The two numbers with a product equal to 192 such that their sum is minimized are:
A = √192 and B = √192
How to find the two numbers?
Let's define A and B as our two numbers, we know that their product must be equal to 192, then we have:
A*B = 192.
Now, the sum of these two numbers is:
A + B.
And we want to minimize this, to do it, we need to use the first equation to rewrite one variable in terms of the other. For example, if we isolate A, we get:
A = 192/B
Replacing this in the sum, we get:
192/B + B
To minimize this, we need to find the values of B that make 0 the differentiation of the above expression.
The differentiation is:
-192/B^2 + 1
Then we need to solve:
-192/B^2 + 1 = 0
192/B^2 = 1
192 = B^2
√192 = B
To get the value of A, we use:
A = 192/B = 192/√192 = √192
Then we can conclude that the two positive numbers such that their product is 192, and their sum is minimized, is:
A = √192 and B = √192.
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Factor out the largest possible term.
12x^5-4x^2+16x^3= ?
(Please include steps if you can)
Add 43.688 + 127.859?
HELP PLEASE! GIVING BRAINLIEST ANSWER. (TRIGONOMETRY)
What is the rate of change from x = 0 to x = pi over 2?
8 over pi
pi over 8
-8 over pi
-pi over 8
The correct option is A )[tex]\frac{8}{\pi }[/tex]
To find the rate of change of a function from x = 0 to x = \\frac{\\pi}{2}, we need to apply the concept of the average rate of change.
This is essentially the change in the function's value divided by the change in x. Assume the function we are analyzing is y = f(x).
Step-by-Step Solution:
Identify the interval: [tex][0, \frac{\pi}{2}].[/tex]Calculate the function values at the endpoints: f(0) and[tex]f{\frac{\pi}{2})[/tex].Calculate the average rate of change using the formula:Average Rate of Change =[tex]\frac{f(\frac{\pi}{2}) - f(0)}{\frac{\pi}{2} - 0}[/tex]
When x = 0, f( x ) = - 4,
When x = π / 2, f( x ) = 0
Average Rate of Change =[tex]\frac{0- (-4)}{\frac{\pi}{2} - 0}[/tex]
Average Rate of Change =[tex]\frac{8}{\pi }[/tex]
The correct option is A )[tex]\frac{8}{\pi }[/tex]
How long does it take to drive 160 miles at 70mph?
Final answer:
To calculate the travel time to drive 160 miles at 70mph, use the formula Time = Distance ÷ Speed. The result is approximately 2.2857 hours, or about 2 hours and 17 minutes.
Explanation:
To calculate how long it takes to drive 160 miles at a constant speed of 70 miles per hour (mph), you can use the basic formula for time, which is Time = Distance ÷ Speed.
Distance to be traveled is 160 miles.
Speed of travel is 70 mph.
By plugging the numbers into the formula, we get:
Time = 160 miles ÷ 70 mph = 2.2857 hours.
To convert this time into minutes, we multiply by 60 (the number of minutes in an hour), so:
2.2857 hours × 60 minutes/hour = 137.1428 minutes, which is approximately 2 hours and 17 minutes.
Find the complete perimeter of the sector that intercepts arc AC.
Round to the nearest hundredth.
In the triangle below, what ratio is cos θ?
Answer:
[tex]cos(theta)=\frac{5}{13}[/tex]
Ratio is 5:13
Step-by-step explanation:
We are given with right angle triangle with side lengths
cos theta ratio is adjacent side divide by hypotenuse
In the triangle , adjacent side for theta is 5 and hypotenuse is 13
[tex]cos(theta)=\frac{adjacent}{hypotenuse}[/tex]
[tex]cos(theta)=\frac{5}{13}[/tex]
Mario and Luigi want to purchase some extra controllers for their friends.each controller costs 29.99. Use an algebraic expression to describe how much they spend in total,before sales tax,based on purchasing the console(299.00)the number of games(59.99 each) and the number of extra controllers
Write the sum using summation notation, assuming the suggested pattern continues. -9 - 3 + 3 + 9 + ... + 81
Honestly I believe this is correct:
∑ 15 at the top, n =0 (-9+6n)
What conjecture can you make about the sum of the first 30 odd numbers
The sum of the first 30 odd numbers is equal to the square of 30. To find the sum, we can use a formula for the sum of an arithmetic series. Plugging in the values, we get a sum of 900.
Explanation:Conjecture: The sum of the first 30 odd numbers is equal to the square of the 30. To prove this conjecture, we can use a formula for the sum of an arithmetic series which is given by: S = n/2(2a + (n-1) d), where S is the sum of the series, n is the number of terms, a is the first term, and d is the common difference. In this case, the first term a is 1, the common difference d is 2 (since we are adding odd numbers), and the number of terms n is 30. Plugging in the values, we have: S = 30/2(2(1) + (30-1)2) = 15(2 + 58) = 900. Thus, the sum of the first 30 odd numbers is 900, which is equal to the square of 30.
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A hypothesis is only tentative: to make sure it's valid, you have to ___________.
Find the measure of the central angle with a radius of 18 inches and the area of a sector measuring 40.5π square inches.
The perimeter of a square is in p inches. Write expressions, in terms of p, for the length of the side of the square and the area of the square.
how to factor 6x^2+5x+1
I spent 20% of my weekly income on food. What was my weekly income if I spent $186 ?
If I spent $186. Then my weekly income will be $930.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred.
I spent 20% of my weekly income on food.
If I spent $186.
Then my weekly income will be
Let x my weekly income.
0.2x = $186
x = $930
More about the percentage link is given below.
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Which choices are real numbers? Check all that apply.
