Answer:
2.47 feet
Step-by-step explanation:
Let l, b, and h be the length, width, and height of the box.
As the length is twice the width, so l=2b ...(i)
The volume of the box is 20 cubic feet, so
lbh=20
(2b)bh=20 [by using (i)]
[tex]h=\frac {20}{2b^2} \\\\h= \frac {10}{b^2} ...(ii)[/tex]
The material required= surface area, S, of the open box
S= lb+2bh+2lh
By using equation (i) and (ii), we have
[tex]S= 2b(b)+2b\times \frac {10}{b^2} +2(2b)\times \frac {10}{b^2}[/tex]
[tex]S= 2b^2+ \frac {20}{b} + \frac {40}{b} \\\\S= 2b^2+ \frac {60}{b} \cdots(i)[/tex]
Now, we have the surface area, S, as the function of width, b.
Differentiate S with respect to b then equate it to zero to get the extremum values, as
[tex]\frac {dS}{db}=0 \\\\\frac {d}{db}(2b^2 +60/b)=0 \\\\4b-\frac{-60}{b^2}=0 \\\\4b=\frac{60}{b^2} \\\\b^3=\frac{60}{4} \\\\b=(15)^{1/3}[/tex]
b=2.47 feet.
Now, by second differentiation, checking the nature of extremum value.
[tex]\frac {d^2S}{db^2}=4+\frac {120}{b^3}[/tex]
For [tex]b>0, \frac {d^2S}{db^2} >0[/tex]
So, the width of the box, b=2.47, is the minima for the area, S(b).
Hence, the width of the box that can be produced using the minimum amount of material is 2.47 feet.
What is the equation of the line with slope 3 through the point (5, 1) in point-slope form?
y-5=3(x-1)
y-1=3(x-5)
y=3x-14
y=3x+2
12___24
1. >
2.=
3.<
I don’t know which one to pick
Answer:
<
I hope it will be useful.
solve for x. Enter your answer in interval notation using grouping symbols. x^2+9x<-20
Step-by-step explanation:
x^2+9x<-20
x^2+9x+20<0
( x+5)(x+4)<0
x+5<0,x+4<0
x<-4 (because x<-5 is extraneous solution)
Complete the description of the slope of the line that joins the points
positive
negative
0
undefined
Answer:
The slope of the line that joins the points is negative.
i.e m = -6/5
Step-by-step explanation:
Taking two points from the graph to determine the slope
(-3, 4)(2, -2)Finding the slope between (-3, 4),(2, -2)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]'
[tex]\left(x_1,\:y_1\right)=\left(-3,\:4\right),\:\left(x_2,\:y_2\right)=\left(2,\:-2\right)[/tex]
[tex]m=\frac{-2-4}{2-\left(-3\right)}[/tex]
[tex]m=-\frac{6}{5}[/tex]
Therefore, the slope of the line that joins the points is negative.
i.e m = -6/5
Help me fast ASAP pls
Answer:
C
Step-by-step explanation:
I got it right
The price of gold rose from $790 per ounce to $860 per ounce what percent increase does this amount represent round to the nearest 10th of a percent
What is the probability that the same result (heads or tails) shows twice in a row exactly once in the ten tosses?
Answer:
1/512
Step-by-step explanation:
The probability is 2 out of 2^10 , because there are only two sequences when same result (heads or tails) shows twice in a row exactly once in the ten tosses (HTHTHTHTHT and THTHTHTHTH) out of 2^10 possible sequences.
2/2^10 = 2/1024 =1/512
The function c(x) = 18x -10 represents the cost in dollars. How many tickets can you buy?
Note: It seems you may have unintentionally missed writing the complete question. As total cost is missing.
So, I am assuming how many tickets Mr. XYZ can buy if he/she pays 170 dollars.
The solution would still clear your concept though.
Answer:
Please check the explanation.
Step-by-step explanation:
Given the function
[tex]c(x) = 18x -10[/tex]
The slope-intercept form of the line equation
We know that the slope-intercept form of the line equation
y=mx+b
where m is the slope and b is the y-intercept
so
[tex]c(x) = 18x - 10[/tex]
comparing with the slope-intercept form of the line equation
here:
rate of change = 18c(x) or y represents the costand
'x' represents the number of tickets
Assuming the total cost i.e. c(x) = $170
In order to determine the value of x, set c(x) = 170
i.e.
