A rectangular poster is to contain 578 square inches of print. The margins at the top and bottom of the poster are to be 2 inches, and the margins on the left and right are to be 1 inch. What should the dimensions of the poster be so that the least amount of poster is used?
Answers
Answer:
19 by 38
Step-by-step explanation:
The area of the poster, A=xy
Margin at both up and bottom is 2inches, at the right and left is 1 inch
Then we can say
(x-4)(y-2)= 578
Let us make y subject of the formula
(y-2)= 578/(x-4)
y=[ 578/(x-4)] + 2
If we substitute into the area A equation we have
A= x { [ 578/(x-4)] + 2}
A= 2x + (578x)/(x - 4)
If we differentiate we have
A'(x)= [2+578(x-4)+578x ]/ (x-4)^2
=[ 2(x-4)^2 + 578(x -4) + 578x ] / (x-4)^2
=[ 2(x^2 - 8x +16) + 578(x-4) + 578x ] /(x-4)^2
If we simplify this we have
=[ 2x^2 -16x +32+578x -578x - 2312]/ (x-4)^2
=( 2x^2 -16x - 2312) / (x-4)^2
At A'(x)= 0
= ( x^2 - 8x - 2312) / (x-4)^ =0
If we divide through by 2 we have
x^2 - 8x - 1156= 0
Solving the quadratic eqn( CHECK THE ATTACHMENT)
X= 38 or -30 then we choose the positive one, then x= 38
Then from area of the poster
A= (x-4)(y-2)= 578
Substitute 38 as value of x
(38-4)(y-2)= 578
34(y-2)=578
34y-68=578
34y=646
y=19
Hence dimensions of the poster is 19 by 38
CHECK THE ATTACHMENT FOR QUADRATIC SOLUTION
Related Questions
find the amount and the compound interest on rupees 12000 at 6% p.a. compounded half yearly for 3/2 years
Answers
Answer:
A= ₹3,112.72
CI = ₹1,112.72
Step-by-step explanation:
Here P = ₹ 12000
Since, interest is compounded half yearly.
Therefore, R = 6/2 = 3%
n = 3/2* 2 = 3 half years
[tex] \because A= P\bigg(1+\frac{R}{100}\bigg)^n [/tex]
[tex] \therefore A= 12000\times \bigg(1+\frac{3}{100}\bigg)^3 [/tex]
[tex] \therefore A= 12000\times \bigg(\frac{100+3}{100}\bigg)^3 [/tex]
[tex] \therefore A= 12000\times \bigg(\frac{103}{100}\bigg)^3 [/tex]
[tex] \therefore A= 12000\times \bigg(1.03\bigg)^3 [/tex]
[tex] \therefore A= 12000\times 1.092727 [/tex]
[tex] \therefore A= 13,112.724 [/tex]
[tex] \therefore A=Rs. \:13,112.72 [/tex]
CI = A - P
CI = 13,112.72 - 12000
CI = ₹1,112.72
In the figure, angle I measures 56° and angle A measures 38°.
The measurement of angle B, C, F is
Answers
Answer:
B = 34 C = 108 F = 94
Step-by-step explanation:
Answer:
B = 34 C = 108 F = 72
Step-by-step explanation:
It's not my answer look in the comments for the other answer :P
There are 9 members on a board of directors. If they must form a subcommittee of 3 members, how many different subcommittees are possible?
Answers
explanation: 9/3=3
3 in each sub committee
Assuming each person can only be in 1 subcommittee....
9/3 is correct (3 is the answer)
If persons can serve on multiple committees, the number would be much larger. Closer to 81
What is the value of x?
Enter your answer in the box.
Answers
Answer:
7
Step-by-step explanation:
What is the image point of (-8, 7) after a translation right 5 units and up 5 units?
Answers
Answer:
(-3,12)
Step-by-step explanation:
find the median for each set of data 4,12,7,6,10,5,11,8
Answers
Answer:
7.5
Step-by-step explanation:
The median is the middle data in a set. To find the median first order the set for least to greatest. In this case, 4,5,6,7,8,10,11,12. Then find the number in the middle, however, because there is an odd number of data you must take the mean of the two middle numbers. The two numbers in the middle are 7 and 8, so to find the mean of these numbers add them then divide by the number of terms, aka 2. (7+8)/2=7.5, therefore the median must be 7.5.
