Answers
Answer:
a. The length of the box = (40 - 2·x) cm
The height of the box = x cm
The width of the box = (25 - 2·x) cm
b. The formula for the volume of the box as a function of x is 4·x³ - 130·x² + 1000·x
c. The value of x that would maximize the volume of the box is x = 5 cm
d. The largest volume of the box is 2250 cm³
Step-by-step explanation:
a. The given parameters are;
The length of the cardboard = 40 cm
The width of the cardboard = 25 cm
The length of the box = (40 - 2·x) cm
The height of the box = x cm
The width of the box = (25 - 2·x) cm
b. The formula for the volume of the box = The area of the base of the box × Height of the box
The area of the base of the box = (40 - 2·x) × (25 - 2·x) = 1000 - 80·x - 50·x + 4·x²
∴ The area of the base of the box = 4·x² - 130·x + 1000
The height of the box = x
The volume of the box = (4·x² - 130·x + 1000) × x = 4·x³ - 130·x² + 1000·x
The volume of the box in terms of x, V = 4·x³ - 130·x² + 1000·x
c. At the extremum point, dV/dx = 12·x² - 260·x + 1000 = 0
x = (260 ± √((-260)² - 4 × 12 × 1000))/(2 × 12)
x = (260 ± 140)/(24)
x = 5 or x = 16.[tex]\bar 6[/tex]
At x = 5, the volume of the box is V = 4×5³ - 130×5² + 1000×5 = 2250
The volume of the box is V = 2250 cm³
At x = 16.67, the volume is 4×16.67³ - 130×16.67² + 1000×16.67 = -925.[tex]\overline {925}[/tex]cm³
Therefore, the value of x that would maximize the volume of the box is x = 5 cm
d. The largest volume of the box is 4×(5 cm)³ - 130×(5 cm)² + 1000×(5 cm) = 2250 cm³.
Related Questions
Which of the following is the equation of an ellipse centered at (4,-1) having a
horizontal minor axis of length 14 and a major axis of length 20?
Answers
Answer:
B for me
Step-by-step explanation:
Yun lang po correct me if iam wrong
The Required equation for the ellipse is given by [tex]\frac{(x-4)^2}{49}+\frac{y+1}{100} = 1[/tex] Option B. is correct
What is an ellipse?Ellipse is cross-section part of a cone structure when cutting it out a horizontal cross-section of a cone.
(x-h)^2/a^2 + (x-k)^2/b^2 = 1
(h,k) = centre of the ellipse.
a, b = semi minor or major axis,
[tex]\frac{(x-4)^2}{49}+\frac{y+1}{100} = 1[/tex]
thus, the required equation of ellipse is given by [tex]\frac{(x-4)^2}{49}+\frac{y+1}{100} = 1[/tex].
Learn more about ellipse here:
https://brainly.com/question/14281133
#SPJ2
help !!! find the value of x, please show how you solved it
Answers
Answer:
x = 48°
Step-by-step explanation:
Since the 2 legs are congruent then the triangle is isosceles and the base angles are congruent, that is
x = 48°
Bookers father sells computer and earns a 4.25 commission on every software package he sells. How much commission would he earn on software package that sold for 15,725 round to the nearest cent
Answers
Answer:
Commission= $668
Step-by-step explanation:
Giving the following information:
Commission rate= 4.25% = 0.0425
Sales= $15,725
To calculate the commission earned, we need to use the following formula:
Commission= commission rate*sales
Commission= 15,725*0.0425
Commission= 668.3125
Commission= $668
36 + 15(40 - 35)
Evaluate
Answers
36+15x5
36+75
111
Select the correct answer.
Solve the system of equations.
y = x + 2
y = x2 + 7x + 10
A.
(-2,0) and (-4,-2)
B.
(-2,-4) and (-4,-6)
C.
(-2,-2) and (-4,0)
D.
(2,4) and (4,6)
Answers
Answer:
(-2,0) and (-4,-2)
Step-by-step explanation:
The solution to the system of equations is where the two graphs cross
They cross at (-2,0) and (-4,-2)
Answer:
The answer is A
Step-by-step explanation:
Go through each one and just plug in the equation
ALso a easier way is just look at the graph and look at the two lines that are shown *when the blue thingy crosses the line* (My vocabulary sucks rn)
ANd there are 2 points there, identify and you should be fine
ALso for equation purposes
y=x+2
B and C dont work
Only A and C
But the second one
Only A woris so A
Simplify 7 + (−3) pls help its due today afternoon
Answers
Answer:
4
Step-by-step explanation:
You can rewrite this equation like this
7-3
which equals 4
In right-angled ∆ ABC, ∟B=90⁰. ∆ ABC is in the first and second quadrant on the graph paper. The coordinates of the points A and C are (2,5) and (-2,3). How do you find the possible pairs of coordinates of B?
