Find the maximum area of a rectangle that is inside of the triangle forms by the x-axis and the lines y=-3x+12 and y=3x+12. The base of the triangle is on the x-axis and the two upper verticies are on the lines y=-3x+12 and y=3x+12.
With this question. Obviously the are of the rectangle is lw or xy... I have figured out that x = (8-2x) and y=(12-y). Im not sure of the next step.. Could someone help?

Answers

Answer 1

The maximum area of rectangle is 24, that can be calculated using the derivatives.

The area of rectangle = length * breadth,

The length of the rectangle is 2x units and the breadth is 3x+12 units,

So, A(x)=2x*(-3x+12)

=2x(-3x+12)

=-6x^2+24x

The derivative A'(x)=0

-12x+24=0

x=+2

Therefore, x=+2 is the critical point.

The second derivative.

The 2d derivative measures the immediately rate of alternate of the 1st derivative. The signal of the second derivative tells us whether or not the slope of the tangent line to is growing or decreasing.

A"(x)=-12<0

By the second derivative test, A(x) has maximum value at x=+2

Thus, the maximum are is

A(x)=2x(-3x+12)

A(2)=2(2)(-3(2)+12)

=4(6)

=2

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Related Questions

set up, but do not evaluate, a triple integral that gives the volume of the right circular cylinder enclosed by the surfaces x^2 +y^2 =4,z=−10, and z=0

Answers

This triple integral gives the volume of the right circular cylinder which is enclosed by the given surfaces and extends from z = 0 to z = -10.

What in mathematics is an integral?

Mathematicians define an integral as either a number equal to the area under the graph of a function for a certain interval or as a new function whose derivative is the original function (indefinite integral).

                       In general, the word "integral value" refers to the result of integrating or summing the terms of a function that has an infinite number of terms.

The triple integral that gives the volume of the right circular cylinder enclosed by the surfaces x^2 + y^2 = 4 , z=-10 and z=0 is:

∫∫∫dV = ∫∫∫dx dy dz

where the limits of the integration are:

0 ≤ x ≤ 2*sqrt(2), -2*sqrt(2) ≤ y ≤ 2*sqrt(2), 0 ≤ z ≤ -10.

This triple integral gives the volume of the right circular cylinder which is enclosed by the given surfaces and extends from z = 0 to z = -10.

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5 1/2x + 2/3x =37
Solve for x and show your work

Answers

The value of x will be;

⇒ x = 6

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

The expression is,

⇒ 5 1/2x + 2/3x = 37

Now,

Since, The expression is,

⇒ 5 1/2x + 2/3x = 37

Solve for x as;

⇒ 11/2x + 2/3x = 37

⇒ (33 + 4)x/6 = 37

⇒ 37x = 37 × 6

⇒ x = 6

Thus, The value of x = 6

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6x^2 + 36x + 3 in standard form

Answers

Answer:

its the

Step-by-step explanation:

X
y
13
45° I need this

Answers

Answer:

Step-by-step explanation:

you times 13 times 45 degrees and that equals to 585

A container that weighs 23 2/5pounds
holds sports equipment. Of the
equipment in the container, of the
1
3
weight is baseball equipment. What is the
weight of the baseball equipment?

Answers

The weight of the baseball equipment will be 39/5 pounds.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A container that weighs 23 2/5pounds holds sports equipment.

And, Of the equipment in the container, of the 1/3 weight is baseball equipment.

Now,

Since, A container that weighs 23 2/5pounds holds sports equipment.

And, Of the equipment in the container, of the 1/3 weight is baseball equipment.

Hence, The weight of the baseball equipment = 23 2/5 × 1/3

                                                                         = 117/5 × 1/3

                                                                         = 39/5 pounds

Thus, The weight of the baseball equipment =  39/5 pounds

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Find dy/dx for the indicated function y

Answers

The derivative of the function [tex]y = 5^x + e^7[/tex] with respect to 'x'

is  [tex]\frac{dy}{dx} = 5^xln5 + 0[/tex].

