The dimensions of the rectangular solid with maximum volume and surface area 13.5 square centimeters are 3 cm by 3 cm by 0.375 cm.
Let's denote the side length of the square base as x, and the height of the rectangular solid as y. Then, the surface area of the rectangular solid can be expressed as:
SA = x^2 + 4xy
And, the volume of the rectangular solid can be expressed as:
V = x^2y
We want to maximize the volume of the rectangular solid subject to the constraint that its surface area is 13.5 square centimeters. This can be expressed as an optimization problem:
Maximize V = x^2y
Subject to SA = x^2 + 4xy = 13.5
We can solve for y in terms of x from the constraint equation:
x^2 + 4xy = 13.5
y = (13.5 - x^2) / 4x
Substituting this expression for y into the formula for V, we get:
V = x^2 (13.5 - x^2) / 4x
V = (13.5 / 4) x^2 - (1 / 4) x^4
To find the maximum volume, we can take the derivative of V with respect to x, and set it equal to zero:
dV/dx = (27/4) x - x^3/4 = 0
27x = x^3
x = 3
So, the maximum volume occurs when x = 3. To find the corresponding height, we can substitute x = 3 into the expression for y:
y = (13.5 - 3^2) / (4 × 3) = 0.375
Therefore, the dimensions of the rectangular solid with maximum volume and surface area 13.5 square centimeters are 3 cm by 3 cm by 0.375 cm.
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A building meets the ground at a right angle. the top of a 10-foot ladder is placed against the bottom edge of a window in the building, and the base of the ladder is placed 6 feet from where the building meets the ground.
The bottom edge of the window is 8 inches above the ground, computed using the Pythagoras Theorem.
According to the Pythagoras Theorem, in a right triangle, the square of the hypotenuse, that is, the side opposite to the right angle is equal to the sum of the square of the legs, that is, the two other sides.
If in a right triangle, c is the hypotenuse, and a and b are the two legs, then by the Pythagoras Theorem, we can write:
a² + b² = c².
In the question, we are informed that a building meets the ground at a right angle. The top of a 10-foot ladder is placed against the bottom edge of a window in the building, and the base of the ladder is placed 6 feet from where the building meets the ground.
We are asked to draw a diagram that represents the situation and find the height of the bottom edge of the window from the ground.
We assume the building to be DB, meeting the ground BC at a right angle. At point C, the ladder meets the ground and meets the bottom edge of the window at point A.
The diagram is attached.
Now, we get a right triangle ABC, right-angled at B.
By Pythagoras' Theorem, we know that:
AB² + BC² = AC²,
or, AB² + 6² = 10²,
or, AB² = 10² - 6² sq. inches,
or, AB² = 100 - 36 sq. inches,
or, AB = √64 inches,
or, AB = 8 inches.
Thus, the bottom edge of the window is 8 inches above the ground, computed using the Pythagoras Theorem.
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The provided question is incomplete. The complete question is:
"A building meets the ground at a right angle. The top of a 10-foot ladder is placed against the bottom edge of a window in the building, and the base of the ladder is placed 6 feet from where the building meets the ground. Draw a diagram that represents this situation. How far up from the ground is the bottom edge of the window?"
In a binomial experiment, the probability of success is. 6. What is the probability of two successes in seven trials?.
The probability of two successes in seven trials is 0.0774144.
We can find the probability as shown below:The probability can be found using the binomial formula.
The probability of success is given as 0.6.
Therefore, the probability of failure is 0.4.
We have to find the probability of two successes in seven trials.
It is given by:
[tex]P = nC_x p^{n} q^{n-x}\\=7C_{2} (0.6)^{2} (0.4)^{7-2} \\=7C_{2} (0.6)^{2} (0.4)^{5} \\=\frac{(7)(6)}{(1)(2)} (0.36)(0.01024)\\=0.0774144[/tex]
The probability of two successes in seven trials is found to be 0.0774144.