Answers
Answer:
The given coordinates of the points A and C of the right triangle ABC are (2, 5) and (-2, 3) respectively
The possible pairs of the coordinates of the point B are found as follows;
1) Draw a horizontal line from the point C to the right and a vertical line down from the point A to get the point B at (2, 3) which is the point of the perpendicular intersection of the two constructed lines above
2) Draw a vertical line from the point C upwards and a horizontal line to the left from the point A to get the point B at (-2, 5) which is the point of the perpendicular intersection of the two newly constructed lines here
Step-by-step explanation:
Find the value of x.
3x-10
25
X+15
Answers
Which of the following does not Belong in the second column of a formal proof
Answers
Answer:
Uh were u supposed to add a pic?
Step-by-step explanation:
A formal proof of a statement is a sequence of steps that links the hypotheses of the ... The statement does not even name the vertical angles formed. ... Your mission is to show that these two angles are congruent.
Please help help help !!!!!!!1
Answers
Three consecutive integers have a sum of 87. Find the integers.
Answers
Answer:
28, 29, 30Step-by-step explanation:
Let the integers be x- 1, x and x +1, then:
x - 1 + x + x + 1 = 873x = 87x = 29The integers are 28, 29, 30
Answer:
Let the numbers be (x-1), x and (x+1)
According to the above problem,
[tex](x - 1) + x + (x + 1) = 87 \\ 3x = 87 \\ \boxed{x = 29}[/tex]
Therefore, the numbers are 28, 29 and 30.
Solve the equation
3/2x - 2 > 7
Answers
You can multiply each side of equation by the denominator to eliminate the fraction.
Work:
Giving brainliest!!!!!!!!!!!!!!!!!!
Answers
Answer:
D
Step-by-step explanation:
6+13 = 19 not 19.
In this case X=5 so No it isn't solution.
you say me when you start at 21 and count by tens. I am after 91. I am before 111. What number am i?
Answers
Answer:
101
Step-by-step explanation: it is before 111 and after 91
Answer:
101
Step-by-step explanation:
91, 101, 111. 101 is above 91, but below 111, while it is also counting by tens starting from 21
Shape A and shape B are each made from five identical squares.
Not drawn
accurately
Shape A
Shape B
The perimeter of shape A is 60 cm.
I
Work out the perimeter of shape B.
Answers
Answer:
the answer is 60
Step-by-step explanation:
Answer:
Step-by-step explanation:
Answer= 50
What numbers do I put if I am regrouping using the numbers 279,389-191,492
Answers
In a school, 60% of the students are girls.
50% of the girls walk to school.
20% of the boys walk to school.
What percentage of the students walk to school?
Answers
Answer:
Not entirely sure but 38%
Step-by-step explanation:
Answer:
38%
Step-by-step explanation:
How many positive four-digit integers have the three digits the same and a different fourth digit (in some order)
Answers
Answer:
81 * 4 = 324.
Step-by-step explanation:
There are 81 * 4 = 324 such integers.
There are 9000 four-digit integers from 1000 to 9999. Let’s refer to the digit that occurs three times as the triplet and the digit that occurs once as the singleton.
In the first (most significant) position there are 9 possible values for the singleton, 1 through 9. In each case there are also 9 possible values for the triplet. For example if the singleton was a 1, the triplets could be anything but a 1: 1000, 1222, 1333, …, 1999. So there are 9 * 9 = 81 cases with the singleton in the first position.
A singleton in the second position can have 10 possible values, 0 through 9. If it’s a 0 there are 9 possible values for the triplet: 1011, 2022, 3033, …, 9099. If it’s anything else there are only 8 possible values for the triplet since the triplet cannot be 0: 2122, 3133, 4144, …, 9199. So there are 9 + (8 * 9) = 81 cases with the singleton in the second position.
The third and fourth positions work just like the second. So the grand total is 81 * 4 = 324.
If you plot the 9000 four-digit integers as a 100 x 90 grid of squares and color the integers with three same digits in red, an interesting pattern occurs:
There are 81 * 4 = 324 such integers.
There are 9000 four-digit integers from 1000 to 9999. Let’s refer to the digit that occurs three times as the triplet and the digit that occurs once as the singleton.
In the first (most significant) position there are 9 possible values for the singleton, 1 through 9. In each case there are also 9 possible values for the triplet. For example if the singleton was a 1, the triplets could be anything but a 1: 1000, 1222, 1333, …, 1999. So there are 9 * 9 = 81 cases with the singleton in the first position.
A singleton in the second position can have 10 possible values, 0 through 9. If it’s a 0 there are 9 possible values for the triplet: 1011, 2022, 3033, …, 9099. If it’s anything else there are only 8 possible values for the triplet since the triplet cannot be 0: 2122, 3133, 4144, …, 9199. So there are 9 + (8 * 9) = 81 cases with the singleton in the second position.
The third and fourth positions work just like the second. So the grand total is 81 * 4 = 324.
