The lengths of the edges of a rectangular box with a volume of 32 cm³ that would give the minimum surface area would all be equal, and that would be the cubic root of the volume, which is approximately 3.17 cm.
Explanation:The subject is Mathematics, specifically dealing with optimization of geometric shapes. This problem is related to the minimization of the surface area of a closed rectangular box given a fixed volume.
Given that the volume of a rectangular box, or a cuboid, is V = lwh where l is length, w is width, h is height. We know the volume is 32 cm³, we have the equation lwh = 32.
To minimize the surface area, we should make the box as close to a cube as possible because a cube has the smallest surface area for a given volume. So, to minimize the surface area, the lengths of the edges should all be equal, i.e., l = w = h.
Hence, the box that has the minimum surface area is a cube with edge length of the cubic root of the volume, which is ∛32 cm = approximately 3.17 cm.
Learn more about Optimization of Geometric Shapes here:https://brainly.com/question/34673373
#SPJ3
a car travels 300 km in 6 hours what is the average speed of the car in kilometers per hours
Answer: 50 Km per hour
Step-by-step explanation: divide 300 by 6 and it will give 50 km and per hour means over one so 50 km over 1 which means per hour . The rule for getting the average speed is distance over time so divide 300(distance ) by 5 which is the time . Please brainliest .
A line passes through the points (2, –2) and (–6, 2). The point (a, –4) is also on the line. What is the value of a? mc023-1.jpg
Answer:
[tex]a=6[/tex]
Step-by-step explanation:
We have been given coordinates of three points on the same line and we are asked to find the value of 'a'.
First of all, we will find the equation of the line in slope-intercept form of equation [tex]y=mx+b[/tex].
Let us find slope of our given line using coordinates of point [tex](2,-2)[/tex] and [tex](-6,2)[/tex].
Upon substituting the coordinates of the given points in slope formula we will get,
[tex]m=\frac{2--2}{-6-2}[/tex]
[tex]m=\frac{2+2}{-8}[/tex]
[tex]m=\frac{4}{-8}[/tex]
[tex]m=-\frac{1}{2}[/tex]
Now, we will substitute [tex]m=-\frac{1}{2}[/tex] and coordinates of point [tex](2,-2)[/tex] in slope-intercept form of equation to find the y-intercept.
[tex]-2=-\frac{1}{2}*2+b[/tex]
[tex]-2=-1+b[/tex]
[tex]-2+1=-1+1+b[/tex]
[tex]-1=b[/tex]
Therefore, the equation of line passing through the given points is [tex]y=-\frac{1}{2}x-1[/tex].
To find the value of 'a' we will substitute coordinates of point [tex](a,-4)[/tex] in our equation as:
[tex]-4=-\frac{1}{2}*a-1[/tex]
[tex]-4+1=-\frac{1}{2}*a-1+1[/tex]
[tex]-3=-\frac{1}{2}*a[/tex]
Upon multiplying both sides of our equation by -2, we will get
[tex]-3*-2=-\frac{1}{2}*a*-2[/tex]
[tex]6=a[/tex]
Therefore, the value of a is 6.
Answer:
A = 6
Step-by-step explanation:
I think this is late but i got this right hope this helps :D
Part b given the information found in part a, find the time t it takes to jane to transfer enough cranberry juice into the orange juice glass to make her favorite drink if h0=10.0 centimeters. assume that the flow rate of the liquid is constant, and that the glasses are cylindrical with a diameter of 7.0 centimeters and are filled to height 14.0 centimeters. take the diameter of the straw to be 0.4 centimeters.
the Time required to fill the cranberry juice is 3.8d.
What is volume?Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m3), a derived unit, is the SI unit of volume. Volume is another word for capacity.
Given, Jane goes to a juice bar with her friend Neil. She is thinking of ordering her favorite drink, 7/8 orange juice and 1/8 cranberry juice, but the drink is not on the menu, so she decides to order a glass of orange juice and a glass of cranberry juice and do the mixing herself.
Part A:
The initial height of the inlet of the straw from the surface of the cranberry juice is d and the height of the outlet of the siphon from the surface is h. Using Bernoulli's equation, the initial velocity of cranberry juice that flows out of the straw is determined.
for the surface of the upper reservoir:
ν²/2 -gd +Patm/ρ = Constant
The velocity of the surface of the upper reservoir is zero by considering the reservoir would be infinity and then the above equation becomes:
0²/2 -g*0 + Patm/ρ = Constant
Bernoulli's equation for the outlet of the siphon
ν²/2 -g*h +Patm/ρ = Constant
Both these equations are equal as the siphon is a single system, therefore the initial velocity of the outflow is
ν = √(2gh)
Part B:
time = volume/flow rate
Since Volume to be filled:
V = 1/8 * pi * r² * h
V = 6.731* 10⁻⁵ m³
Thus,
Flow rate,
Q = ν*A
Q = √(2gh) * (pi * r² * h)
Q = 1.758 * 10⁻⁵ m³/s
Therefore, the time required to fill the cranberry juice is:
t = V/Q
t = 3.8s
Therefore, the Time required to fill the cranberry juice is 3.8d.
Learn more about Volume here:
https://brainly.com/question/1578538
#SPJ6
Complete question:
What conclusion can be made based on this division problem?
24 ÷ 4 = 6
Twenty-four is 2 times greater than 6.
Twenty-four is 6 times greater than 4.
Six is 2 times greater than 4.
Six is 24 times greater than 4.
Answer:
Twenty-four is 6 times greater than 4.
Step-by-step explanation:
Here, the given expression,
[tex]24\div 4=6[/tex]
That is,
[tex]\frac{24}{4}=\frac{6}{1}[/tex]
By cross multiplication,
[tex]24=6\times 4[/tex]
⇒ 24 = 6 times of 4
Hence, by the given expression it is clear that twenty-four is 6 times greater than 4.
SECOND OPTION is correct.
which expression is represented by the model below?
Answer:
The answer is B 4x3
In circle O, RT and SU are diameters. If m = m, what is m? 47° 52° 64° 87°
Answer:
64
Step-by-step explanation:
WILL GIVE BRAINEST
if f(x)=2x-5 and g(x)=x2.....
Tran planned a rectangular pool and made a scale drawing using centimeters as the unit of measurement. He originally planned for the length of the pool to be 40 m but decided to change it to 32 m. If the length of the pool in his scale drawing is 8 cm, which statement about the change of scale is true?
When Tran changes the actual length of the pool but keeps the scale drawing the same, the scale changes too. The original scale was 1 cm:5 m and the new scale is 1 cm:4 m.
Explanation:The question is about understanding the change in scale in a scale model. Tran's original scale was 8 cm (in the drawing) to 40 m (actual pool length), i.e., a ratio of 1 cm : 5 m. When he changes the length of the pool from 40 m to 32 m but keeps the drawing the same, the new scale becomes 1 cm: 4 m, since 8 cm (in the drawing) now corresponds to 32 m (actual pool length). Thus, the scale has been reduced proportionately.
Scale models and their measurements are an important concept in mathematics, particularly in understanding dimensions and ratios. In this scenario, the ratio of the drawing to the actual length of the pool changes when the dimensions of the pool change, but the drawing stays the same.
Learn more about Scale Changes here:https://brainly.com/question/31302959
#SPJ2
se an Addition or Subtraction Formula to simplify the equation. sin θ cos 3θ + cos θ sin 3θ = 0
A pizza shop charges $9.50 for a pizza, plus $1.90 for each topping.
If the total charge for a pizza is dependent on the base price of the pizza plus the number of toppings ordered, what is the value of y at the y-intercept of the line representing this situation?
The value of y at the y-intercept for the given situation, representing the cost of a pizza without any toppings, is $9.50.
The value of y at the y-intercept represents the cost of a pizza without any toppings. When we graph the cost of the pizza as a function of the number of toppings, the y-intercept occurs when the number of toppings is zero (meaning no toppings were added).
Since the pizza shop charges $9.50 for a pizza without toppings, this is the value of y at the y-intercept. We can represent this relationship with a linear equation y = mx + b, where m is the slope (the cost per topping) and b is the y-intercept (the base price of the pizza). In this case, m is $1.90 and b is $9.50, so the equation would be y = 1.90x + 9.50. Therefore, the y-intercept is $9.50.
63 is 75% of what number?
Enter your answer in the box.
Simplify the function f(x)=1/3(81)^3x/4 . Then determine the key aspects of the function.
Answer:
the answers are
1/3
27
All real numbers
y>0
Step-by-step explanation:
To simplify the function f(x) = 1/3(81)^3x/4, we identify 81 as 3^4 and then apply exponent rules which lead to the simplified form f(x)=3^(3x-1). The base indicates exponential growth, and the exponent determines the growth rate and vertical scaling. Additional analysis would involve graphing to observe its behavior.
Explanation:To simplify the function f(x)=1/3(81)^3x/4, we must first recognize that 81 is a power of 3, specifically 3^4. Thus, when raised to the 3x/4 power, we multiply these exponents to get 3^(4*3x/4) which simplifies to 3^(3x). Our function now looks like f(x)=(1/3)*3^(3x). By properties of exponents, this can further simplify to f(x)=3^(3x-1).
Key aspects of this function include the base of the exponential (which is 3), indicating that the growth is exponential, and the exponents indicate how quickly this growth occurs. The term '-1' in the exponent shows a vertical scaling factor of 1/3 on the base function 3^x.
To analyze the function in more detail, one could use a graphing calculator or computer software to visualize the growth pattern. However, it should be noted that in this case, a graphing calculator can't solve for x using the zero function as we don't have an equation set to zero.
Rewrite the following fractions as division problems. a. 7⁄11 b. 5⁄2 c. 9⁄10 d. 7⁄15
Final answer:
Fractions 7⁄11, 5⁄2, 9⁄10, and 7⁄15 can be rewritten as division problems by expressing each as the division of the numerator by the denominator.
Explanation:
To rewrite the given fractions as division problems, you simply need to express each fraction as a division of its numerator by its denominator. Here's how the fractions can be rewritten:
7⁄11 can be written as 7 divided by 11.
5⁄2 can be written as 5 divided by 2.
9⁄10 can be written as 9 divided by 10.
7⁄15 can be written as 7 divided by 15.
Each fraction represents a division problem where the numerator is the dividend and the denominator is the divisor.
In the Numbers Game, a state lottery, four numbers are drawn with replacement from an urn containing balls numbered 0-9, inclusive. Find the probability that a ticket holder has the indicated winning ticket.
The first two digits in exact order.
Final answer:
The probability of winning the indicated ticket in the Numbers Game is 1/100 or 0.01.
Explanation:
To find the probability of winning the indicated ticket in the Numbers Game, we will calculate the probability of the first two digits in exact order.
There are 10 numbers (0-9) to choose from in each digit, and since replacement is allowed, the probability of choosing the correct first number is 1/10. Similarly, the probability of choosing the correct second number is also 1/10.
Since the two selections are independent, we can multiply the probabilities together to find the probability of both selections being correct. Therefore, the probability of winning the indicated ticket is (1/10) * (1/10) = 1/100 or 0.01.
Kelly drives 448 miles on the highway to visit her xousin. She uses cruise control to drive at a constant speed . Kelly travels 192 miles in the first 3 hours. At that rate, how long will the trip take?
192 miles divided by 3 hours = 64 miles per hour
448 miles / 64 miles per hour = 7 hours total for the trip
Answer:
Trip will take 7 hours to complete.
Step-by-step explanation:
Kelly drives 192 miles in the first 3 hours.
Speed of Kelly to cover 192 miles = [tex]\frac{\text{Distance}}{\text{Time}}[/tex]
= [tex]\frac{192}{3}[/tex]
= 64 miles per hour
Kelly travels with the same speed to cover the whole distance.
Therefore, time taken to cover 448 miles = [tex]\frac{\text{Distance}}{\text{Speed}}[/tex]
= [tex]\frac{448}{64}[/tex]
= 7 hours
Kelly will meet his cousin after 7 hours.
What does the equation x = 6 represent in the set of real numbers2?
James bought 12 cookies and ate 3 of them. He ate ____% of the cookies.