What is differentiation?

Differentiation, in mathematics, process of finding the derivative, or rate of change, of a function also known as the slope.

We know, [tex]\frac{dy}{dx} a^x = a^xlna[/tex], where 'a' is a constant.

Given, [tex]y = 5^x + e^7[/tex].

Now, The derivative of the function with respect to 'x' is,

[tex]\frac{dy}{dx} = 5^xln5 + 0[/tex], As [tex]e^7[/tex] is a constant, and the derivative of any constant term is zero because the slope of a constant term is zero.

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pls help due 5 minutes ago!!!!!

Answers

Answer:

[tex]-1 < x < 0\\0 < x < 1[/tex]

Step-by-step explanation:

At those range, the slope is negative. As the line is going right, it is going down.

HELP IM IN K12 AND THERS MORE OF THESE

Answers

the first missing blank should be 650 the second should be 7

Helppp! I need an answer asap pls!

Answers

Answer: (2*sqrt3)/3

Step-by-step explanation:

csc(x)=1/sin(x)

sin(q)= 15/(10*sqrt3)= 3/(2*sqrt3)

1/(3/(2*sqrt3))= (2*sqrt3)/3

38. A furniture store buys a couch for $500 and sells it for $900. What it the percent of
markup?

Answers

The mark-up, as a percentage =80%

What is Markup?

The term "markup" describes the discrepancy between a product's selling price and its actual cost. It is specified as a percentage over the price. In other words, the seller makes a profit when the price of the commodity.

A unit's gross profit, which is the sales price less the cost to create or buy it for resale, is divided by its cost to determine the markup %. The markup percentage is computed as (12 - 8) / 8 and is equal to 50% if an item costs the business $8 to produce but is sold for $12.

Markup percentage = [(selling price - unit cost)/unit cost]*100

                                 = [(900-500)/500]*100

                                 =  [ 400/500] *100

                                 = 80%

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A heavy rope, 40 ft long, weighs 0.5 lb/ft and hangs over the edge of a building 90 ft high. (Let x be the distance in feet below the top of the building. Enter xi* as xi.) (a) How much work W is done in pulling the rope to the top of the building? Show how to approximate the required work by a Riemann sum. lim( lim n-00 ) i = 1 Express the work as an integral. 160_v (10.5x , ) Jo Evaluate the integral. 900 X ft-lb (b) How much work W is done in pulling half the rope to the top of the building? Show how to approximate the required work by a Riemann sum. lim n7009 i = lim E(L Dax 1 Express the work as an integral. dx Evaluate the integral. ft-lb

Answers

According to Riemann sum and expressing the work as an integral,400 ft/lb work is done in pulling the rope to the top of the building.

Given,

heavy rope length = 40ft

weighs = 0.5 lb/ft

building height = 90 ft

If we divide rope into small parts with length Δx, rope weighs 0.5 lb/ft force work on each section is x*i is a point in i the such intervals.

The work done on ith part is

                                          x*i0.5Δx

So the total done is

[tex]\lim_{n \to \infty}[/tex]= ∑0.5x*iΔx expressing work as an integral

         [tex]\int\limits^40_0 {(0.5x)} \, dx[/tex] = [0.5 × x²/2]

                             = [0.5 × 40²/2 - 0.5 × 0²/2]

                             = [0.5 × 1600/2 - 0]

                             =  0.5 × 800 - 0

                             = 400 - 0

                             = 400 ft/lb

The work done in lifting the pieces in upper half of rope is

  x*i0.5Δx

The work done in lifting lower half of the rope is

0.5Δx × 20

10Δx

Total workdone,

                 [tex]\lim_{n \to \infty}[/tex]∑0.5x*iΔx + [tex]\lim_{n \to \infty}[/tex]∑10Δx

                = [tex]\lim_{n \to \infty}[/tex]∑(0.5x*i + 10)Δx work as an integral

[tex]\int\limits^25_0 {0.5} \, dx[/tex] + [tex]\int\limits^50_25 {10} \, dx[/tex]

