Multiply the moduli and add the arguments.Step-by-step explanation:First write out the two terms being multiplied: z1z2= [r1(cos(theta 1) + isin(theta 1))][r2(cos(theta 2)+ isin(theta 2))] z1z2= r1r2 (cos(theta 1) + isin(theta 1))(cos(theta 2)+ isin(theta 2)) z1z2= r1r2(cos(theta 1)cos(theta 2))+(icos(theta 1)sin(theta 2))+(icos(theta 2)sin(theta 1))+(i^2 sin(theta 1)sin(theta 2)) Next group and rewrite the like term with the sums and differences. Your answer is the multiplication of the moduli and the addition of the arguments: z1z2= r1r2[cos(theta 1 + theta 2) + i sin (theta 1 and theta 2)].
The product complex number is [tex]z_1z_2[/tex]= [tex]r_1r_2[/tex][cos (θ1+θ2) + i sin (θ1+θ2)].
What is Complex number?A real number and an imaginary number are effectively combined to create a complex number. The complex number is written as a+ib, where a and ib are real and imaginary numbers, respectively.
We have,
z1=r1 (cos θ1 +i sin θ1)
z2=r2 (cos θ2 +i sin θ2)
where r-radius/radii
and, m-modulus/moduli
Now, the product is
[tex]z_1z_2[/tex] = r1 (cos θ1 +i sin θ1) x r2 (cos θ2 +i sin θ2)
[tex]z_1z_2[/tex] = r1 r2(cos θ1 . cos θ2 +i cos θ1 sin θ2 + i sin θ1 cos θ2 + i² sin θ1 sin θ2)
[tex]z_1z_2[/tex] = r1 r2(cos θ1 . cos θ2 +i cos θ1 sin θ2 + i sin θ1 cos θ2 - sin θ1 sin θ2)
We know,
cos (a + b)= cos a cos b - sin a sin b
sin (a+b) = sin a cos b + cos a sin b
Thus, [tex]z_1z_2[/tex] = [tex]r_1r_2[/tex][cos (θ1+θ2) + i sin (θ1+θ2)].
Learn more about complex number here:
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#SPJ2
Minerals and deposits are connected because
Step-by-step explanation:
This particular mineral was found in Finland. A mineral is a naturally occurring crystalline solid that cannot be physically broken down into smaller components. Deposits of minerals form when a medium that contains and transports mineral-making ore releases and deposits the ore.
If f(1) =12 and f(n)= f(n-1) - 4 then which of the following represents the value of f (40)
Solve It for an arithmetic sequence
First term=a=12Common difference=d=-4So
a_n=a+(n-1)dHence
a_40:-
a+(40-1)da+39d12+39(-4)12-156-144Answer:
[tex]f(40)=-144[/tex]
Step-by-step explanation:
Given:
[tex]f(1)=12[/tex][tex]f(n)=f(n-1)-4[/tex]This is a recursive arithmetic sequence since each term is defined using the previous term.
To find the nth term, convert the recursive formula to an explicit formula.
Explicit form of an arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]
where:
[tex]a_n[/tex] is the nth terma is the first termd is the common difference between termsWe have been given the first term: [tex]a=12[/tex]
To get any term from its previous term we subtract 4, so the common different (d) is -4.
Therefore, the formula for the nth term is:
[tex]\implies a_n=12+(n-1)(-4)[/tex]
[tex]\implies f(n)=16-4n[/tex]
To find [tex]f(40)[/tex] simply substitute n = 40 into the explicit formula:
[tex]\implies f(40)=16-4(40)=-144[/tex]
Which expression is equivalent to
(3^2) ^-2. -81 , -12 , 1/81 , 1/12
Answer:
1/81
Step-by-step explanation:
First lets simplfy the equation :
(3^2)^-2
(remember that you can mutiply the exponent outside the paranthesis by the exponent inside so -2*2=-4)
3^-4
Now lets evaluate this further!
3^-4
(negative exponets mean that you have to raise the number but as the denominator of a fraction)
1/3^4
Now we can solve it fully
1/3^4
1/81
What is the value of x in the figure below?
15
C
D
B
X
20
A.
20
15
B. 10
C. 300
D. 5
E 20
OF
F.
45
4
Answer:
choice f
Step-by-step explanation:
take ∆ abc
ab^2 = ac^2 + ab^2
400 = 225 + ab^2
ab =√ 175
∆aDB
bd = 20-x
ad^2 = 175 -(20-x)^2
∆acd
225 = x^2 + 175 - 400+ 40x - x^2
225 = -225 + 40x
450 = 40x
x = 45/4
3/5 x 4 as a fraction
Assume that Quick Release lets go of the ball 6 feet above the ground and the receiver
catches it 6 feet above the ground. The ball reaches a maximum height of 16 feet above
the ground halfway to the receiver. Write an algebraic rule that models the path of the
football. Show all your work and explain your reasoning.
