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Given a rectangular box with an open top and square base, the dimensions of the box are:
[tex]a\times a\times b[/tex]The volume can be calculated as:
[tex]V=a\cdot a\cdot b=a^2\cdot b[/tex]The area of the sides is:
[tex]A_L=a\cdot b[/tex]The area of the base:
[tex]A_B=a^2[/tex]There are 4 lateral sides and 1 base (the top is open), so the total surface area is:
[tex]A_{\text{total}}=4\cdot A_L+A_B=4\cdot a\cdot b+a^2[/tex]We have a fixed volume of 2048 in³, then:
[tex]\begin{gathered} a^2\cdot b=2048 \\ b=\frac{2048}{a^2} \end{gathered}[/tex]Using this result on A_total:
[tex]A_{\text{total}}=4\cdot a\cdot\frac{2048}{a^2}+a^2=\frac{8192}{a}+a^2[/tex]To find the minimum surface area, we take the derivative:
[tex]\begin{gathered} \frac{dA_{total}}{da}=-\frac{8192}{a^2}+2a=0 \\ a^3=4096 \\ a=16 \end{gathered}[/tex]Now, we calculate the minimum total area using a:
[tex]A_{\text{total}}=\frac{8192}{16}+16^2=768in^2[/tex]Related Questions
Jordan plotted the graph below to show the relationship between the temperature of his city and the number of cups of hot chocolate he sold daily:A scatter plot is shown with the title Jordans Hot Chocolate Sales. The x axis is labeled High Temperature and the y axis is labeled Cups of Hot Chocolate Sold. Data points are located at 20 and 20, 30 and 18, 40 and 20, 35 and 15, 50 and 20, 45 and 20, 60 and 14, 65 and 18, 80 and 10, 70 and 8, 40 and 2.Part A: In your own words, describe the relationship between the temperature of the city and the number of cups of hot chocolate sold. (2 points)Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate the slope and y-intercept. (3 points)
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A.
Overall it has a relation that there are more sold cups when the temperature is lower. On the other hand, based on the 40 degrees part, that have to different values of two different days, we can say is not the only factor.
B.
The best lineal approach is the line created with the points at 20 and 80 degrees. First the slope:
[tex]m=\frac{y1-y2}{x1-x2}=\frac{20-10}{20-80}=\frac{10}{-60}=-\frac{1}{6}[/tex]Now the intercept with y axis, b:
[tex]\begin{gathered} y=mx+b \\ 20=20(-\frac{1}{6})+b \\ 20+\frac{20}{6}=b=23.33=\frac{70}{3} \end{gathered}[/tex]The final line formula is:
[tex]y=-\frac{x}{6}+\frac{70}{3}[/tex]Given the definitions of f(a) and g(x) below, find the value of (19)( 1),f (x) = x2 + 3x – 11g(x) = 3a + 6
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The given functions are,
[tex]\begin{gathered} f(x)=x^2+3x-11_{} \\ g(x)=3x+6 \end{gathered}[/tex]Fog can be determined as,
[tex]\begin{gathered} \text{fog}=f(g(x)) \\ =f(3x+6) \\ =(3x+6)^2+3(3x+6)-11 \\ =9x^2+36+36x+9x+18-11 \\ =9x^2+45x+43 \end{gathered}[/tex]The value of fog(-1) can be determined as,
[tex]\begin{gathered} \text{fog}(-1)=9(-1)^2+45(-1)+43 \\ =9-45+43 \\ =7 \end{gathered}[/tex]Thus, the requried value is 7.
mrs smith took her 3 kids and 3 of thejr friends to the Strawberry field. how many kids are there?
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Mrs.Smith took : her 3 kids + 3 of their friends = 3 + ( 3x 3 ) = 12 kids
Answer:
There are 3 kids, and 3 friends.
3 + 3 = 6
there are a total of 6 kids.
X+87°2x⁰ i have to solve for x it’s a 180 angle HELP ME!!!!!!!!!
Answers
Collect Like terms
X+2x°=180°-87°
3x=93°
Divide both sides by 3 to eliminate the coefficient of “x”
3x/3=93°/3
X=31°
how can you use the vertical line test and the horizontal line test to determine whether a graph represents a function and whether the graph is invertible?
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
vertical line test = ?
horizontal line test = ?
