Answer:
c
Step-by-step explanation:
The base of an aquarium with given volume V is made of slate and the sides are made of glass. If the slate costs seven times as much (per unit area) as glass, use Lagrange multipliers to find the dimensions of the aquarium that minimize the cost of the materials. (Enter the dimensions as a comma separated list; Note that the variable volume is a capital V and must be entered as such, using the shift rather than caps-lock key)
Answer:
[tex]l = \sqrt[3]{\frac{2V}{7}}[/tex] [tex]b = \sqrt[3]{\frac{2V}{7}}[/tex] [tex]h = \sqrt[3]{\frac{49V}{4}}[/tex]
Step-by-step explanation:
Represent the volume of the box with V and the dimensions with l, b and h.
The volume (V) is:
[tex]V = l * b * h[/tex]
Make h the subject of the formula
[tex]h = \frac{V}{lb}[/tex]
The surface area (S) of the aquarium is:
[tex]S = lb + 2(lh + bh)[/tex]
Where lb represents the area of the base (i.e. slate):
The cost (C) of the surface area is:
[tex]C = 7 * lb + 1 * 2(lh + bh)[/tex]
[tex]C = 7lb + 2(lh + bh)[/tex]
[tex]C = 7lb + 2h(l + b)[/tex]
Substitute [tex]\frac{V}{lb}[/tex] for h in the above equation
[tex]C = 7lb + 2*\frac{V}{lb}(l + b)[/tex]
[tex]C = 7lb + \frac{2V}{lb}(l + b)[/tex]
[tex]C = 7lb + \frac{2V}{b} + \frac{2V}{l}[/tex]
Differentiate with respect to l and with respect to b
[tex]C_l=7b - \frac{2V}{l^2}[/tex] [tex]=0[/tex]
[tex]C_b=7l - \frac{2V}{b^2}[/tex] [tex]=0[/tex]
To solve for b and l, we equate both equations and set l to b (to minimize the cost)
[tex]7b - \frac{2V}{l^2}=7l - \frac{2V}{b^2}[/tex]
[tex]7l - \frac{2V}{l^2}=7b - \frac{2V}{b^2}[/tex]
By comparison:
[tex]l =b[/tex]
[tex]C_l=7b - \frac{2V}{l^2}[/tex] [tex]=0[/tex] becomes
[tex]7l - \frac{2V}{l^2}=0[/tex]
[tex]7l = \frac{2V}{l^2}[/tex]
Cross Multiply
[tex]7l^3 = 2V[/tex]
Solve for l
[tex]l^3 = \frac{2V}{7}[/tex]
[tex]l = \sqrt[3]{\frac{2V}{7}}[/tex]
Recall that: [tex]l =b[/tex]
[tex]b = \sqrt[3]{\frac{2V}{7}}[/tex]
Also recall that:
[tex]h = \frac{V}{lb}[/tex]
[tex]h = \frac{V}{\sqrt[3]{\frac{2V}{7}}*\sqrt[3]{\frac{2V}{7}}}[/tex]
[tex]h = \frac{V}{\sqrt[3]{\frac{4V^2}{49}}}[/tex]
Apply law of indices
[tex]h = \sqrt[3]{\frac{49V^3}{4V^2}}[/tex]
[tex]h = \sqrt[3]{\frac{49V}{4}}[/tex]
The dimension that minimizes the cost of material of the aquarium is:
[tex]l = \sqrt[3]{\frac{2V}{7}}[/tex] [tex]b = \sqrt[3]{\frac{2V}{7}}[/tex] [tex]h = \sqrt[3]{\frac{49V}{4}}[/tex]
6500 divide by 100. step by step
Answer:
6500 / 100 = 65
Step-by-step explanation:
if you are dividing a number that has zeros by 10/100/1000... you can cancel out the zeros to find the answer.
A bank loaned out $12,00, part of it at the rate of 9% per year and the rest at 19% per year. If the interest received in one year totaled $1,500, how much was loaned at 9%
Answer:
$7,800 was invested at 9% and $4,200 at 19%.
Step-by-step explanation:
Given that a bank loaned out $ 12,000, part of it at the rate of 9% per year and the rest at 19% per year, if the interest received in one year totaled $ 1,500, to determine how much was loaned at 9% the following calculation must be performed:
12,000 x 0.09 + 0 x 0.19 = 1,080
10,000 x 0.09 + 2,000 x 0.19 = 1,280
8,000 x 0.09 + 4,000 x 0.19 = 1,480
7,900 x 0.09 + 4,100 x 0.19 = 1,490
7,800 x 0.09 + 4,200 x 0.19 = 1,500
Thus, $ 7,800 was invested at 9% and $ 4,200 at 19%.