The equation that models the path of the football released from the given position is h(t) = -10 + 25.37t - 16.1t².
Initial velocity of the ball
The initial velocity of the ball is determined by applying third kinematic equation as shown below;
Vf² = V₀² - 2gh
at maximum height, the final velocity, Vf = 0maximum height reached from the point of projection, = 16 ft - 6ft = 10 ft0 = V₀² - 2gh
V₀² = 2gh
V₀ = √(2gh)
V₀ = √(2 x 32.17 x 10)
V₀ = 25.37 ft/s
Equation of motion of the ballThe equation of the ball's motion can be modelled as follows;
h = V₀t - ¹/₂gt²
10 = 25.37t - ¹/₂(32.17)t²
10 = 25.37t - 16.1t²
h(t) = -10 + 25.37t - 16.1t²
Thus, the equation that models the path of the football at any given position is h(t) = -10 + 25.37t - 16.1t².
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How much time has passed? Start time: 1:18 a.m. End time: 3:09 a.m.
Answer:
1 hour and 51 minutes
Step-by-step explanation:
Find the difference between the time.
If vector r = ❬4, 9❭ and s = ❬7, –5❭ then which is r – s?
r – s = ❬–3, 14❭
r – s = ❬3, –14❭
r – s = ❬–11, 4❭
r – s = ❬11, 4❭
Answer:
(a) <-3, 14>
Step-by-step explanation:
Addition and subtraction of vectors and matrices is done on a term-by-term basis.
__
The difference is ...
r - s
= <4, 9> -<7, -5>
= <4 -7, 9 -(-5)>
= <-3, 14> . . . . . . . matches the first choice
Please help me answer this
Answer:
d is the answerbecause a= 1,1 then 1+1 = 2
the sum of the polynomials shown below
(10x2 + 3x - 6)
(2x2 9x - 12)
Answer:
[tex] \longrightarrow \sf \purple{ \boxed{ \bold{ \: 12x² + 12x – 18}}}[/tex]
Step-by-step explanation:
Simplify
10x² + 3x – 6 + 2x² + 9x – 12
Steps
1Ox² + 3x- 6 - 2x² + 9x - 12
Step 1:- Group like terms:
= 10x² + 2x²+ 3x + 9x - 6 - 12
Step 2:- Subtract the numbers: – 6–12 = -18
= 10x² + 2x² + 3x + 9x – 18
Step 3:- Add similar elements: 10x² + 2x² – 12x²
= 12x² + 3x + 9x – 18
Step 4:- Add similar elements: 3x + 9x – 12x
= 12x² + 12x – 18
3. Every morning, Matthew fills his dog’s water dish with 16 oz of water. If his dog
finishes his water every day, how many ounces will his dog drink in a week?
How many cups is this?
How many pints is this?
How many quarts is this?
Need help pronto! If you aren't sure then dont answer please :)
100 points
Note the rules
(+)(+)=(+)(-)(-)=(+)(-)(+)=(-)(+)(-)=(-)So
Option A -->Negative
Option B-->Positive
Option C –»Negative
Option D —»Positive
Positive product:
[tex]\left(-\dfrac 23 \right) \left(- \dfrac 23 \right)~ \text{and}~ \left(\dfrac 23 \right) \left(\dfrac 23 \right)[/tex]
Negative product:
[tex]\left(-\dfrac 23 \right) \left(\dfrac 23 \right)~ \text{and}~ \left(\dfrac 23 \right) \left(-\dfrac 23 \right)[/tex]
Drag each tile to the correct box.
Match the expression to the exponent property that you use first to simplify the expression.
Answer:
First box, second from the left,
Second box, first on the left.
Third box, third from the left.
Fourth box, Last on the right.
Step-by-step explanation:
Welcome.
Consider the following two quantities:
•Quantity A:
The slope of graphed line.
•Quantity B:
The y-value of the graphed line’s y-intercept.
Use the graph of the line K to decide which of the following statement is true?
a) Quantity A is greater
b) Quantity B is greater
c) The two quantities are equal
d) The relationship cannot be determined from the indicated information.
The slope of the line is -2.5 and the y-intercept is 2. This shows that the Quantity B is greater that A
How to find the intercept of a lineThe intercept is the point where the line intersects
Determine the slope of the graph using the coordinate points (0, 2) and (0.8, 0)
Slope = -2/0.8
Slope = -2.5
The slope of the line is -2.5 and the y-intercept is 2
This shows that the Quantity B is greater than A
Learn more on equation of a line here:https://brainly.com/question/13763238
If f(x) = 2x2 + x − 6 and g(x) = x − 7, find the following limits.