170 = 18x -10
switch sides
18x - 10 = 170
add 10 to both sides
18x - 10 + 10 = 170 + 10
18x = 180
Divide 18 to both sides
18x/18 = 180/18
x = 10
Therefore, if you can buy x = 10 tickets if you pay 170 dollars.
Dannon has $10.80 in dimes and quarters. If dannon has 32 more quarters than dimes, how many dimes does he have?
Answer:
he should have 28 dimes
Step-by-step explanation:
Answer:
0.34
Step-by-step explanation:
10.80 DIVIDED BY 32 IS 0.3375 IF YOU ROUND THAT IT WOULD BE 0.34
To be labeled as a jumbo egg, the egg is supposed to weigh 2.5 oz. Mia buys a carton of jumbo eggs and measures one of the eggs as 2.4 oz. What is the percent error? *
Answer: 4.17%
Step-by-step explanation:
Formula for percentage error = [tex]\dfrac{|\text{Estimated weight - Actual weight}|}{\text{Actual weight}}\times100[/tex]
Given: Estimated weight = 2.5 oz
Actual weight = 2.4 oz
Percentage error = [tex]\dfrac{2.5-2.4}{2.4}\times100\%[/tex]
[tex]=\dfrac{0.1}{2.4}\times100\%\\\\=\dfrac{100}{24}\%=4.17\%[/tex]
Hence, the percent error = 4.17%
Put the following numbers in order from least to greatest:
10, -10, -7, 5, -3, 0, 2, -1, -2, -23, 23, 2, 15, 3, - 15
Answer:
-23, -15, -10, -7, -3, -2, -1, 0, 2, 2, 3, 5, 10, 15, 23
Step-by-step explanation:
:)
21 = 4x - 9 - x
what is x?
Answer:
x = 10
Step-by-step explanation:
21 = 4x - 9 - x
21 = 3x - 9
30 = 3x
10 = x
Answer:
x = 10
Step-by-step explanation:
Given
21 = 4x - 9 - x, that is
21 = 3x - 9 ( add 9 to both sides )
30 = 3x ( divide both sides by 3 )
10 = x
Emiliana pays 6% sales tax on a cupcake that costs 3 dollars. How much does the sales tax add to the purchase price? Please tell me how you got the answer. (answer choices: $0.018, $18, $0.18, $3.18)
Answer:
$0.18 sales tax will be added to the purchase price.
Step-by-step explanation:
Given that:
Cost of cupcake = $3
Sales tax applied = 6%
Amount of sales tax = 6% of cost of cupcake
Amount of sales tax = [tex]\frac{6}{100}*3[/tex]
Amount of sales tax = 0.06 * 3 = $0.18
Hence,
$0.18 sales tax will be added to the purchase price.
what is the answer please ?
Answer:
10
Step-by-step explanation:
i think
Can I get some help plz?
Answer:
X=20 degree
Step-by-step explanation:
∆A+∆D+∆O=180
2x+10+2x+90=180
collect like terms
2x+2x=180-100
4x=80
(4x)/4=(80)/4
x=20 degree
Answer:
[tex]angles \: of \: triangle \: add \: up \: to \: {180}^{0} \\ {(2x + 10})^{0} + {(2x)}^{0} + {90}^{0} = {180}^{0} \\ 4x = {(180 - 90 - 10)}^{0} \\ 4x = {80}^{0} \\ x = {20}^{0} [/tex]
Bruce overdrew his checking account by $19, for which his bank charged him a $35 overdraft fee. If he deposits $60, what will his balance be?
$
NEED ASAP PLESDE through (-2,7) perpendicular to 5y+x=20
(Show in point slope form and slope/intercept form )
Answer:
y = 5x + 16
Step-by-step explanation:
5y + x = 20
5y = -x + 20
y = [tex]-\frac{1}{5}[/tex]x + 20
Points: (-2, 7)
Slope (m⊥): = 5
y = 5x + b
7 = 5 ( -2 ) + b
6 = -10 + b
b = 16
y = 5x + 16
Can some help me with number 2 please
The number line that represents opposite numbers is (a) number line 1
How to determine the number line?From the question, we understand that:
The numbers are opposite numbers
Take for instance, we have a number x.
The opposite of the number x is -x
So, the number line that represents opposite numbers must have points at x and -x
Let x = 10.