Therefore, we have found that the probability of two successes in seven trials is 0.0774144.
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True or false: f(x) is a function.
A. True
Step by step explanation:
1. if we where given a graph and told to determine whether it's a function or not, we would have used a VERTICAL LINE TEST.
2. In this case we have points, and for every x value we have one corresponding y value which makes it a function that is a ONE-TO- ONE FUNCTION
[tex]x^{8}+x^{4}+1[/tex]
You did not provide directions. What do you want us to do with your 8th degree polynomial?
Which is the graph of f(x) = }(4)*2
Answer: D
Step-by-step explanation:
Where the x-intercept is 0.25.
Which of the following polynomials has a remainder of -7 when divided by x - 2?
ANSWER : -7x + 14
EXPLANATION, to reverse division multiply
slope:
y-intercept:
HELP
Answer:
Slope: 1
Y-intercept: -1
Step-by-step explanation:
The line touches the y-axis at -1, and using rise over run for the slope, it would be 1, since you go up 1 unit and move to the right 1 unit. 1/1 which is our rise/run would be 1 and that would make the slope 1.
I hope it helps! Have a great day!
bren~
If the bottom row as a result of sythetic division is 1 3 0 4 0, then the quotient is which of the following? Select one:
The quotient of the synthetic division is x^3 + 3x^2 + 4
How to determine the quotient?The bottom row of synthetic division given as:
1 3 0 4 0
The last digit represents the remainder, while the other represents the quotient.
So, we have:
Quotient = 1 3 0 4
Introduce the variables
Quotient = 1x^3 + 3x^2 + 0x + 4
Evaluate
Quotient = x^3 + 3x^2 + 4
Hence, the quotient of the synthetic division is x^3 + 3x^2 + 4
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43. A Pop Warner football team had a total loss of 85 yards in penalties on 5 plays. Then triple their yards in penalties on the next 17 plays. What was the final yards the team loss?
Answer:
240 yards lost, if I understand the question correctly.
Step-by-step explanation:
If I read this correctly the team lost 85 yards lost in 8 plays. Then they tripled their loss on the next 17. 3 x 85 = 255 yards lost in the last 17 plays.
Total yards lost was (85 + 255) = 240 yards in 22 plays.
Explain how you could use the dimensions of a reduced rectangle and one given measurement of an original rectangle to find a missing measure?
Using the dimensions of a reduced rectangle and one given measurement of an original rectangle:
Set up a proportion using the corresponding partsSolve the proportion to find the missing measureWhat is Reduction?Reduction is a type of dilation that reduces the size of an original figure to form a new figure that is similar to the original. The corresponding lengths of both figures are therefore proportional.
Assuming the dimensions of the reduced rectangle are 10 cm by 4 cm, and the length of the original rectangle is given as 8 cm, to find the missing measure (x), do the following:
Set up a proportion using the corresponding parts
10/8 = 4/x
Solve the proportion using cross products to find x:
10x = (8)(4)
10x = 32
x = 32/10
x = 3.2 cm
The missing length is 3.2 cm.
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Answer:
Using the given measurements of both figures, set up a proportion that has the corresponding parts in the same position. Then solve the proportion using cross products to find the value for the unknown.
Step-by-step explanation:
Set up a proportionCorresponding sides are in the same place in the proportion.Use cross products in the proportion to solve for the unknown.CAN ANYONE HELP ME WITH QUESTION 7
Answer:
x = 4.
Step-by-step explanation:
Each angle in an equilateral triangle is 60 degrees, so we have:
10x + 20 = 60
10x = 40
x = 4.
Answer:
X = 4
Step-by-step explanation:
The angles of a triangle add up to 180 degrees and this is an equilateral triangle which means that all the angles are the same. which means you set up the equation:
10x + 20 + 10x + 20 + 10x + 20 = 180
Simplify: 30x + 60 = 180
- 60 - 60
You have : 30x = 120
(Divide by 30)
You end up with: X = 4
If 111 is divided into pieces that are each \dfrac19
9
1
start fraction, 1, divided by, 9, end fraction of a whole, how many pieces are there?