If you plot the 9000 four-digit integers as a 100 x 90 grid of squares and color the integers with three same digits in red, an interesting pattern occurs:
(If you zoom in, the four-digit number is printed inside each red square - not sure whether or not that will come through after Quora processes the image.)
Hope this helps!
Brain-List?
Answer:
81
Step-by-step explanation:
4 digit number: xxxy
x=1 y can be 0,2,3,4,5,6,7,8,9 ...9 possibility
x can be 1,2,3,4,5,6,7,8,9 ....9 too
9 x 9 = 81
My best guess, wish it's right.
What is the following difference? 2ab * (root(3, 192a * b ^ 2)) - 5(root(3, 81a ^ 4 * b ^ 5))
Answers
Answer:
C
Step-by-step explanation:
it was correct for me on edge
What is the value of the 6 in the number 734,906,257 need fasttt
Answers
Answer:
6 thousands
Step-by-step explanation:
hope it helps
Write the point-slope form of the equation for a line that passes through (6, -1) with a slope of 2.
The value of xi is
The value of yı is
The point-slope form of the equation is
Answers
9514 1404 393
Answer:
the value of x1 is 6the value of y1 is -1the point-slope equation is: y +1 = 2(x -6)Step-by-step explanation:
Point-slope form is ...
y -y1 = m(x -x1) . . . . . . line with slope m through point (x1, y1)
The given point is (6, -1), so ...
x1 = 6
y1 = -1
The given slope is 2, so ...
m = 2
Substituting these into the point-slope form above gives ...
y -(-1) = 2(x -6)
y +1 = 2(x -6)
Answer:
y+1= 2(x-6)
Step-by-step explanation:
Hi! Before we begin answering the question, we need to recall the formula for Point-Slope Form which is y- yı= m(x-xi), in which m is the slope of the function. With this given information, we just need to plug in the point (6,-1) and the slope 2 into the given function.
This will look like:
y- (-1) = 2 (x-6)
Notice that two negatives will make a positive, so the left side of the equation is the same as y+1.
Therefore, our answer is y+1= 2(x-6) .
plzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
Answers
Answer:
3a
Step-by-step explanation:
Here we have to divide like terms that means 9 by 3, a^3 by a^2 and b by b. 9 by 3= 3, a^3 by a^2=a after subtracting power 3 and 2 we get 1 and b by b are both cut like dividing 2 by 2 is cut and we get 1 which is not necessary to write as there would be no difference in ans.
Hope this helps you
a^3 /a^2 is a
b/b is 1
So answer is 3a
Is someone kind and available enough to do this work for me
I need it really
Answers
Answer:
D. 40.0km
Step-by-step explanation:
When rounding to 3 significant figures, we will have to look at the 4th significant figure. If that figure is 1-4, you round the 3rd figure down. If that figure is 5-9, you round the 3rd figure up.
In this case, the 3rd figure is the tenth 9 and the 4th figure is the hundredth 7.
Since 7 is from 5-9, you round the tenth 9 up. This adds one whole to 39, which makes it 40. You also need to keep 3 significant figures so the decimal zeros are significant. Thus, the answer is 40.0km
If 7 toothpaste tubes cost $40.50, how much does one tube cost?
Answers
Answer:
40.5/7=(answer)
What is the simplified form of StartRoot StartFraction 2,160 x Superscript 8 Baseline Over 60 x squared EndFraction EndRoot? Assume x ≠ 0. 36x3 36x2 6x3 6x2
Answers
Answer:
6׳ is your answer.
Step-by-step explanation:
Edge2020
Answer:c
Step-by-step explanation:
Solve for X 3(x•2)=10•x
Answers
Step by step explanation:
3(x*2)=10*x - use the commutative property to reorder the terms
3*(2x)=10x - remove unnecessary parentheses
3*2x=10x - calculate the product
6x=10x - move the variable to the left hand side and change its sign
6x-10x=0 - collect like terms
-4x=0 - divide both sides of the equation by -4
X=0
On a test, Jim answered 28 problems correctly. He answered 80% of the questions correctly.
How many questions were on the test?
Answers
Answer:
35
Step-by-step explanation:
If a video is getting 12,000 views every 4 hours, how long will it take to reach 30,000 views?
Answers
Step-by-step explanation:
12,000 views = 4 hours
=> 30,000 views = 4 * (30000/12000) = 10 hours.
Hence it will take 10 hours.
Answer:
10
Step-by-step explanation:
Since we know every 4 hours the vid recieves 12,000 views, we divide 12,000 by 4 to see how many views it recieves in 1 hour. We get 3,000. So 3,000 views every hour. Divide 30,000 by 3,000, to get 10 hours.
Jason purchased 3 popcorns and 2 soft drinks for a total of $15.50.
Ann purchased 4 popcorns and 3 soft drinks for a total of $22.00.
how much does a single soft drink cost?
Answers
F(X) = 5(X) - 6, Find the value of X if F(X) = 44
Answers
Answer:
x=10
Step-by-step explanation:
just use ur brain