= [ 0.5 * x²/2] + [10x]

= [0.5 * 20²/2] +[10(40-20)]

= [0.5 * 400/2] + [10*20]

= 100 + 200

= 300 ft/lb

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Use the given information to prove that ΔPQR ≅ ΔPSR.
Given: QR ≅ SR
PQ ≅ PS
Prove: ΔPQR ≅ ΔPSR

Answers

Based on the given information , the proof of triangle PQR ≅ triangle PSR is shown below .

In the question ,

two triangles PQR and PSR are given where ;

it is given that side  QR ≅ SR

and  PQ ≅ PS .

we have to prove that ΔPQR congruent to ΔPSR .

In triangle PQR and triangle PSR .

side QR = side SR              .....given that QR ≅ SR ;

side PQ = side PS              .....given that PQ ≅ PS ;

side PR = side PR              .....because PR is the common side ;

Hence by SSS congruence , triangle PQR ≅ triangle PSR .

Therefore , it is proved that  triangle PQR ≅ triangle PSR  .

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Evaluate the surface integral. S (x + y + z) dS, S is the parallelogram with parametric equations x = u + v, y = u − v, z = 1 + 2u + v, 0 ≤ u ≤ 8, 0 ≤ v ≤ 6.

Answers

The parallelogram with the parametric equations 1 + 2u + v is the surface integral.

What is the explanation?

The surface element is

dS is equal to || r/u x r/dv || du dv.

where

r (u, v) is equal to x (u, v) I plus y (u, v) j plus z (u, v) k

r (u, v) = (u + v) I plus (u -v) j plus (1 + 2u + v) k

is the surface S's vector parameterization.

The surface's normal vector is

R / u x R / d

= I + j + k + 2) x I - j + k)

= 3 I + j - 2 k

as well as norm

|| r/dv x u r/u || = √(3² + 1² + (-2)²) = √(14) (14)

Calculate the integral now:

∫∫ (x + y + z) dS = √(14) ∫₀¹ ∫₀² (1 + 2u + v) = ((u + v) + (u - v)) du dv

= (14)... 01... 02 (3u + v + 1) du dv

= (14), 01 (3/2 u2, uv, and u), |02 dv

= √(14) ∫₀¹ (8 + 2v) dv

= √(14) (8v + 2v²) |₀¹

= 10 √(14) (14).

The parallelogram with the parametric equations x = u + v, y = u â' v, and z = 1 + 2u + v is the surface integral.

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NEED HEEEEELP PLEEEEASE HEEEEELP Solve. 4/5x+9/10=5 1/5 Enter your answer as a mixed number in simplest form in the box. x =

Answers

The value of x in the fraction 4/5x+9/10=5 1/5 is 5 3/8.

How to calculate the fraction?

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, the fraction is given as:

4/5x + 9/10 = 5 1/5

0.8x + 0.9 = 5.2

Collect like terms

0.8x = 5.2 - 0.9

0.8x = 4.3

Divide

x = 4.3 / 0.8

x = 5.375

x = 5 3/8

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a vector function representing the curve intersection between the cylinder and the plane is given by

Answers

the vector function represents the curve of the intersection between a cylinder and a plane in 3-dimensional space.r(t) = (cos(t), sin(t), 2t)

The vector function represents the curve of the intersection between a cylinder and a plane. The function is given by r(t) = (cos(t), sin(t), 2t). This means that the x-coordinate of the point on the curve is given by cos(t), the y-coordinate of the point on the curve is given by sin(t), and the z-coordinate of the point on the curve is given by 2t.