Evaluate |3x-2y|+5
if x=-3 and y=2
Answers:
-8
-2
18
-13
Answers
Answer:
18
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
|Absolute Value| makes any negative number positiveStep-by-step explanation:
Step 1: Define
|3x - 2y| + 5
x = -3
y = 2
Step 2: Evaluate
Substitute: |3(-3) - 2(2)| + 5Multiply: |-9 - 4| + 5Subtract: |-13| + 5Evaluate: 13 + 5Add: 18Answer:18
Step-by-step explanation:
|3x-2y|+5
|3(-3)-2(2)|+5
|-9-4|+5
|-13|+5
13 + 5
18
3(x-6)
it says too expand and simplify it plz help
Answers
Answer:
3x-18
Step-by-step explanation:
To expand this you must use the distributive property to distribute the 3. Using this property you can multiply the x and -6 by 3. So the expanded equation would first look like x*3 + -6*3. Then simplify to get 3x-18.
Answer:
3x-18 expanded
Step-by-step explanation:
x-6 simplified
use the distributive property to expand the expression
3*x= 3x
3*-6=-18
to simplify,
find the GCF and solve
gcf= 3
3x/3=1x or just x
-18/3=-6
hope this helps
please mark brainliest
help me please im dumb
Answers
Answer:
I believe the answer is true.
Step-by-step explanation:
Parentheses are the first operation in PEMDAS but when there is brackets I was always told to do what was inside them first. Hope this helps <3
Answer:
its true.
because BEDMAS.
^
|
B( bracket )
Find the value of x
is this correct?
Answers
Quadrilateral ABCD with AB= 5.5cm,BC= 3.5cm,CD= 4cm,AD= 5cm and <A= 45°.
Answers
Answer:
⇒ Draw a line segment AB=5.5cm
⇒ Take A as a center and draw an angle of 45
o
.
⇒ Cut off AD=5cm
⇒ Take D as a center with radius 4.5cm and draw an arc.
⇒ Take B as a center with radius 3.5cm and draw an arc, which meets previous arc at point C.
⇒ Join BC and CD.
∴ ABCD is a required quadrilateral.
Step-by-step explanation:
hope this helps!
Circle D is shown. Line segment G D is a radius, D F is a radius, and D E is a radius. Angle G D F is 126 degrees, and angle F D E is 41 degrees. Point C is on the circle within angle G D F and point H is on the circle within angle G D E. Which statements are correct? Check all that apply.
Answers
Answer:
2,3,4 are correett
Step-by-step explanation:
1,5,6 are wroongg
Answer: 2 3 4 are your answers
please help i have a c
Answers
Answer: the last option
Step-by-step explanation:
the top right is I, the top left is II, the bottom left is III, and the bottom right is IV
Answer:
D. R is in the 4 quadrant
I need help please Will mark brainliest
Answers
Answer:
which ones do you need answered
Step-by-step explanation:
Kurt has 26 plant on his porch his neighbor gives him p more plants. Now he has 31 plants in all a. Write an equation to represent the situation
Answers
Answer:
26 + 5 = 31
Step-by-step explanation:
Please pick me as brainliest
Answer:
31-26=p
Step-by-step explanation:
if you need the p value, its 5
to find the p value, subtract 26 from 31
hope this helps
please mark brainliest
PLS HELP ASAP!!! MARKING BRAINLIEST AND GIVING 30 POINTS!! PLEASE EXPLAIN YOUR WORK AND GET THIS CORRECT!!
Mr. Ruiz reads that 408 students at Oakdale Middle School take the bus. Bus riders represent 60% of the total number of students at the school. Mr. Ruiz wants to know the total number of students at Oakdale Middle School
Answers
can someone help me !
Answers
Answer:
45
Step-by-step explanation:
180 - 75 = 105
105 - 15 = 90
45 x 45 = 90
Answer:
75+2x+15=180
2x=90. x=45
Emma says that Function A has a greater initial value. Is Emma correct? Justify your response.
Answers
Answer:
the answer is B I think sorry if I'm wrong
We want to check if function A has a greater initial value than function B. We will see that Emma is incorrect, the correct option is the third one.
Linear equations:A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept (we can also call the y-intercept as the initial value).
For function A we can see that the initial value is y = -2
While for function B we need to find it, but by looking at the table, we can see that for each increase of 2 units in the x-variable we have an increase of one unit on the y-variable.
Then we can see that for x = 0, we would have y = 1.
Meaning that the initial value of function B is y = 1, which is greater than the one for function A.
Then Emma is incorrect, the correct option is the third one.