Step 02:
vertical line test ===> function
any vertical line intersect the graph at only one point
horizontal line test ===> invertible
any horizontal line intersect the graph at only one point
graph:
horizontal line test = red
vertical line test = brown
That is the full solution.
omg i lost my tutor in the middle of math i need another one btw in fith grade not in middle school yet
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by definition the division of fractions can be found by
[tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{b\cdot c}{a\cdot d}[/tex]According to this
[tex]\frac{\frac{6}{10}}{\frac{1}{5}}=\frac{6\cdot5}{10\cdot1}=\frac{30}{10}=3[/tex]HELP PLEASEEEEE!!!!!!
Answers
The solutions of the indices are;
1) 2^7
2) 3^-4
3) 3^4
4) 2^4
What is the power?We know that in this case, we would have to apply the laws of indices and the particular law that we are to apply in each case is dependent on the nature of the problem that have been posed. Let us recall that we are asked to ensure that we express the answer or the solution to the problem as a single power.
1) 64 * 256/128
2^6 * 2^8/2^7
2^6 + 8 - 7 = 2^7
2) 3^4/3^3 * 3^5
3^4 - (3 + 5) = 3^-4
3) 3^9/ (3^4)^1/2 * 3^3
3^9/ 3^2 * 3^3
3^9 - (2 + 3)
3^4
4) (2^3)^4 * 2^4 ÷ 32/ 2 * 64
2^12 * 2^4 ÷ 2^5/2^1 * 2^6
2^12 + 4 -5/2^1 + 6
2^16 -5/2^7
2^11/2^7
2^11 - 7
2^4
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A 14 m long ladder is placed against a tree. The top of the ladder reaches a point
13 m up the tree.
How far away is the base of the ladder from the base of the tree?
Give your answer in metres (m) to 1 d.p.
Answers
Answer:
Approximately 5.2 meters
Step-by-step explanation:
This formation will make a right triangle. The ground to the point in the tree is one of the legs. The base of the tree to the base of ladder is another leg and the length of the ladder is the hypotenuse. In this case, we already have the hypotenuse and one of the legs, so we need to find the value of another leg.
We can do so by using the Pythagorean Theorem which is [tex]a^2+b^2=c^2\\[/tex].
a and b represent the values of the two legs, and c is the hypotenuse. Since we already have the hypotenuse, we can change this equation a bit to find the other leg.
Let's assign the missing value, b in the theorem.
The new equation will be [tex]b^2=c^2-a^2[/tex].
We can insert the values for c and a and solve for b.
The new equation will be [tex]b^2 = 14^2-13^2[/tex].
[tex]b^2=196-169[/tex]
[tex]b^2=27[/tex]
[tex]\sqrt{b^2} =\sqrt{27}[/tex]
The square root of [tex]b^2[/tex] cancels out.
The approximate square root of 27 is 5.19 which we can round to 5.2.
Function g is a transformation of the parent function exponential function. Which statements are true about function g?
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For the given function, The following are true statements:
Four units separate function g from function f.There is a y-intercept for function g. (0,4)Function g has a range of (3,∞ ).Over the range (-, ∞), function g is positive.It may be seen from the graph below that
The g function's graph is 4 units higher than the parent exponential function's graph.
All of the input values for which the function is defined are referred to as the function's domain. The domain of the function is (-, ∞ ) according to the graph of function g.
The location where a function's graph crosses the y-axis is known as the y-intercept. G's graph crosses the y-axis at (0, 4). As a result, the Function g's y-intercept is (0,4).
growing function g across the range (- ∞, 0).
Function output values are referred to as the function's range. It can be seen from the graph that the range of function g is (3, ∞ ).
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find the x value (6x+9)° (4x-19)°
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In this problem m and n are parallel lines, and the first angle is an exteriar angle an the secon is a interior angle.
this two condition give us that the two angles are complementary anlges so the sum of them should be 180 so:
[tex]6x+9+4x-19=180[/tex]and we can solve for x so:
[tex]\begin{gathered} 10x-10=180 \\ 10x=180+10 \\ x=\frac{190}{10} \\ x=19 \end{gathered}[/tex]In the diagram shown, ray CD is perpendicular to ray CE. If the measure of DCF is 115then what is the measure of ECF?
Answers
m∠FCE =25º
1) Since the measure of ∠DCF = 115º and ∠DCE = 90º then by the Angle Addition postulate we can state that
∠DCF = ∠DCE +∠FCE Plugging into that the given values
115º = 90º + ∠FCE Subtracting 90º from both sides
115-90=∠FCE
25º =∠FCE
2) Then the measure of ∠FCE is 25º
Is (6, –21) a solution to the equation y = –5x − –9?