1\div\dfrac19=1÷
9
1
=1, divided by, start fraction, 1, divided by, 9, end fraction, equals
The results of dividing 1 into pieces that are each 1/9 of a whole is 9
Division of fraction1 ÷ 1/9
multiply by the reciprocal of 1/9 which is 9/11 ÷ 1/9
= 1 × 9/1
= (1 × 9) / (1 × 1)
= 9/1
= 9
Complete question:
If 1 is divided into pieces that are each 1/9 of a whole, how many pieces are there
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8. A company has 350 workers. The
president of the company wants to know
what percent increase in employment
would be necessary for the number of
workers to be greater than 375.
Help!
The percent increase in employment would be necessary for the number of workers to be greater than 375 is 25%
How to determine the rates?The given parameters are:
Initial = 350
Final = 375
The rate is calculated as:
Rate = Final/Initial - 1
So, we have:
Rate = 375/300 - 1
Evaluate
Rate = 1.25 - 1
This gives
Rate = 0.25
Express as percentage
Rate = 25%
Hence, the percent increase in employment would be necessary for the number of workers to be greater than 375 is 25%
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what is the result of 6 divided by 15
Answer:
If you have 6 chocolate and you have to divide that into 15 people than the answer will be 2 upon 5 or 0.4 for each.
If my mother has 5 boys and my father has 4 girls, what is the probability of one being a boy?
Answer:
5/9
Step-by-step explanation:
4+5=9 and there are 5 boys
help me please.bnt8349rf8
Answer: No solutions
Step-by-step explanation: there would be no solutions, because these equations have the same slope and different y-intercepts, so they would end up being parallel from each other, and would never intersect or be equivalent.
Answer:
No solution.
Explanation:
Given equations:
(1) y - 4x = -3
(2) y = 4x + 7
Substitute equation 2 into 1
y - 4x = -3
4x + 7 - 4x = -3
7 = -3
As L.H.S ≠ R.H.S, There are no solution.
The lines are parallel and do not intersect each other. Their slope is same.
Faith purchased a new car in 1998 for $32,900. the value of the car has been depreciating exponentially at a constant rate. if the value of the car was $19,900 in the year 2003, then what would be the predicted value of the car in the year 2007, to the nearest dollar?
The predicted value of the car in the year 2007 is 13310
Given the purchased value of new car in 1998 is $ 32,900
The value of car was $ 19,900 in the year 2003
We need to find the value of the car in the year 2007
Let the predicted value be x
The exponentially constant rate in 2003
32900*x^5 = $19900 (∵ x^5 = 5 years difference that is 1998 to 2003 )
Now In year 2007
2007 = 32900*x^9
x = 0.9043
The predicted value of the car is 0.09043
But we want the predicted value in 2007
Therefore ,
In 2007 ≈ x = 13310.02
Rounding off to the nearest dollar is $13310
Therefore the predicted value of the car in 2007 is $13310
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You conduct a poll in which you randomly select 1000 registered voters from New York City and ask if they approve of the job their mayor is doing. The population for this study is
The population for this study is all registered voters from New York City.
What is the population for a study?
it is given that the poll has been carried out among 1000 registered voters from New York City. These 1000 people have been selected randomly from the population of the study.
The available study subset of the target population for a study, for instance, schizophrenics in the researcher's hometown, is known as the study population or population of the study. The sample chosen for the study is known as the study sample.
Study Population In This Case
In this case, out of all the New Yorkers, only the registered voters of the city are eligible for making the target subset. Hence, the registered voters of the New York city make the study population. Furthermore, since 1000 random registered voters are chosen for the poll, those 1000 registered voters make the study sample.