The parameter t is defined as t [tex]$\in$[/tex] [tex][0, $\pi$/2],[/tex] which means that the domain of t is from 0 to [tex]$\pi$[/tex]/2. Therefore, the vector function represents the curve of the intersection between a cylinder and a plane in 3-dimensional space.

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Henry correctly factored 42? + 52 - 6 as (4% - 3)(₴ + 2)
• He then claimed that the zeros of that quadratic function are located at
*=-=
and r = 2 . Did Henry correctly find the zeros of the function?
O Yes, Henry correctly found the zeros of the function.
O No, the zeros of the function are at x = 4 and =-2
• No, the zeros of the function are at z = - 5 andx = 2.
• No, the zeros of the function are at & = 4 and ≥ = -2


I attached the question and answer choices

Please help

Answers

Answer:

No, the zeros of the function are at x = 3/4 and x = 2

Step-by-step explanation:

the equation

4x² + 5x – 6 = 0

(note: since there is a coefficient of x² we need to multiply it to the last term(6))

4x² + 5x – 24 = 0

the factors are :- 8x and – 3x

4x² + 8x – 3x – 6 = 0

4x( x + 2) –3( x + 2) = 0

( 4x – 3)( x + 2) = 0

the zeros will be

4x – 3 = 0

4x = 3

[tex]x = \frac{3}{4} [/tex]

x + 2 = 0

x = – 2

the zeros are x= 3/4 or –2

i hope this helps


Zachariah paid $126 for 6 concert tickets. At this rate, what is the cost of 10 concert tickets?

Answers

The answer to your question is 210

I'm not sure how to solve the probability for the question.



Thank You for your help

Answers

The statement that corresponds to P(X = 48), using continuity correction, is given as follows:

c. P(47.5 < x < 48.5).

What is continuity correction?

Continuity correction is used as a "correction" when a continuous distribution is used to approximate a discrete distribution. One example of this is the approximation of the binomial distribution to the normal distribution.

Hence, using continuity correction, the range of values that corresponds to a number of exactly x is given as follows:

x - 0.5 < x < x + 0.5.

Thus the range for exactly 48 successes is of:

47.5 < x < 48.5.

Meaning that option c is correct.

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Which statement regarding the equation below is true?
x²+y²-3 x+6 y=7 x+2
A. It has a diameter of 18 units.
B. It has an area of 36 π square units.
C. It has a center at (-5,3).
D. It has a center at (-2,-3).
A
B
C
D

Answers

The true statement regarding the equation x² + y² - 3x + 6y = 7x + 2 is that it has a area of 36π sq. unit ,  correct option is (b) .

In the question ,

it is given that ,

the equation is x² + y² - 3x + 6y = 7x + 2 ,

On simplifying and rewriting the equation ,

we get ,

x² - 10x + 25 + y² + 6y + 9 = 36

further it can be written as ;

(x - 5)² [tex]+[/tex] (y [tex]+[/tex] 3)² [tex]=[/tex] 36

(x - 5)² + (y + 3)² = 6²

the equation represents a circle .

So , the from the above equation we can conclude that :

the center of the circle will be  = (5,-3) .

the radius is = 6 units .

the diameter will be = 12 units , and

the area of the circle will be = πr² = 36π square units .

So , the statement that matches with the information is that the area is 36π square units .  

Therefore , the True statement is (b) it has a area of 36π sq. units  .

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Help quick please!! I don’t know if it’s D or C??

Answers

Answer:

I think the answer is B

Step-by-step explanation:

1.2 * 10^6 is 1,200,000

1.38 * 10^7 is 13,800,000

you just have to divide 13,800,000 by the numbers until you get to 1,200,000. So, 13,800,000 / 11.5 is 1,200,000

Hope this helps! Have an amazing day :)

Answer:

11.5

Step-by-step explanation:

we will need to divide both of them

1.38 × 10^7 ÷ 1.2 × 10^6

1.38÷1.2 × 10^7-6

= 1.15 × 10¹

= 11.5

The video production teacher buys a wireless mic and
tripod for 12 students in the class. The wireless mics
each cost $32. The teacher spends a total of $552 on
both the mic and tripod for all 12 students.
Write an equation that models the situation with P, the
cost of one tripod. Then solve the equation.