A. (-131072)^1/7
B. (-531441)^1/12
C. (-1024)^1/5
D. (-256)^1/8
The real numbers are:
A. [tex]\((-131072)^{1/7}\)[/tex]
C. [tex]\((-1024)^{1/5}\)[/tex]
These have odd roots, resulting in real numbers.
To determine which of the given expressions are real numbers, we need to check if the roots of negative numbers are defined within the set of real numbers.
A. [tex]\((-131072)^{1/7}\)[/tex]
The expression [tex]\((-131072)^{1/7}\)[/tex] is the 7th root of [tex]\(-131072\)[/tex]. Since 7 is an odd number, the 7th root of a negative number is defined and is a real number.
So, [tex]\((-131072)^{1/7}\)[/tex] is a real number.
B. [tex]\((-531441)^{1/12}\)[/tex]
The expression [tex]\((-531441)^{1/12}\)[/tex] is the 12th root of [tex]\(-531441\)[/tex]. Since 12 is an even number, the 12th root of a negative number is not defined within the set of real numbers.
So, [tex]\((-531441)^{1/12}\)[/tex] is not a real number.
C. [tex]\((-1024)^{1/5}\)[/tex]
The expression [tex]\((-1024)^{1/5}\)[/tex] is the 5th root of [tex]\(-1024\)[/tex]. Since 5 is an odd number, the 5th root of a negative number is defined and is a real number.
So, [tex]\((-1024)^{1/5}\)[/tex] is a real number.
D. [tex]\((-256)^{1/8}\)[/tex]
The expression [tex]\((-256)^{1/8}\)[/tex] is the 8th root of [tex]\(-256\)[/tex]. Since 8 is an even number, the 8th root of a negative number is not defined within the set of real numbers.
So, [tex]\((-256)^{1/8}\)[/tex] is not a real number.
Summary:
- A. [tex]\((-131072)^{1/7}\)[/tex] is a real number.
- B. [tex]\((-531441)^{1/12}\)[/tex] is not a real number.
- C. [tex]\((-1024)^{1/5}\)[/tex] is a real number.
- D. [tex]\((-256)^{1/8}\)[/tex] is not a real number.
There is a state soccer tournament with 128 teams competing for 1st place. Each week, half of the teams get eliminated. How many teams remain after 6 weeks?
A.
16
B.
8
C.
4
D.
2
State whether the given measurements determine zero, one, or two triangles. b = 84°, b = 28, c = 25
Solve log 1/100 = log(10^x+2)
A.) x= 0
B.) x= -2
C.) x= -4
D.) x= 4
Question 6 jessica drive 380 miles using 14 gallons of gas. at this rate, how many gallons of gas would she need to drive 418 miles
Help with geometry...
When a researcher needs to compare means for a variable grouped into two categories based on some less-than interval variable, an _ in appropriate?
When a researcher needs to compare means for a variable grouped into two
categories based on some less-than interval variable, a t-test is appropriate.
To add, The analysis of two populations means through the use of
statistical examination is called a t-test. Small sample sizes commonly
use a t-test with two
samples. What statisticians call as test statistics are
identified as t-values. A systematized value that is calculated from sample
data during a hypothesis test is called a test statistic. The procedure that
calculates the test statistic compares your data to what is expected under the null
hypothesis.
You already have an experience with the basic principles behind a t-test if you’ve
tried to communicated with a distracted teenager.
ΔZAP has coordinates Z (−1, 5), A (1, 3), and P (−2, 4). A translation maps point Z to Z' (1, 1). Find the coordinates of A' and P' under this translation.
To solve this problem, we should first identify the number of units that point Z was translated. The number of units of movement of point Z should be similar to the number of units of movement of points A and P.
Let us say that the movement is Δx and Δy for horizontal and vertical translations respectively.
From Z to Z’:
Δx = 1 – (-1) = 2
Δy = 1 - 5 = - 4
Therefore the translation is in the form of (x + 2 , y – 4). Points A and P then becomes:
A’ = (1 + 2 , 3 – 4)
A’ = (3, -1)
P’ = (-2 + 2, 4 – 4)
P’ = (0, 0)
Answers:
A’ = (3, -1)
P’ = (0, 0)
Answer:
Step-by-step explanation:
lets be honest whos reading this when theres an expert answer
A diner asked its customers, 'Did you cook dinner last night?' The results on the survey are shown in the table below: Male Female Cooked dinner 305 279 Did not cook dinner 152 459 What is the probability that one of the customers chosen from this survey was a female and cooked dinner? 0.23 0.38 0.47 0.61
Answer:
0.23
Step-by-step explanation:
Find AB if AP and HQ are altitudes and ΔABC ~ ΔHGI
Which equation illustrates the additive inverse property?Select one of the options below as your answer:A. c + d = d + cB. c × d = d × cC. -c + (-c) = 0D. d + (-d) = 0
What is the answer??
The graph of a linear equation may not be a straight line.
A. True
B. False
One eighth of the students in the seventh grade are in the school band there are fourty four students in the school band find the number of students in the seventh grade
0=2x+3(3x-4)-(-x+14)
Fraction answer need help!!!
Bob is driving along a straight and level road toward a mountain. At some point on his trip, he measures the angle of elevation to the top of the mountain and finds it to be 21°44'. Find the height of the mountain to the nearest foot if Bob is 13,428.7 feet from the center of the mountain at the base.
A. 5453 ft
B. 5353 ft
C. 53,534 ft
D. 535,342 ft
Answer:
Option B is the correct answer.
Step-by-step explanation:
The arrangement is given in the below figure.
We have height of the mountain = x
We also have
[tex]tan(21^044')=\frac{x}{13428.7}\\x=5352.98ft[/tex]
Height of the mountain to the nearest foot = 5353 ft
Option B is the correct answer.