Answers
Answer:
Explanation:
Given the equation:
[tex]y=-5x-(-9)[/tex]When x=6:
1. what is the area of the board shown on the scale drawing? explain how you found the area.2. how can Adam use the scale factor to find the area of the actual electronics board? remember, he uses a different method than Jason.3. what is the area of the actual electronics board?
Answers
Answer:
1. 1800 square cm.
2. See below
3. 45000 square cm.
Explanation:
Part 1
The dimensions of the drawing are 36cm by 50cm.
[tex]\begin{gathered} \text{The area of the board}=36\times50 \\ =1800\operatorname{cm}^2 \end{gathered}[/tex]Part 2
Given a scale factor, k
If the area of the scale drawing is A; then we can find the area of the actual board by multiplying the area of the scale drawing by the square of k.
Part 3
[tex]\begin{gathered} \text{Area of the scale drawing}=1800\operatorname{cm}^2 \\ \text{Scale Factor,k=5} \end{gathered}[/tex]Therefore, the area of the actual drawing will be:
[tex]\begin{gathered} 1800\times5^2 \\ =45,000\operatorname{cm}^2 \end{gathered}[/tex]how many pennies are in a dollar
Answers
Answer: 100
Step-by-step explanation:
$1 =100 pennies
Complete the table for y=-3x + 5 and graph the resulting line. -
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We fill the table as follows:
*We assign values for x and solve for y, that is:
*x = 0:
[tex]y=-3(0)+5\Rightarrow y=5[/tex]So, the value of y when x = 0 is 5.
*x = 1:
[tex]y=-3(1)+5\Rightarrow y=2[/tex]So, the value of y when x = 1 is 2.
*x = 2:
[tex]y=-3(2)+5\Rightarrow y=-1[/tex]So, the value of y when x = 2 is -1.
*x = 3:
[tex]y=-3(3)+5\Rightarrow y=-4[/tex]So, the value of y when x = 3 is -4.
***The table should look like this:
x | y
0 | 5
1 | 2
2 | -1
3 | -4
***The graph is:
The relation between the number of batteries (n) and the maximum height reached by the drone (h) in feet (ft) is given. Complete the table and check the correct box(es) given below.
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We use the equation: h = 100(n + 2), so:
For n = 1:
[tex]h=100(1+2)=100(3)=300[/tex]For n = 3:
[tex]h=100(3+2)=100(5)=500[/tex]We can see that this is the correct equation. Therefore, given h we find n:
For h = 700
[tex]\begin{gathered} 700=100(n+2) \\ \frac{700}{100}=\frac{100}{100}(n+2) \\ 7=n+2 \\ 7-2=n+2-2 \\ n=5 \end{gathered}[/tex]For h = 900
[tex]\begin{gathered} 900=100(n+2) \\ \frac{900}{100}=\frac{100}{100}(n+2) \\ 9=n+2 \\ 9-2=n+2-2 \\ n=7 \end{gathered}[/tex]Answer:
(n): 1 3 5 7
(h): 300 500 700 900
Correct equation: h = 100(n + 2)
select all of the following equations which represent a function?
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To verify that something is a function, we use the horizontal line rule. That is, if the horizontal line passes through two points, then the graph is not a function, like this:
Then the circles and the ellipses are not functions. Then the functions in the problem would be:
1, 3 and 6.
Solve each equation for the variable. h/2 + 3.5 = 7.1
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To answer this question, we can proceed as follows:
[tex]\frac{h}{2}+3.5=7.1[/tex]1. Subtract 3.5 to both sides of the equation:
[tex]\frac{h}{2}+3.5-3.5=7.1-3.5\Rightarrow\frac{h}{2}+0=3.6[/tex]2. Multiply by 2 to both sides of the equation:
[tex]2\cdot\frac{h}{2}=2\cdot3.6\Rightarrow h=7.2[/tex]We can check this result as follows:
[tex]\frac{7.2}{2}+3.5=3.6+3.5=7.1\Rightarrow7.1=7.1[/tex]This result is TRUE. Then, the value for h = 7.2.