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500 +126 200 + 129 129+100 123+34 123+123 1000+12 2013+1200 123+120 100+304 123+103 104+1200
3,471,738 this is the answer
Simplify: x^3-1/x^2-1
Answer:(x-1)(x^2+x+1) / (x+1)(x-1)
Step-by-step explanation:
For x^3-「1」→ 1=1^3
For x^2-「1」→ 1=1^2. this way of thinking might help you understand better:)
You can just use a formula of factorizationヾ ^_^♪
If there is a crossword that has three squares that need to be filled, how many possible three letter arrangements are there (assuming they do not have to make a real word, and no letter can be repeated)
There is a crossword that has three squares that need to be filled, how many possible three letter arrangements is 26!/23.
To find the number of possible three letter arrangements.
what is permutation and combination?An arrangement of things in a certain sequence is what we refer to as a permutation. The constituents or components of sets are presented in this section in a sequential or chronological fashion. A coming together or merging of several parts or characteristics in which each of the constituent parts or traits retains its unique identity.
Given that:
26 possible letters
assuming you can repeat them
26*26*26
no listed
ok, lets assume that you can't repeat them
that is 26 times 25 times 24 (because you used 1 each time)
that is 26!/23 (because 26*25*24*23!=26!)
Hence, the number of possible three letter arrangements is 26!/23.
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Option is missing
A.26!
B.26!/3!
C.23!
D.26!/23
x+y = 8 and 2x-y=7
Anyone can help
Step-by-step explanation:
x=8-y
2x-y=7
2(8-y)-y=7
16-2y-y=7
-3y=-9
y=3
x=8-y
x=8-3=5
Answer:
Hello
Step-by-step explanation:
Méthode par combinaisons linéaires:
[tex]\left\{ \begin{array}{ccc|c|c}x+y&=&8&1&-2\\2x-y&=&7&1&1\\\end {array} \right.\\\\\\\left\{ \begin{array}{ccc}3x&=&15\\-3y&=&-9\\\end {array} \right.\\\\\\\boxed{\left\{ \begin{array}{ccc}x&=&5\\y&=&3\\\end {array} \right. }\\[/tex]
Proof:
5+3=8 and 2*5-3=7
Plss help...
Write down the rule in the form y=
Answer:
yxthgggggyhfffghgggggvggvvggvv
A canadian goose and a Great blue heron took off in opposite directions. The goose flew at 20 mph, and the heron flew at 10 mph. when they landed, they were 180 miles apart. Altogether, they flew for 14 hours. How long did each bird fly?
The Canadian goose flew for 4 hours and the Great blue heron flew for 10 hours
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let a represent the time flown by the goose and b represent the time flown by the heron. Hence:
a + b = 14 (1)
Also:
20a + 10b = 180 (2)
From equation 1 and 2:
a = 4, b = 10
The Canadian goose flew for 4 hours and the Great blue heron flew for 10 hours
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What are the x-intercepts of the function y = 22 -x - 120? Check all that apply. O (-120. 0) O (-11.466, 0) O (-10.466, 0) O (0, -120) (10.466, 0) O (11.466, 0)
The x-intercepts of the function y = 2x^2 -x - 120 are (-7.5, 0) and (8, 0)
How to determine the x-intercept?The function is given as:
y = 2x^2 - x - 120
Set the function to 0
2x^2 - x - 120 = 0
Factor out 2
2(x^2 - 0.5x - 60) = 0
Divide by 2
x^2 - 0.5x - 60 = 0
Expand the function
x^2 + 7.5x - 8x - 60 = 0
Factorize the function
(x + 7.5)(x - 8) = 0
Split
x + 7.5 = 0 and x - 8 = 0
Solve for x
x = -7.5 and x = 8
Hence, the x-intercepts of the function y = 2x^2 -x - 120 are (-7.5, 0) and (8, 0)
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Given: ABCD is a rectangle.
Prove: ABCD has congruent diagonals.
Rectangle A B C D is shown.
Identify the steps that complete the proof.
♣ =
♦ =
♠ =
By SAS property, ABC ≅ DCB.