If you want to learn more about linear functions, you can read:
https://brainly.com/question/4025726
What is the Y-intercept of the graph of the linear function? What is the slope?
Answers
Answer:
The Y intercept is -5 and the slope is -5/2
Kylie is creating a scale drawing of her bedroom. The actual length of her bodis 75 inches fi inch on her drawing represents 2 feel how long should her bed
be in the drawing?
Answers
Answer:
77 feet
Step-by-step explanation:
A tropical punch recipe calls for 300 ml of sugar for every 222 flavor packages. Write an equation that shows the relationship between s, the amount of sugar in milliliters, and f, the number of flavor packages for this recipe.
Answers
Answer:
s = 150f
Step-by-step explanation:
A tropical punch recipe calls for 300 ml of sugar for every 2 flavor packages. Write an equation that shows the relationship between s, the amount of sugar in milliliters, and f, the number of flavor packages for this recipe.
The amount of sugar in milliliters = s
The amount of flavor packages for these recipe = f
The relationship between 2 variables
= y ∝ x
y = kx
k = constant of proportionality
Hence:
s ∝ f
s = kf
Note ,
s = 300
f = 2
300 = 2k
k = 300/2
k = 150
Therefore, the equation that shows the relationship between s, the amount of sugar in milliliters, and f, the number of flavor packages for this recipe is:
s = kf
s = 150f
Answer:
2=150f
Step-by-step explanation:
khan said so
Find the equation of the line y=___x+___
Answers
Answer:
y = 3x + 3
Step-by-step explanation:
...............................
Terry the plumber charges a base fee of $40 for each visit to someone's home plus $25 each hour for
labor. When Kathy received her bill after he came to fix a leak in her sink, the total charge was $152.50.
How many hours did Terry work on Kathy's sink?
Answers
Answer:
4.5 hours
Step-by-step explanation:
what do you do with points
Answers
Answer: i think you need them to ask questions
Step-by-step explanation: whenever you ask a question it shows your questions and how many you need, so you have to answer questions to get some.
The following are the last 10 run scores Colin got in cricket:
32, 2, 0, 25, 34, 24, 6, 23, 17, 34
a) Work out Colin's mean score.
b) Colin plays cricket again on Sunday. He gets 23 runs.
What is his new mean score?
Give your answers as decimals.
Answers
Given : last 10 run scores Colin got in cricket: 1, 16, 5, 25, 26, 32, 5, 7, 1, 7
Colin plays cricket again on Sunday. He gets 29 runs.
To find : a) Work out Colin's mean score.
b) What is his new mean score
Solution:
last 10 run scores Colin got in cricket
1, 16, 5, 25, 26, 32, 5, 7, 1, 7
Total Score = 1 + 16 + 5 + 25 + 26 + 32 + 5 + 7 + 1 + 7 = 125
Total Innings = 10
Mean Score = 125/10 = 12.5
Colin plays cricket again on Sunday. He gets 29 runs.
=> New Total Score = 125 + 29 = 154
New Total Innings = 10 + 1 = 11
New Mean Score = 154/11 = 14
Mean Score = 12.5
New Mean Score = 14
Hope this helps! ;)
Answer:
The following are the last 10 run scores Colin got in cricket:
32, 2, 0, 25, 34, 24, 6, 23, 17, 34
a) Work out Colin's mean score.
b) Colin plays cricket again on Sunday. He gets 23 runs.
What is his new mean score?
Give your answers as decimals.
Step-by-step explanation:
Solve the inequality.
n - 21 > 16
Answers
Why:cause I’m pretty sure it should be that
Answer:
n>37
Move all all terms not containing n to the side of the inequality.
Pls help! It has to be due by 5pm.
Answers
Answer:
11 and 3/4 in further.
Answer:
I think he has to jump 11 3/4 inches further
Step-by-step explanation:
pls mark me as brainliest!
Someone please help and tell me what Y is with which X. I don’t understand this and need a good grade.
Use the line of symmetry to complete the table then graph f(x) = x^2+4x+2.
X -4, -3,-2,-1,0
y-
Answers
Is this correct? I’m too tired and confused to understand this..
Answers
Answer:
yes
Step-by-step explanation:
I think ur right because ur smart :)
Answer:
yeah lol
Step-by-step explanation:
What’s the measurement of the angle
Answers
Answer:
Step-by-step explanation:
Answer:
i think c
Step-by-step explanation:
not completely sure tho