Find the number of terms in the the following arithmetic sequence
8, 11, 14, 17, .... 68
Answer:
number of term is 21
Step-by-step explanation:
Please mark as brainliest
Answer:
21
Step-by-step explanation:
The first numbers we ever learn to count with are the ones on our fingers - 1, 2, 3, 4, and on and on and on. Wouldn't it be nice, then, if we could somehow transform this sequence into that one that's so familiar to us? If we could do that, we could find the number of terms just by looking at the last one.
Arithmetic sequences evolve predictably - we start with a specific number and continue adding another number (called the common difference) to one term to get the next.
Here, our common difference is 3, since 8 + 3 = 11, 14 + 3 = 17... you get the picture. If we ultimately want to get our sequence down to the counting numbers (1, 2, 3...) we should start by getting them down to the multiples of 3 (3, 6, 9...). To do that, we'll subtract 5 from each term in the sequence. This gets us from
8, 11, 14, 17, ... 68
to
3, 6, 9, 12, ... 63
From here, we'll divide each term by 3, finally giving us back a sequence of counting numbers:
1, 2, 3, 4, ... 21
Now, we can look at the last term sequence to find that there are 21 terms in it.
A line contains the points (6,-4) and (0,-2). What is the equation of the line?
Answer:
The equation of the line is:
[tex]y = -\frac{1}{3}x - 2[/tex]
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
[tex]y = mx + b[/tex]
In which m is the slope and b is the y-intercept, that is, the value of y when x = 0.
(0,-2)
This means that the y-intercept is -2, that is, [tex]b = -2[/tex]. So
[tex]y = mx - 2[/tex]
Finding the slope:
When we have two points, the slope is given by the change in y divided by the change in x.
We have points (6,-4) and (0,-2).
Change in y: -2 - (-4) = -2 + 4 = 2
Change in x: 0 - 6 = -6
Slope: [tex]m = \frac{2}{-6} = -\frac{1}{3}[/tex]
So the equation of the line is:
[tex]y = -\frac{1}{3}x - 2[/tex]
Write a polynomial function of least degree that has real coefficients, the following zeros: 1,5,3+i and a leading coefficient of 1
Answer:
no te entiendo
yo también la busco
Factorise the expressions.
mn + m + n + 1
m(n +1) + (n+1)
( n + 1) ( m + 1)
x (y+ z) -5 (y + z)
( y + z ) ( x- 5 )
99165+67894321-9872345
Answer:
58121141
Step-by-step explanation:
99165+67894321= 67993486
67993486-9872345= 58121141
A theory predicts that the mean age of stars within a particular type of star cluster is 3.3 billion years, with a standard deviation of .4 billion years. (Their ages are approximately normally distributed.) You think the mean age is actually greater, and that this would lend support to an alternative theory about how the clusters were formed. You use a computer to randomly select the coordinates of 50 stars from the catalog of known stars of the type you're studying and you estimate their ages. You find that the mean age of stars in your sample is 3.4 billion years.
Answer:
The answer to this question can be defined as follows:
Step-by-step explanation:
Please find the complete question in the attached file.
Lets [tex]\mu[/tex] in trillions of years be the maximum likelihood age of galaxies in a certain type of star cluster.
Calculating the Hypotheses:
Null hypothesis value:[tex]H_o : \mu = 3.3[/tex]
Alternative hypothesis value: [tex]H_A : \mu > 3.3[/tex]
11. The length of a rectangle is double its width, If its width is 15cm, What is its area. Show
your steps.
Answer:
450 cm squared
Step-by-step explanation:
W=15
L=2W =30
A= LxW
A= 15X30
A=450
The dimensions of a beach ball are shown in the diagram below.
17 in
Which measurement is the closest to the volume of the beach ball in cubic
inches?
Answer:
Volume = 2572.44 in.³
Step-by-step explanation:
The volume of the beach ball = volume of a sphere = ⁴/3πr³
r = ½(17) = 8.5 in.
Plug in the value
Volume = ⁴/3 × π × 8.5³
Volume = ⁴/3 × π × 614.125
Volume = 2572.44 in.³
The diagonals of square ABCD intersect at point E. If BE = 2x + 1, and AC = 3(6x – 4), find BD.
A1
B3
C6
D9
Answer: c6
Step-by-step explanation:
The measure of the diagonal BD is 15 units.
What is a square?A square is a quadrilateral with four equal sides. There are many objects around us that are in the shape of a square. Each square shape is identified by its equal sides and its interior angles that are equal to 90°.
Given that, the diagonals of square ABCD intersect at point E.
Here, BE = 2x + 1, and AC = 3(6x-4)
Now, AC=BD
BD=2BE
So, 3(6x-4)=2(2x+1)
18x-12=4x+2
18x-4x=2+12
14x=14
x=1
So, BD=3(6x-1)=15
Therefore, the measure of the diagonal BD is 15 units.