Answers

ANSWER:

let P as the amount of tripod

12(32 + P) = 552

384 + 12P = 552

12P + 384 - 384 = 552 - 384     (subtract 384 from both sides)

12P = 168

P = 14

CHECKING:

12(32 + 14) = 552

12(46) = 552

552 = 552

Therefore, the amount of one tripod is $14.

#APPROVED

Step-by-step explanation:

heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ  -{ elyna s }-

the symbol a || b represents that lines a and b are perpendicular lines.


True


False

Answers

False.It represents that a is parallel to b.

Write 2 equations and solve for the numbers

Answers

Answer:

y + x = 87

y = x + 35

x = 26

y = 61

Step-by-step explanation:

y + x = 87

y = x + 35

substitute y with x + 35 in the first equation:

(x + 35) + x = 87

2x + 35 = 87

2x = 87 - 35

2x = 52

x = 52/2

x = 26

Find y by substituting x with 26:

y = (26) + 35

y = 61

The rectangular floor of a classroom is 24 feet in length and 3o feet in width. A scale drawing of the floor has a length of 4 inches. What is the area, in square inches, of the floor in the scale drawing?​

Answers

Answer:

4 inches multiply 4 inches

a sequential circuit has two jk flip-flop a and b and one input x. the circuit is described by the following flip-flop input equations:

Answers

D flip flop stands for a delay flip flop that produces output that is identical to input after a brief delay. The flip flop's input and next state are equal.

Z is an output, and x and x inputs.

x'y + xA = DA= A*

B* = x'B + xA

z=A (output is independent of input) (output is independent of input)

The next states are A(t+1) and B(t+1). We must provide the next state value to D of the D flip flop in order to obtain the next states A(t+1), and B(t+1) for A, B(present state). So the sequential circuit will be:

To get the next state as A(t+1)= x’A + xA, B(t+1)= x’B + xA, we have to give them to DA, DB of D flip flop because for D flip flop whatever is given to DA, DB will appear at output A, B.

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Complete the proof of the identity by choosing the Rule that justifies each step. Sin^2x + 4cos^2x = 4 -3sin^2x To see a detailed description of a Rule in the Rule menu, select the corresponding question mark. Statement Rule sin^2 x + 4cos^2 x sin^2 x + 4 (1 -sin^2 x) Rule? sin^2 x + 4 -4sin^2 x Rule? 4 -3sin^2 x Rule? Reciprocal identities: sin u = 1/csc u cos u = 1/sec u tan u = 1/cot u csc u = 1/sin u sec u = 1/cos u cot u = 1/tan u Quotient identities: tan u = sin u/cos u cot u = cos u/sin u Pythagorean identities: sin^2u + cos^2u = 1 tan^2u + 1 = sec^2 u cot^2 u + 1 = csc^2 u Odd/Even function identities: sin(-u) = -sin(u) cos(-u) = cos(u) tan(-u) = -tan(u) csc(-u) = -csc(u) sec(-u) = sec(u) cot(-u) = -cot(u)
Previous question

Answers

Hence, the proof is completed by choosing the identities of the rules.

Trigonometry identities

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation. There are various distinct trigonometric identities involving the side length as well as the angle of a triangle. The trigonometric identities hold true only for the right-angle triangle.

Given that :

Complete the proof of the identity by choosing the Rule that justifies each step.