So, we have:
Opposite numbers = 10 and -10
So, the number line that represents opposite numbers must have points at 10 and -10
Hence, the number line that represents opposite numbers is (a) number line 1
Read more about number lines at:
https://brainly.com/question/4727909
#SPJ1
I need to find the value of X if someone could help that’ll be great thank you!
help me simplify this question
5p-3-(1+p)+(2p)
Answer:
This is the answer. All the very best
Find the distance between −8 and 9 on a number line. _____ unit(s)
here are 5 number cards
Answer:
im doind the same question on mahswatch what is it
Step-by-step explanation:
help please !! it's asking "find the measure of the missing angle" yet there's nothing ??
Answer:
60 degrees
Step-by-step explanation:
All the angles are the same so 180 divided by 3 is 60
I’ll give brainliest plz quick
Describe this number line and the numbers and fractions shown.
A number line going from negative 2 to positive 2 in increments of 1. There are 4 equal spaces between each number.
Answer:
Please check the number line attached below.
Step-by-step explanation:
Please check the attached graph below.
The line graph is representing that a number line:
Going from negative 2 to positive 2 in increments of 1. There are 4 equal spaces between each number.From the graph, it is clear that the point 0 is taken as arbitrary. The left side number units from 0 represent the negative values and the right-sided number units from 0 represent the positive values.
When we move on the right side from the 0, the numbers increase and when you move on the right side from the 0, the number decreases.
Answer:
The number line shows -2 through 2, divided into fourths, with zero in the middle. The numbers increase as you move right and decrease as you move left.
Step-by-step explanation:purrr
Write a function g whose graph represents the indicated transformation of the graph of F. Let g be a translation 4 units down and a horizontal shrink by a factor of of the graph of f(x) = x.
Answer:
g(x) = 6x+4
Step-by-step explanation:
The given function f(x)=x
Let p(x) be an intermediate function after translation of f(x).
So, after the translation 4 unit down, the new function
p(x) = f(x) - 4
p(x) = x-4
Now, there is a horizontal shrink by a factor of 6, so the required function g(x) is
g(x) = p(6x) [here 6 is the horizontal shrink factor]
g(x) = 6x-4
Hence, the required function is g(x) = 6x+4
what is the volume of the cone to the nearest cubic centimeter?
Answer:
301.44
Step-by-step explanation:
Describe the lines below as parallel, perpendicular,or neither.
3x+6y=42 and y=2x-1
Answer:
They are neither perpendicular nor parallel.
Step-by-step explanation:
Find the gradient of 2x + 6y = 42 by rearranging it in the form y = mx + c:
6y = -2x + 42
y = -(1/3)x + 7
The gradient is the co-efficient of x
Therefore the gradient is -(1/3)
The gradient of y = 2x - 1 is 2.
If they were parallel they would have the same gradient.
If they were perpendicular then the gradient of one would be the negative reciprocal of the other, e.g: if one was 2, the other would be -(1/2).
Neither of these are true, so they are neither perpendicular nor parallel.
The lines 3x+6y=42 and y=2x-1 are perpendicular
Two lines are parallel if they have equal slope
Two lines are perpendicular if the product of their slopes equals -1
The given lines are:
3x+6y=42 and y=2x-1
Rewrite each of the equations in the form y = mx + c
For line 3x + 6y = 42:
[tex]6y = -3x + 42\\\\y=\frac{-3}{6} x+\frac{42}{6}\\\\y=-0.5x+7[/tex]
The slope, m₁ = -0.5
For line y = 2x - 1
The slope, m₂ = 2
Since m₁ ≠ m₂, lines 3x+6y=42 and y=2x-1 are not parallel
m₁ m₂ = -0.5(2)
m₁ m₂ = -1
Since the product of the slopes equals -1, the lines 3x+6y=42 and y=2x-1 are perpendicular
Learn more here: https://brainly.com/question/20093063
The ratio of boys to girls in a class is 5:4. There are 36 students in the class. How many
students are girls?
Answer:
16 students are girls.
Step-by-step explanation:
5:4=36
5x+4x=36
9x=36
x=4.
So we can multiply the ratio by 4.
4(5+4)
20+16.
Since girls is 4, there are 16 girls.
Hope this helps plz hit the crown :D
Answer:
let ratio of boys and girl be 5x and 4x
now
5x+4x=36
9x=36
x=36÷9
x=4
now
number of boys in class is 5x=5*4=20
Number of girls in class is= 4x
=4*4
=16 ans
Help please asap!! I will mark you as brainliest :)
Answer:
k=4
Step-by-step explanation:
cross multiply so it would be:
8k+24=56
subtract 24 from 56
8k+24-24=56-24
8k=32
divde
8k/8=32/8
k=4