Answer: 4, -40, -3
Step-by-step explanation: got it right
Answer:
4, -40, -3
I hope this helps :)
could i have some help?
if you want another 50 you could answer the question i asked before this one lol
Answer:
Factoring out Greatest Common Factor (GCF)
[tex]6xy+12x^2y^2-4x^3y^3[/tex]
Factor out greatest common term [tex]2xy[/tex]:
[tex]\implies 2xy(3+6xy-2x^2y^2)[/tex]
Factoring by Grouping
[tex]20x^2+11x-3[/tex]
[tex]\implies a=20, b=11, c=-3[/tex]
[tex]\implies ac=20 \cdot -3=-60[/tex]
Find 2 two numbers that multiply to ac (-60) and sum to b (11)
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Therefore, the two numbers are 15 and -4
Rewrite b as the sum of these 2 numbers:
[tex]\implies 20x^2+15x-4x-3[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies 5x(4x+3)-1(4x+3)[/tex]
Factor out the common term (4x + 3):
[tex]\implies (5x-1)(4x+3)[/tex]
Factoring by Grouping
[tex]3x^2+3xa-2x-2a[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies 3x(x+a)-2(x+a)[/tex]
Factor out the common term (x + a):
[tex]\implies (3x-2)(x+a)[/tex]
Simplify this expression.
7ײ+9ײ-ײ
Step-by-step explanation:
7x² + 9x² - x²
when you wrote the expression you used the "multiplication ×" and not "x".
anyway, when you have terms of the same variable of the same exponent, then the combination variable and exponent become an item. and the same items can simply be added in an expression.
this is similar to
7 apples + 9 apples - 1 apple
what would you do there ?
see ?
and the same we are doing now for the given expression : we are adding the terms up :
7x² + 9x² - x² = (7 + 9 - 1)x² = 15x²
and in the middle I gave you even the reason why we can do that.
please, let me know, if this is still unclear.
Help picture below problem 5
[tex]\angle F+ \angle E = 180^{\circ}\\\\ \implies \angle F + 164^{\circ} = 180^\circ\\\\\implies \angle F = 180^\circ - 164^\circ\\\\\implies \angle F= 16^\circ[/tex]
Find the number of permutations of the letters of the word LOOPHOLE
Answer:
6!/3!=6x5x4x3x2/3x2=6x5x4=120
Step-by-step explanation:
There are L, O, O, P, H, O, L, E; 8 letters in LOOPHOLE. However, three letters repeat: OOO. That means we cannot count them as different and use ! for them.
L,P,H,L,E,O are the letters not double counted. There are SIX letters, so 6!, however, you still have to divide since there are the Os you have to consider.
You have to divide by 3! as they repeat 3 times.
Thus, 6!/3!
"There is a subset of permutations that takes into account that there are double objects or repetitions in a permutation problem. In general, repetitions are taken care of by dividing the permutation by the factorial of the number of objects that are identical" -www. ck12. org > probability > lesson > permutation
A (1,7)
B(8,-5)
distance formula
Answer:
The distance betweem the two points is about 14
Step-by-step explanation:
The distance formula is [tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
According to the problem: [tex]x_{2}=8[/tex], [tex]x_{1} =1[/tex], [tex]y_{2} =-5[/tex], and [tex]y_{1} =7[/tex]
Substitute these numbers into the problem to get [tex]d=\sqrt{(8-1)^{2}+(-5-7)^{2}}[/tex]
[tex](8-1)^2=(7)^2=49[/tex]
[tex](-5-7)^2=(-12)^2=144[/tex]
[tex]\sqrt{49+144}=\sqrt{193} =13.8923349894[/tex]
You can round this number to approximately 14.
Solve the equation.
7 t − 3 = − 59
t=_____
Hey there!
7t - 3 = -59
ADD 3 to BOTH SIDES
7t - 3 + 3 = -59 + 3
CANCEL out: -3 + 3 because it give you 0
KEEP: -59 + 3 because it help solve for the t-value
NEW EQUATION: 7t = -59 + 3
SIMPLIFY IT!
7t = -56
DIVIDE 7 to BOTH SIDES
7t/7 = -56/7
CANCEL out: 7/7 because it give you 1
KEEP: -56/7 because it help solve for the t-value
NEW EQUATION: t = -56/7
SIMPLIFY IT!
t = -8
Therefore, your answer is: t = -8
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
A savings account with compounded interest can be modeled by which type of graph?
O quadratic
O cubic
O exponential
O linear
Answer:
The answer is a linear graph
Step-by-step explanation:
Which angles are adjacent to each other? Select all that apply. 3 2 23 and 24 22 and 23 22 and 24 Z2 and 1
Answer:
angle 2 and angle 4
The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.
