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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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
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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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
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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Whqt is y +4=-6(x+6) written in standard form
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
a vector function representing the curve intersection between the cylinder and the plane is given by
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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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.
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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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.
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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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
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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6x^2 + 36x + 3 in standard form
Answer:
its the
Step-by-step explanation:
Help quick please!! I don’t know if it’s D or C??
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
Helppp! I need an answer asap pls!
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
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
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
HELP IM IN K12 AND THERS MORE OF THESE
pls help due 5 minutes ago!!!!!
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.
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)
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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I'm not sure how to solve the probability for the question.
Thank You for your help
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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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.
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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Find dy/dx for the indicated function y
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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the symbol a || b represents that lines a and b are perpendicular lines.
True
False
False.It represents that a is parallel to b.
38. A furniture store buys a couch for $500 and sells it for $900. What it the percent of
markup?
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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Use the given information to prove that ΔPQR ≅ ΔPSR.
Given: QR ≅ SR
PQ ≅ PS
Prove: ΔPQR ≅ ΔPSR
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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Zachariah paid $126 for 6 concert tickets. At this rate, what is the cost of 10 concert tickets?
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:
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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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?
Answer:
4 inches multiply 4 inchesThe 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.
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.
#APPROVEDStep-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-5 1/2x + 2/3x =37
Solve for x and show your work
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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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
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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Write 2 equations and solve for the numbers
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
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?
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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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 =
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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X
y
13
45° I need this
Answer:
Step-by-step explanation:
you times 13 times 45 degrees and that equals to 585