Learn more about the square here:
brainly.com/question/28776767.
#SPJ6
Rafael is training for a triathlon, which includes swimming, biking, and running. The graph shows the total hours he spent swimming over the first 4 weeks of his training. Swim Training 0 Is the relationship between the time spent swimming and the number of weeks proportional? Complete the statements. 30 27 The points ? a straight line that 24 21 ? 4 through the origin. 18 Time (h) 15 12 6 3 0 1 2 3 4 5 6 7 8 9 10 0
Answer:
For people that are doing this lesson on I-Ready
The points Lie on a straight line that goes through the origin.
The graph shows a relationship that is Proportional.
Step-by-step explanation:
Answer:
Step-by-step explanation:
lie on
goes
Kiki was one of 8 children to share in a prize of $34.24. Kiki was hoping to win $5.
What is the difference between the amount of money Kiki won and the amount she hoped to win?
Answer:
She didn't get as much money that she hoped for
Step-by-step explanation:
A jewelry store offers its own brand of customizable charm bracelets. You are able to choose from 9
different charms for your bracelet.
How many different charm bracelets is it possible to create?
Answer:
By the way that it is worded, I believe that you are only allowed to put 1 charm on the bracelet, so there are 9 ways to pick a charm.
Hope this helps(and also if you have a more refined wording please put it in the comments)!
Answer:
By the way that it is worded, I believe that you are only allowed to put 1 charm on the bracelet, so there are 9 ways to pick a charm.
How can you use tables, graphs and equations to compare functions
Answer:
A graph is a chart or drawing that shows the relationship between changing things.
- They are a diagram displaying the relationship between numbers or amounts.
- A graph is one of the easiest ways to compare numbers.
- A graph or chart is used to present facts in visual form.
- They are a drawing that displays the relative sizes of numerical quantities.
- Graphs can be used to illustrate many types of data.
- They should be used to make facts clearer and more understandable.
- it shows trends over time.
- Forceful -- Emphasizes main point
- Convincing -- proves a point, see and hear
- Compact way to convey information
- More interesting than just talk or print
- Quick way for the audience to visualize what you are saying -- numbers trends up or down
- To bring facts to life
- To show and compare relationships
- To show and compare changes
- They are much easier to understand then a large
table of numbers
- without
the need to understand what each and every number in a table means.
They help you visually see the difference between two or more values.
Hope this helps!
Carter is solving for x by the process of completing the square for the following
problem:
3x^2+ 12x-24 = 0
He got to this point below:
Type the number that goes in the "?" spot:
(x+?)2 = 12
Answer:
The number that goes in place of the question mark is 2.
Step-by-step explanation:
Let's solve it!
3x² + 12x - 24 = 0
First we can factor 3 out of each term:
x² + 4x - 8 = 0
Now we'll add 12 to both sides to complete the square:
x² + 4x + 4 = 12
And finish it off:
(x + 2)² = 12
So the answer to the question is 2
Bonus:
We can also now solve this for x:
(x + 2)² = 12
x = √12 - 2
x = 2√3 - 2
x ≈ 2 × ±1.732 - 2
x ≈ 1.464, -5.464
x²-12x+a=(x+b)² find a and b
Answer:
Step-by-step explanation:
x² - 12x + a = (x + b)²
x² - 12x + a = x² + 2xb + b²
-12 = 2b and a = b²
b = -6
a = b² = 36
The value of a is 36 and b = -6.
What is the quadratic equation?The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of: ax² + bx + c = 0.
The given expression is;
[tex]\rm x^2-12x+a=(x+b)^2[/tex]
The solution of the equation is determined in the folllowing steps given below.
[tex]\rm x^2-12x+a=(x+b)^2\\\\x^2-12x+a=x^2+2xb+b^2\\\\2xb + b^2 = a-12x[/tex]
On comparing the equation
[tex]\rm 2b =-12\\\\b =\dfrac{-12}{2}\\\\b=-6[/tex]
The value of a is;
[tex]\rm a=b^2\\\\b=-6\\\\a=(-6)^2\\\\a=36[/tex]
Hence, the value of a is 36 and b = -6.
Learn more about equation here;
https://brainly.com/question/15339001
#SPJ2
Determine the missing side length:
Answer
35
Step-by-step explanation:
Using Pythagoras theorem since it's a right angle triangle,
The missing side, say h,is the hypotenuse
28²+21²= h²
784+441=h²
√1225=√h²
h=35
What is exponential growth and exponential decay?