Zeros are (-5,0) and (1,0)
Hence
y=-x²-4x+5y=-[x²+4x-5]y=-[x²+5x-x-5]y=-[x(x+5)-1(x+5)y=-(x-1)(x+5)Yes this is the parabola given
Convert to Vertex form a(x-h)²+kSo
y=-[x²+4x-5]y=-[x²+2(2)(x)-5+9-9]y=-[x²+2(2x)+4-9]y=-[(x+2)²-9]y=-(x+2)²+9As for any real x the function will give a real value [square present] the domain is set of real numbers ≤-2
vertex is maximum
Highest value of y is 9
Hence.
range is ≤9Or in interval notation
range=(-oo,9]Answer:
The range of the function is all real numbers less than or equal to 9.
Step-by-step explanation:
Given:
[tex]f(x)=-x^2-4x+5[/tex]vertex = (-2, 9)x-intercepts = (-5, 0) and (1, 0)Domain: input values (x-values)
Range: output values (y-values)
The domain of the function is not restricted, so the domain is all real numbers.
The leading coefficient of the function is negative, therefore the parabola opens downwards. This means that the vertex is the maximum point.
Therefore, the range will be f(x) ≤ 9 → all real numbers less than or equal to 9.
Different names are written onto sticks and placed into a cup. A
stick is chosen 100 times, out of which Lyla's name is chosen 23
times. Based on the results, how many times should Lyla expect her
name to be drawn if 320 sticks are drawn?
Answer:
73.6 (or actually 74 - you can't have 0.6 times)
Step-by-step explanation:
here, you're effectively just multiplying fractions.
it is 23/100 that were drawn but 320 is 3.2 X 100 so all you have to do is multiply 23 by 3.2 which is 73.6
The difference between the squares of two numbers is 15. Three times the square of the first number increased by the square of the second number is 49. Find the numbers
Answer: 256,1
Step-by-step explanation:
[tex]\sqrt{x} - \sqrt{y} =15\\\sqrt{y} = 49-3\sqrt{x} \\\\\sqrt{x} -(49-3\sqrt{x} ) =15 \\so, x=256\\substitute \{x}\ :\\\\\sqrt{y} = 49-3\sqrt{256} =y=1[/tex]
so, 256=x
and, y=1
Hope this Helped!
Answer:
1, 4 or -1, -4
Step-by-step explanation:
Let the two numbers be x and such that x > y.
According to the first condition:
[tex]x^2 -y^2= 15[/tex]
[tex]\implies x^2 =y^2+15[/tex]......(1)
According to the second condition:
[tex]3x^2 +y^2= 49[/tex]
[tex]\implies 3(y^2+15) +y^2= 49[/tex]
(From equation 1)
[tex]\implies 3y^2+45 +y^2= 49[/tex]
[tex]\implies 4y^2 =49-45[/tex]
[tex]\implies 4y^2 =4[/tex]
[tex]\implies y^2 =\frac{4}{4}[/tex]
[tex]\implies y^2 =1[/tex]
[tex]\implies y =\pm 1[/tex]
When y = 1
[tex]\implies x^2 =(1)^2+15=1+15=16[/tex]
[tex]\implies x =\pm 4[/tex]
When y = -1
[tex]\implies x^2 =(-1)^2+15=1+15=16[/tex]
[tex]\implies x =\pm 4[/tex]
Thus, the required numbers are either 1, 4 or -1, -4
3 more than the product of a number and six is equal to 2
6x + 3 = 2
its the answer
easy peasy
Answer:
3 + 6(x) = 2
Step-by-step explanation:
Given statement:
3 more than the product of a number and six is equal to 2
Converting the statement into an equation:
{3} {more} than {the product of a number and six} is {equal to} {2}
↓ ↓ ↓ ↓ ↓
3 + 6 × x = 2
⇒ Equation formed: 3 + (6 × x) = 2
⇒ Equation formed: 3 + 6(x) = 2
Question 1 of 20 :
Select the best answer for the question.
1. Solve the equation 2y2 - y - 5 = -3 using the quadratic formula.
A. y=-
B. y =
1121
2
11/17
4.
1137
2
1: 121
C. y=-
Do y=
2
Mark for review (Will be highlighted on the review page)
Answer:
B. (solved using the quadratic formula)
GIVING BRAINLIEST
What is the approximate distance between points A and B?
3.61
9.22
10.35
12.62
Answer:
9.22
I really hope it helps
let me know am i right to be shure
Answer:
[tex]9.22[/tex]
Step-by-step explanation:
You would need to use the distance formula to find the approximate distance between points A and B.
[tex]distance=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^2}[/tex]
[tex]\sqrt{((-2)-4)^{2} +((-4)-3)^2}[/tex]
[tex]\sqrt{(-6)^{2} +(-7)^2}\\[/tex]
[tex]\sqrt{36 +49}[/tex]
[tex]\sqrt{85}[/tex]
[tex]\sqrt{85}=9.219544457=9.22[/tex]
Therefore, the approximate distance between points A and B is 9.22.