Use the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. Hint solve this problem using P and Q's and synthetic division f(x) = x^3 + 2x^2 - 5x - 6A -3, -1, 2; f(x) = (x + 3)(x + 1)(x - 2)B-1; f(x) = (x + 1)(x2 + x - 6)C-3; f(x) = (x + 3)(x2 - x - 2)D-2, 1, 3; f(x) = (x + 2)(x - 1)(x - 3)
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Since all coefficients are integers, we can apply the rational zeros theorem.
The trailing coefficient is -6 with the following factors (possible values for p):
[tex]p\colon\pm1,\pm2,\pm3,\pm6[/tex]The leading coefficient is 1, with factors:
[tex]q=\pm1[/tex]Therefore, all the possible values of p/q are:
[tex]\frac{p}{q}\colon\pm\frac{1}{1},\pm\frac{2}{1},\pm\frac{3}{1},\pm\frac{6}{1}[/tex]Simplifying, the possible rational roots are:
[tex]\pm1,\pm2,\pm3,\pm6[/tex]Next, we have to check if they are roots of the polynomials by synthetic division, in which the remainder should be equal to 0.
0. Dividing ,f (x), by ,x−1,. Remainder = ,-8, ,+1, is ,NOT ,a root.
,1. Dividing ,f (x), by x+,1,. Remainder = 0, ,-1, ,IS ,a root.
,2. Dividing ,f (x), by x-2. Remainder = 0, ,+2, ,IS ,a root.
,3. Dividing ,f (x), by ,x+2,. Remainder = ,4, ,-2, is ,NOT ,a root.
,4. Dividing ,f (x), by ,x−3,. Remainder = 24,, ,+3, is ,NOT ,a root.
,5. Dividing ,f (x), by ,x+3,. Remainder = 0,, ,-3, IS ,a root.
,6. Dividing ,f (x), by ,x−6,. Remainder = 252,, ,+6, is ,NOT ,a root.
,7. Dividing ,f (x), by ,x+6,. Remainder = -120,, ,-6, is ,NOT ,a root.
Actual rational roots: A. -3, -1, 2; f(x) = (x + 3)(x + 1)(x - 2)
what does this mean i dont get it please help me thanks, :)
Answers
It means that you are supposed to group The like terms together and simplify them
you will find that 2t is the liketerm with -5t and -u is a like term with -6u
As a results we have
[tex] = 2t - 5t - u - 6u \\ = - 3t - 7u[/tex]
as indicated I have shown you the answer .
good luck
On a 7 question multiple-choice test, where each question has 2 answers, what would be the probability of getting at least one question wrong?Give your answer as a fraction
Answers
Solution
- This is a Binomial probability question. The formula for Binomial probability is:
[tex]\begin{gathered} P(r)=\sum\text{ }^nC_rp^rq^{n-r} \\ where, \\ n=The\text{ total number of trials} \\ r=\text{ The number of successful trials\lparen where answer is correct\rparen} \\ p=\text{ The probability of success \lparen The probability of getting a question } \\ right) \end{gathered}[/tex]- We have been given:
[tex]\begin{gathered} n=7 \\ \text{ since there can only be two answers, it means that the} \\ \text{ probability of getting a question correct is:} \\ p=\frac{1}{2} \\ q=1-p=\frac{1}{2} \\ \\ \text{ The probability of getting at least 1 question wrong means the } \\ probability\text{ of getting 1, 2, 3, 4, 5, 6, or 7 question wrong.} \\ \\ \text{ Instead of calculating all these probabilities, we can simply say} \\ P(1)+P(2)+P(3)+P(4)+P(5)+P(6)+P(7)=1-P(0) \end{gathered}[/tex]- Thus, we have:
[tex]\begin{gathered} P(0)=^7C_0(\frac{1}{2})^0(\frac{1}{2})^7 \\ P(0)=\frac{1}{128} \\ \\ 1-P(0)=1-\frac{1}{128}=\frac{127}{128} \end{gathered}[/tex]Final Answer
The answer is
[tex]\frac{127}{128}[/tex]helppppppppppppppppppppppppppp
Answers
Step-by-step explanation:
make the fractions decimals and put them on the plot
use and show all conversion factors to convert 352 inches per second to miles per hour. 352 inches divided by 1 second
Answers
Okay, here we have this:
We need to convert 352 inches per second to miles per hour. So we obtain the following:
[tex]\begin{gathered} \frac{352in}{1sc}\cdot\frac{1mile}{63360in}\cdot\frac{3600sc}{1h} \\ =\frac{20\text{miles}}{h} \end{gathered}[/tex]Finally we obtain that 352 inches per second 20 are miles per hour.
A train travels at 100 mph any equation can be written that compares the time with the distance to find the domain and range
Answers
ok
speed = distance / time
time = distance/speed
[tex]\text{ time = }\frac{dis\tan ce\text{ }}{speed}[/tex][tex]\text{ time = }\frac{dis\tan ce\text{ }}{100}[/tex]or
[tex]\text{ distance = 100 x time}[/tex]he multiplication table below can be used to find equivalent ratios.
A multiplication table.
Which ratio is equivalent to the ratio 18:24?
15:20
20:15
30:36
36:30
Answers
Answer:
15:20
Step-by-step explanation:
18:24 can be written [tex]\frac{18}{24}[/tex] if I simplify this by dividing the top and bottom by 6, I get [tex]\frac{3}{4}[/tex]
I am looking for what other ration will reduce to [tex]\frac{3}{4}[/tex]
[tex]\frac{15}{20}[/tex] Divide the top and bottom by 5 and you will get [tex]\frac{3}{4}[/tex]
What is the measure of ?ХvO A. 46°42°42"38°NуvO B. 42°O C. 40°O D. 38°
Answers
The value Z is denoted as the center of the circle. Therefore, arc UV and arc XY should be the same .
[tex]undefined[/tex]Answer: A. 42°
Step-by-step explanation:
Hope this helps :)
The height of a pole is 15 feet. A line with banners is connected to the top of the poleto a point that is 8 feet from the base of the pole on the ground. How long would theline with banners need to be in order for the pole to be at a 90° angle with the ground?Explain your reasoning.
Answers
In order to have a 90º angle (right angle) the length of the line with banners needs to fullfit the Pythagorean theorem: In a right triangle the squared hypotenuse is equal to the sum of the legs squared:
[tex]h^2=l^2+l^2[/tex]In the given situation the hypotenusa is the line with banners, and the legs are the pole and the 8ft ground from the base of the pole to the end of the line with banners:
h= x
l= 15ft
l= 8ft
[tex]x^2=(15ft)^2+(8ft)^2[/tex]Solve the equation to find the value of x:
[tex]\begin{gathered} x^2=225ft^2+64ft^2 \\ x^2=289ft^2 \\ x=\sqrt[]{289ft^2} \\ x=17ft \end{gathered}[/tex]Then, to make a right triangle the length of the line witg banners need to be 17ftMarcy baked 132 cookies . She is packaging boxes of eight cookies to give as a gift to he friends how many boxes will she make .
Answers
She will make 16 boxes.
To answer this question we simply have to divide the number of cookies (132) by the number of cookies that each box can contain.
Mathematically speaking:
[tex]132/8\text{ }[/tex][tex]16.5[/tex]Since we can´t have half boxes, we have to round the number to 16.
16 boxes.
9. If L 1 equals 120 then what is the measure of its supplement <2=
Answers
Supplementary angles are angles whose addition sums up to 180 degrees.
Therefore, if angle 1 measures 120, then its supplement which is angle 2, must mean both add up to 180.
Hence, you have
Angle 1 + Angle 2 = 180
120 + Angle 2 = 180
Subtract 120 from both sides of the equation
Angle 2 = 180 - 120
Angle 2 = 60 degrees
By definiton, two angles are complimentary angles if they both add up to 90 degrees. Hence if angle L5 equals 50 degrees, then its compliment would be derived as 90 - 50 which equals 40. The compliment of angle L5 which is 50 degrees, equals 40 degrees.
Which expression is equivalent to (6 – 3x) + 9x ? 1 A. 8x + 2 B. 8x + 3 C. 10x-2 D. 10x - 6
Answers
Given to solve the expression:
[tex]\frac{1}{3}(6-3x)+9x[/tex]step 1: Expand the bracket by multiplying each term by the factor outside
[tex]\begin{gathered} (\frac{1}{3}\times6)-(\frac{1}{3}\times3x)+9x \\ 2-x+9x \end{gathered}[/tex]step 2: Simplify the expression obtained in step 1
[tex]\begin{gathered} 2-x+9x\text{ } \\ =2+8x \\ =8x+2 \\ \\ \text{The answer is \lbrack{}Option }A\rbrack \end{gathered}[/tex]