Answer:
In exponential growth, the rate of growth is proportional to the quantity present. In other words, y′=ky. Systems that exhibit exponential growth have a constant doubling time, which is given by (ln2)/k. Systems that exhibit exponential decay have a constant half-life, which is given by (ln2)/k
Step-by-step explanation:
There is your answer good luck! - Alexsys
Answer:
In some cases with exponential functions, as the value of x increases, the value of y also increases. This is a direct relationship known as exponential growth. As the value of x increases, the value of y grows rapidly. ... This is an inverse relationship known as decay.
Step-by-step explanation:
I hope this answer has helped you
the equation of a line that is perpendicular to y = 2x + 1 passes through the point (4,-3)
Step-by-step explanation:
perp. -1/2
y + 3 = -1/2(x - 4)
y + 3 = -1/2x + 2
y = -1/2x - 1
The length of a swimming poollane
is 10 more than 2 times the width.
If the area is 300 square meters,
find the width of the lane. Write a
quadratic equation which can be
used to find x, the width of the
pool.
Answer:
x²+5x - 150 = 0
Step-by-step explanation:
Let the length be y and width be x
If the length of a swimming pool is 10 more than 2 times the width, then;
y = 2x+10 ...1
Since the Area is 300m²
A = xy
300 = xy .... 2
Substitute 1 into 2
300 = x(2x+10)
300 = 2x²+10x
Rearrange
2x²+10x - 300 = 0
Divide through by 2
x²+5x - 150 = 0
This gives the required quadratic expression
The weight of adult female panthers in one habitat area are normally distributed with a mean of 82 pounds and a standard deviation of 9.8 pounds. What percent of the panthers weigh less than 76 pounds?
Answer:
27.09% of the panthers weigh less than 76 pounds
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 82 pounds and a standard deviation of 9.8 pounds.
This means that [tex]\mu = 82, \sigma = 9.8[/tex]
What percent of the panthers weigh less than 76 pounds?
The proportion is the pvalue of Z when X = 76. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{76 - 82}{9.8}[/tex]
[tex]Z = -0.61[/tex]
[tex]Z = -0.61[/tex] has a pvalue of 0.2709
0.2709*100% = 27.09%
27.09% of the panthers weigh less than 76 pounds
A Hummingbird moves its wings at a rate of 5460 wingsbeats a minute. Write this rate in wingbeats per second?
PLEASE HELP
Answer:
60 seconds in a minute, so
5460 ÷ 60 = 91 beats per second
About 20,000 fewer babies were born in
California in 1996 than in 1995. In 1995,
about 560,000 babies were born. Which
equation can be used to predict the
number of babies y (in thousands), born x
years after 1995?
Answer:
The answer is B
Step-by-step explanation:
Your substracting the 20,000 from the 560,000
How much will a shopper save on a TV that is on sale for 25% off the regular price of $399.99
Answer: $99.99
Step-by-step explanation:
$399.99 * .25 (discount) = $99.99
Use a t-distribution to answer this question. Assume the samples are random samples from distributions that are reasonably normally distributed, and that a t-statistic will be used for inference about the difference in sample means. State the degrees of freedom used.
Find the endpoints of the t-distribution with 2.5% beyond them in each tail if the samples have sizes n1=16 and n2=21.
Enter the exact answer for the degrees of freedom and round your answer for the endpoints to two decimal places.
Answer:
Don't go on that link its a virus
Step-by-step explanation:
Hey yall I need help
Evaluate the expression |−35|+|7|−|−5|−|−4|−(−5)
Answer: 38
Step-by-step explanation: i dont know
Answer:
38
Step-by-step explanation:
hey there!
so if you didn't know ll means absolute value
the absolute value of -35 is 35
the absolute value of 7 is 7
the absolute value of-5 is 5
the absolute value of -4 is 4
and -(-5) the two negative signs cancel out to make it +5
now we have 35+7-5-4+5
35+7=42
42-5=37
37-4=33
33+5=38
so the answer would be 38
The number of square tiles of side 25cm which can be paved on a rectangular floor of 3m
× 2m is:
Answer:
96 square tiles can be paved on a rectangular floor.
Step-by-step explanation:
First, we need to find the area of the square tiles:
[tex]A_{t} = (25 cm)^{2} = 625 cm^{2}[/tex]
Now, the area of the rectangular floor is:
[tex] A_{f} = 3m*2m = 6 m^{2}*\frac{(100 cm)^{2}}{1 m^{2}} = 60000 cm^{2} [/tex]
Finally, the number of square tiles which can be paved on a rectangular floor is:
[tex] N = \frac{A_{f}}{A_{t}} = \frac{60000 cm^{2}}{625 cm^{2}} = 96 [/tex]
Therefore, 96 square tiles can be paved on a rectangular floor.
I hope it helps you!
What is the correct answer?
Answer:
6 units to the right, 3 units down
Step-by-step explanation: