Describe or show two ways to find the following product: 1/4 x 2/3.
If m and n are two positive real numbers whose product is 10, what is the minimum value of m + 2n
The minimum value of (m + 2n) is 8.95 and this can be determined by using the arithmetic operations.
Given :
If m and n are two positive real numbers whose product is 10.
Given that m and n are two positive real numbers whose product is 10 that is:
mn = 10
[tex]\rm m= \dfrac{10}{n}[/tex] ---- (1)
The minimum value of (m + 2n) can be determined by using the following calculation.
Put the value of m in the given expression.
[tex]\rm = \dfrac{10}{n}+2n[/tex] ---- (2)
Now for minimum value differentiate the above expression with respect to n.
[tex]\rm =-\dfrac{10}{n^2}+2[/tex]
Now equate the above equation to zero.
[tex]\rm \dfrac{10}{n^2}=2[/tex]
[tex]\rm n = \sqrt{5}[/tex]
Now, put the value of n in equation (2).
[tex]\rm Minimum \;Value = \dfrac{10}{\sqrt{5} }+2\sqrt{5}[/tex]
= 8.95
The minimum value of (m + 2n) is 8.95.
For more information, refer to the link given below:
https://brainly.com/question/72395
A customer pays $3.27 for oranges and $4.76 for pears. How many pounds of fruit does the customer buy?
A total of 7 pounds of fruit does the customer buy.
Given that, a customer pays $3.27 for oranges and $4.76 for pears.
The cost of 1 pound orages=$1.09 and the cost of 1 pound pears=$1.19
What is a unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Now, the number of pounds of oranges =3.27/1.09=3 pounds
The number of pounds of pears =4.76/1.19=4 pounds
Total weight=3+4=7 pounds
Therefore, a total of 7 pounds of fruit does the customer buy.
To learn more about the unitary method visit:
https://brainly.com/question/22056199.
#SPJ2
Barb’s class has 18 bikes .tim’s class has some rows of bikes with 5 bikes in each row. Tim’s class has more bikes than barb’s class. How many rows of bikes could tim’s class have?
Given the values of the derivative f′(x) in the table and that f(0)=150, find or estimate f(x) for x=0,2,4,6.
To find or estimate f(x) for x=0,2,4,6, integrate the given derivative f'(x) with respect to x to find the constant term. Then, add each value of f'(x) in the table to the constant term to obtain the values of f(x) for x=0,2,4,6.
Explanation:To find or estimate f(x) for x=0,2,4,6, we need to use the values of the derivative f'(x) given in the table. Since f'(x) represents the rate of change of f(x) at different values of x, we can use the derivative to find or estimate the values of f(x). Given that f(0) = 150, we can start by finding the constant term of the function using this initial condition.
To find the constant term, we need to integrate the derivative f'(x) with respect to x. This will give us the original function f(x).Integrating f'(x) gives us f(x) = 150 + C, where C is the constant term we need to find.Next, we can use the given values of f'(x) in the table to find or estimate the corresponding values of f(x) for x=0,2,4,6.Let's assume that the third column in the table represents the values of f'(x) at different values of x. We can add each value to the constant term C to obtain the values of f(x) for x=0,2,4,6.Therefore, by integrating f'(x) and adding the constant term, we can find or estimate the values of f(x) for x=0,2,4,6.
Learn more about Finding or estimating values of a function using its derivative here:https://brainly.com/question/31732155
#SPJ2
Given that P = (-4, 11) and Q = (-5, 8), find the component form and magnitude of vector QP
Answer:
<1, 3>, square root of ten
Step-by-step explanation:
10 x 6 tens-unit form and standard form
Answer:
Standard form: 600
Unit form: 6 hundreds.
Step-by-step explanation:
We have been given a number [tex]10\times 6[/tex]-tens. We are asked to write our given number in unit form and standard form.
To write our given number in standard form, we will expand our given number as shown below:
6-tens [tex]6\times 10=60[/tex]
[tex]10\times 6[/tex]-tens would be [tex]10\times 60=600[/tex]
Therefore, our given number in standard form would be 600.
We know that unit form is writing a number using place value units.
We can see that our given number has 0 ones, 0 tens and 6 hundreds.
Therefore, our given number in unit form would be 6 hundreds.
We have that the Tens unit form of 10 x 6 and Standard form is mathematically
[tex]6*10^1[/tex]
6tens
From the question we are told that
10 x 6
10 x 6=60
Standard form is a number, between 1 and 10 multiplied by a power of 10
Generally the equation for the Standard form is mathematically given as
x*10^y
Therefore
the Standard form of 10 x 6 is mathematically given as
[tex]6*10^1[/tex]
And
Generally the equation for the Tens unit form of 10 x 6 is mathematically given as
x*tens(10)
Tens-unit form is mathematically given as
6tens
For more information on this visit
https://brainly.com/question/23366835?referrer=searchResults
help!! me asap!! please!!
spiders can walk on walls write the statement in if then form
a 9 pound bag of sugar is being split into containers that hold 2/3 of a pound. how many containers of sugar will the 9 pound bag create?
Answer:
13 1/2
Step-by-step explanation:
write all names that apply to each number 121/121
If the circular opening of the pipe has a diameter of 21 inches and the oil was estimated to be flowing at 30 inches/second, how many cubic feet of oil were leaving the pipe each second? Each day?
To find the flow rate of oil, first calculate the cross-sectional area of the pipe using the formula for the area of a circle, A=πr². Then, multiply the area by the given oil speed to find the volume of oil flowing every second. Multiply this by the number of seconds in a day to find the amount of oil leaving the pipe each day, and remember to convert from cubic inches to cubic feet.
Explanation:The question is asking us to find the volume of oil leaving the pipe per second and per day. To calculate the flow rate of oil, we first find the cross-sectional area of the pipe by using the formula for the area of a circle A=πr², where r is the radius of the pipe (half the diameter). Since the diameter given is 21 inches, the radius is 10.5 inches.
Next, use the given flow rate of 30 inches/second to calculate the volume of oil flowing every second. This is done by multiplying the area by the oil speed V = A * oil speed.
To find the amount of oil leaving the pipe each day, we multiply the volume per second by the number of seconds in a day .
Note: To convert cubic inches to cubic feet (since the question asks for cubic feet), remember there are 1728 cubic inches in 1 cubic foot.
Learn more about Flow rate calculation here:https://brainly.com/question/31054204
#SPJ2
Solve for x.y = mx+b
if a ball is thrown directly upward with a velocity of 40 ft/s, its height (in feet) after t seconds is represented by 40t-16t^2. what is the maximum height attained by the ball?
The maximum height attained by the ball is 25 feet.
Explanation:The maximum height attained by the ball can be found by determining the vertex of the quadratic equation representing the height of the ball. In the given equation 40t - 16t^2, the coefficient of t^2 is negative, indicating a parabolic shape with a maximum point. The formula for the x-coordinate of the vertex is -b/2a, which in this case is -40/(2*(-16)) = 1.25 seconds. Substituting this value into the equation gives the maximum height: 40(1.25) - 16(1.25^2) = 25 feet.
How many kilometers could the red car travel in 12 hours?
The gas tank in the car holds 20 gallons of gasoline. You used up 4 gallons and 1 quart on your trip. How much gasoline is left in the tank?
The correct answer is:
Total capacity of tank in quarts:
20 gallons = 20 × 4 = 80 quarts
Gasoline used in quarts:
4 gallons 1 quart = (4 × 4) + 1 = 17 quarts
Gasoline left in the tank in quarts:
80 − 17 = 63 quarts
Gasoline left in the tank in gallons and quarts:
63 quarts = 63 ÷ 4 = 15 remainder 3 = 15 gallons 3 quarts
Carlos has 5/8 pound of pumpkin seeds. He puts the seeds evenly into 20 envelopes. How much pumpkin seed is in each envelope?
There are 24 student's in a science class. Mr. Sato will give each pair of student's 3 magnets. So far, Mr. Sato has given 9 pairs of students their 3 magnets. How many more magnets does Mr. Sato need zo.that each pair of student's habe exactly 3 magnets?
The perimeter of a square is 26.46 inches. What is the side length of the square?
The side length of a square whose perimeter is 26.46 inches can be calculated by dividing the given perimeter by 4 (the number of sides in a square), resulting in a side length of approximately 6.615 inches.
Explanation:The subject of this question is Mathematics, with the specific topic being measurement and geometry. This question is applicable to Middle School grade levels. The student seeks to determine the side length of a square, knowing the perimeter is 26.46 inches.
To find the side length, we need to recall the formula for the perimeter of a square: P = 4s, where P represents the perimeter and s represents the length of a side. The student's square has a perimeter of 26.46 inches, so the equation would be 26.46 = 4s.
To isolate the value of s, we divide both sides of the equation by 4. This gives us: s = 26.46/4. Upon doing the division, we find that each side of the square is approximately 6.615 inches.
Learn more about Side Length of a Square here:https://brainly.com/question/24584437
#SPJ3
What percentage of 3000 is 330
Answer:
11
Step-by-step explanation:
how to round 254 to the nearest hundred
A salesperson's commission rate is 5 %. What is the commission from the sale of $ 44,000 worth of furnaces? Use pencil and paper. Suppose sales would double. What would be true about the commission? Explain without using any calculations.
a. The commission from the sale of $ 44,000 worth of furnaces is $1,800
b. Commission would double as well.
What is the percentage?A percentage is a minimum number or ratio that is measured by a fraction of 100.
We are given that salesperson's commission rate is 5 %
Then Commission paid on $36,000 worth of furnaces with a rate of 5% is:
= Amount of sales x commission rate
= 36,000 x 5%
= $1,800
If the sales were to double, the commission would be based on double the amount so it would double;
= 36,000 x 2
= $72,000
Commission = 72,000 x 5%
= $3,600
therefore Commission is doubled.
Learn more about percentages;
brainly.com/question/24159063
#SPJ3
The formula s= sa/6 gives the length of the side, s, of a cube with the surface area, sa. How much longer is the side of the cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters ?
Answer with explanation:
Side of cube = S
Surface Area of Cube = S.A
Relation between Side of a cube and surface area
[tex]S=\frac{S.A}{6}[/tex]
→If surface area of cube =180 Square meters
Side of cube (S)
[tex]S_{1}=\frac{180}{6}\\\\=30[/tex] meters
→ If surface area of cube =120 Square meters
Side of cube (S)
[tex]S_{2}=\frac{120}{6}\\\\=20[/tex] meters
[tex]S_{1}-S_{2}=30 -20=10\\\\S_{1}=S_{2}+10[/tex]
Side of cubic having surface area 180 square meters is greater by 10 meters, than a cube with the surface area of 120 square meters.
Carol ate 2/5 of the cake. Dima ate 3/5 of the REMAINING CAKE, mom ate the rest.
How many times more did Carol eat compared to Dima? PLEASE EXPLAIN, GIVING BRAINLIEST, PLEASE HELP.
Cody filled a container with 7 3/16 quarts of iced tea. how many 1/4 quart glasses can be served from the container
The table of values below represents a linear function and shows the height of a tree since it was transplanted. What was the height of the tree when it was transplanted?
The height of the tree when it was transplanted was:
4 feet
Step-by-step explanation:As we could observe that the given table represents a linear function.
The table is given as follows:
Year since it was 4 4.5 5
transplanted
Height (Feet) 12 13 14
We will find the linear function.
Let y denotes height and x denote year since it was transplanted.
We know that any linear function passing through two points (a,b) and (c,d) is given by:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
Here let (a,b)=(4,12) and (c,d)=(5,14)
Hence, the linear function is calculated as follows:
[tex]y-12=\dfrac{14-12}{5-4}\times (x-4)\\\\\\y-12=2(x-4)\\\\\\y-12=2x-8\\\\\\y=2x-8+12\\\\\\y=2x+4[/tex]
Now the height of tree when it was transplanted is the value of y when x=0
Hence, when x=0 we have:
y=4
Hence, the height was:
4 feet
How much pure acid should be mixed with 6 gallons of a 20% acid solution in order to get a 90% acid solution?
To get a 90% acid solution, you should mix 54 gallons of pure acid with the 6 gallons of the 20% acid solution.
Explanation:To solve this problem, we can use the formula for concentration:
Concentration = (Volume of pure acid) / (Total volume of solution)
Let x represent the volume of pure acid to be added. We know that the total volume of the solution after adding the pure acid is 6 gallons + x gallons. We also know that the concentration of the 20% acid solution is 0.2.
Using the formula, we can set up the equation:
0.9 = x / (6 + x)
Multiplying both sides of the equation by (6 + x), we get:
0.9(6 + x) = x
Simplifying the equation, we have:
5.4 + 0.9x = x
Subtracting 0.9x from both sides of the equation, we get:
5.4 = 0.1x
Dividing both sides of the equation by 0.1, we get:
54 = x
Therefore, you should mix 54 gallons of pure acid with the 6 gallons of the 20% acid solution to get a 90% acid solution.
Learn more about Calculating acid concentration here:https://brainly.com/question/29748394
#SPJ11
Find the area of the following circle. Use = 3.14
r = 5 yd.
Find the vertex of the parabola whose equation is y = x2 - 4x + 6.
Solve the system 2x-2y=10 4x-5y=17