What is the GCF of 100xyz and 25xz
The equation 9t = 27.99 models a constant rate situation. Drag and drop the value of 5t in the box. 5t = 3.11 15.55 18.99 36.99
someone help mamd explain
Read the word problem below. A parking garage charges $3 for each of the first three hours. After three hours, the charge is $7 an hour. What is the total cost for five hours of parking? Which strategy that would help solve this word problem?
Brett picked 27 flowers from garden he plans to give an equal number of flowers to each of 3 people how many flowers will each person get
Brett will give 9 flowers to each of the 3 people, as calculated by dividing the total number of flowers (27) by the number of people (3).
Brett picked 27 flowers from the garden and he plans to give an equal number of flowers to each of 3 people. To find out how many flowers each person will get, we divide the total number of flowers by the number of people receiving flowers. So, we calculate 27 ÷ 3, which equals 9 flowers per person.
Use implicit differentiation to find the points where the circle defined by x^2+y^2−6x−4y=-4 has horizontal and vertical tangent lines. List your answers as points in the form (a,b).
what is 150% of 128 ??
Prove that if a is any well-ordered set of real numbers and b is a nonempty subset of $a$, then $b$ is also well-ordered.
Final answer:
To prove that a subset b of a well-ordered set a is also well-ordered, we can assume the opposite and show that it leads to a contradiction. If b is not well-ordered, it means that there exists an element in b smaller than all others, but since b is a subset of a this element must also be in a, contradicting the assumption that a is well-ordered. Therefore, b must be well-ordered as well.
Explanation:
To prove that if a is any well-ordered set of real numbers and b is a nonempty subset of a, then b is also well-ordered, we can use the fact that every well-ordered set has the least element. Let's assume that b is not well-ordered and does not have the least element. This means that there exists an element in b that is smaller than all other elements in b. However, since b is a subset of a, this element must also be in a. But this contradicts the assumption that a is well-ordered and has the least element. Therefore, b must be well-ordered as well.
Ollie used 276 bricks to make 6 fence columns. He used an equal number of bricks to make each column. How many bricks did he use to make each column?
Answer: The answer is 46!
Step-by-step explanation:
Deepak spent 178$ on food last month if he reduces by 15% the next month how much will he spend
Suppose you observe a spot exchange rate of $1.50/€. if interest rates are 5% apr in the u.s. and 3% apr in the euro zone, what is the no-arbitrage 1-year forward rate? $1.5291/€ €1.4714/$ €1.5291/$ $1.4714/€
Find the z-scores that bound the middle 74% of the area under the standard normal curve.
The P values, the z-scores are approximately: z score (left) = -2.22 and z score (right) = 1.13.
We are given that;
The area middle= 74%
Now,
We need to find the z-scores that bound the middle 74% of the area under the standard normal curve.
Since 74% of the middle area is bounded, this means that there is 13% on the left side and another 13% on the right side.
P (left) = 0.13 and P (right) = 1 - 0.13 = 0.87. At these P values, the z-scores are approximately: z score (left) = -2.22 and z score (right) = 1.13
Therefore, by statistics the answer will be -2.22 and 1.13.
To learn more on Statistics click:
brainly.com/question/29342780
#SPJ12
The z-scores that bound the middle 74% of the area under the standard normal curve are approximately -1.04 and 1.04.
Explanation:To find the z-scores that bound the middle 74% of the area under the standard normal curve, we need to find the z-scores that bound 13% on each tail of the curve (100% - 74% = 26%, divided by 2). Using the z-table, we can find the z-scores for these tail areas:
The z-score for the lower tail area of 13% is approximately -1.04The z-score for the upper tail area of 13% is approximately 1.04Therefore, the z-scores that bound the middle 74% of the area under the standard normal curve are -1.04 and 1.04.
I need help please fast
Answer:
16
Step-by-step explanation:
The number of divisors is the product of the powers of the prime factors after 1 has been added to each. In order for the total number of divisors to be 5, the number must be a prime raised to the 4th power. The only one in the given range is 2^4 = 16.
The divisors of 16 are 1, 2, 4, 8, 16.
_____
The smallest number with 5 prime factors is 2^5 = 32, so we assume you mean "divisors" when you say "factors."