How to prove the deductionsIn this question we have to proof ABCD has congruent diagonal. By SAS property and reflexive property it can be proved as follows:
Given:
ABCD is a rectangle.
Prove:
Diagonal AC ≅ Diagonal BD
From the question,
As we can see that, ABCD is a rectangle, it is also a parallelogram.
Thus, ABCD is a parallelogram, opposite sides of a parallelogram are congruent.
⇒ AB ≅ DC
⇒ BC ≅ BC (Reflexive Property of Congruence)
Hence, ∠ABC and ∠DCB are right angles by the definition of rectangle.
∠ABC ≅ ∠DCB (all right angles are congruent)
Therefore, by SAS property, ABC ≅ DCB.
⇒ segment AC ≅ segment BD
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Answer:
♣ = parallelogram side theorem
♦ = SAS
♠ = CPCTC
(Correct On Edgen)
The potential energy p, in a spring is represented using the formula p=1/2kx^2. lupe uses and equivalent equation, which is solved for k to determine the answers to her homework
The value of [tex]k = 2P/x^2[/tex]
We are aware that an object's location might cause it to store energy. When a bow and arrow are used, the energy that is stored when the bow is pulled is what gives the arrow its kinetic energy when it is released.
when a spring is moved away from its equilibrium position, it gains some energy, which we can notice by the tension our hands experience as we stretch it. Potential energy is a type of energy that arises from a change in its position or condition, according to our definition
We know that P=1/2kx^2
Now solving for k
2P = kx^2
Therefore
k = 2P/x^2
Hence the value of k is 2P/kx^2
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The director of research and development is testing a new drug. She wants to know if there is evidence at the 0.01 level that the drug stays in the system for more than 377 minutes. After performing a hypothesis test, she decides to reject the null hypothesis. What is the conclusion
Here null hypothesis is rejected in this problem.
According to the statement
We have a given that the evidence at alpha level is 0.02, ANd the sample size n is 67. And mean time equal to 330 minutes and the variance that is the sigma square is equal to 529 point.
And We have to make the decision to reject or feel fail to reject the null hypothesis to solve this problem.
Firstly we solve alternative and null hypothesis
So, the null hypothesis h naught will be that mu is less than equal to 327 point and alternative hypothesis ha will be.
That mu is greater than 327 point now. This alternative hypothesis is claimed.
Next we will find the value of s which is given by sigma divided by under root n.
So, s = 67/ (529)^1/2
s = 2.8099.
Now we find the value of Z
So, Z = 327 - 330 / 2.8099
Z = 1.0677
Now the critical value of z is 2.05
Critical, we can say fail to reject the null hypothesis, and this is the result from the null hypothesis test.
With this test, we can conclude that the the data do not support that. There is evidence at 0.02 level that the drug stays in the system for more than 327 minutes. So this is the conclusion for the test for the hypothesis test and the answer to the problem.
So, Here null hypothesis is rejected in this problem.
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What is 3x^3+5x^2-11x+3/x+3
The solution to the expression (3x³ + 5x² - 11x + 3)/(x + 3) is (x - 1/3)(x - 1)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the expression:
(3x³ + 5x² - 11x + 3)/(x + 3)
= (x + 3)(x - 1/3)(x - 1) / (x + 3)
= (x - 1/3)(x - 1)
The solution to the expression (3x³ + 5x² - 11x + 3)/(x + 3) is (x - 1/3)(x - 1)
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The typical pole for pole vaulting is 17 feet long. How fast would a pole vaulter have to run (in the direction of the pole) in order for a spectator sitting in the stands to see it 15 feet long
A pole vaulter have to run at 18m/s speed.
According to the statement
The typical pole for pole vaulting is 17 feet long
we use the formula
1/2 m(v)^2 = mgh
Now rearrange the terms
(v)^2 = 2gh
here g = 10 and h = 15 then
substitute the values
(v)^2 = 2*10*15
v = 17.32
So, A pole vaulter have to run at 18m/s speed.
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