         Sin^2x + 4cos^2x = 4 -3sin^2x

        Statement                                    Rule

  [tex]sin^{2} x + 4 cos^{2}x[/tex]

= [tex]sin^{2}x + 4 (1 - sin^{2} x )[/tex]                          [tex]sin^{2}u + cos^{2}u = 1[/tex]

                                                      [by using Pythagorean identities]                        

= [tex]sin^{2}x + 4 - 4 sin^{2}x[/tex]                               [tex](1 - sin^{2}x )[/tex]

                                                          [ multiplied by 4 ]

= [tex]4 - 3 sin^{2}x[/tex]

Sin^2x + 4cos^2x = 4 -3sin^2x

Hence proved.

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Chocolate sprinkles cost as much per pound of sugar find one and 1/10 the bakers total cost for 100 lb of chocolate sprinkles explain the numbers of zeros and the placement of the decimal in your answer using a place value chart.
(The sprinkles is $0.80 per pound)

Answers

The total cost of chocolate sprinkles is $800

Place value charts

This is an implementation of the numeral system that shows the value of each digit in a number using their positions

WHAT IS IMPLENTATION?

What do you mean implementation?

Implementation is the execution or practice of a plan, a method or any design, idea, model, specification, standard or policy for doing something. As such, implementation is the action that must follow any preliminary thinking for something to actually happen.

From the complete question, we have the following parameters:

Unit rate = $8.00

Total pounds = 100

Total cost of chocolate sprinkles

So, the total cost of chocolate sprinkles is calculated using the following formula

Multiply both sides of the equations by 100

Hence, the total cost of chocolate sprinkles is $800

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Whqt is y +4=-6(x+6) written in standard form

Answers

standard form: 6x+y=-40

Answer:

y= -6x-40

Step-by-step explanation:

standard form is y=mx+b

y+4= -6(x+6)

y+4= -6(x) -6(6)

y+4= -6x-36

-4.        -4

y= -6x-40

hopes this helps have a great day

Suppose you have two Single Factor ANOVA experiments with the same degrees of freedom, if the resulting F test statistics are: Experiment 1, F = 2.68 Experiment 2, F = 20.15 Which statement is TRUE in regards to comparing Experiment 1 and Experiment 2? A.Procedure 1 has a smaller test statistic and therefore will result in stronger evidence in favor of the alternative hypothesis. B.Procedure 2 has a larger test statistic and therefore will result in stronger evidence in favor of the alternative hypothesis. C.We should reject the null for both tests. D.Impossible to know without more information.

Answers

TRUE - Procedure 2 has a larger test statistic and therefore will result in stronger evidence in favor of the alternative hypothesis.

what is degrees of freedom?

Degrees of freedom are the maximum number of logically independent, or potentially different, values in the sample of data. One is subtracted from the number of elements in the data sample to determine the degree of freedom.

There are degrees of flexibility in the third column. Degrees of freedom (df1) between treatments equals k-1. df2 = N - k is the degree of freedom for the error. The total degree of freedom is N-1; additionally, (k-1) plus (N-k) equals N-1.

Fisher's Least Significant Difference (LSD) and the Bonferroni Method stand out among the techniques. These two use the t-test as their foundation. According to Fisher's LSD, run an F-test first, then if you find evidence to reject the null hypothesis, run regular t tests on all possible pairs of means. Similar but only requiring that you choose beforehand is the Bonferroni technique.

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Need Help ASAP!!! Giving away 50 pts

Given the equation 7m − 11 = 5m + 43 and the possible solution set S: {2, 27, 54, 86}:
Determine which integer(s) in the solution set makes the equation false. Show all work.

Answers

The required integers from the solution set are 2, 54 and 86.

How to solve a linear equation?

A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.

The given equation is 7m − 11 = 5m + 43.

It can be solved as follows,

7m − 11 = 5m + 43

⇒ 7m - 5m = 43 + 11

⇒ 2m = 54

⇒ m = 27

Now, in the given solution set  {2, 27, 54, 86}, only one integer 27 satisfies the given equation.

Hence, the integers in the solution set that make the equation false are 2, 54 and 86.

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