Assistance please... ln(5x - 6) + ln (x - 3) = ln 18?
Since there is a rule that. A*b= ln a + ln b, removing all the ln, we'll have. (5x-6)(x-3)=18 opening the bracket, we'll have: 5x^2-6x-15x+18=18 with the 18 on the RHS moving to the left, it changes sign from positive to negative. As in: 5x^2-6x-15x+18-18=0 simplifying: 5x^2-21x=0 with -21x moving to the RHS, it changes sign from negative to positive: 5x^2=21x x cancelling out x: 5x=21 x=21/5 x= 4 1/5
What is the value of x in X+2Y=102x?
Notice,[math]X+2Y=102x[/math][math]102x=X+2Y[/math][math]x=\frac{X+2Y}{102}[/math]
What is the formula for (a-b) ^7?
The Binomial Theorem states that [math](x+y)^n = \sum_{k=0}^n {n \choose k} x^{n - k} y^k[/math].Applying this to your question, you can work it out to obtain [math]a^7 - 7a^6b + 21a^5b^2 - 35a^4b^3 + 35a^3b^4 - 21a^2b^5 + 7ab^6 - b^7.[/math]
Which is bigger 2 to the power 1/2 or 3 to the power 1/3?
This question seems tough but its not, in such questions you just need to equate both the powers by taking LCM. So, LCM of 2 and 3 is 6.2^(1/2) can be written as 2^(3/6) => 2^3(1/6) => 8^(1/6) ————— (1)3^(1/3) can be written as 3^(2/6) => 3^2(1/6) => 9^(1/6)—————(2)from (1) and (2), we can conclude that 9>8 , so 9^(1/6) > 8^(1/6) .
A two digit number has 3 in its unit digit. The sum of its digits is one seventh of the number itself. What is the number?
Let digit in tens place = xAnd digit in ones place = 3The two digit number = x * 10 + 3 * 1 = 10x + 3Sum of the two digits (x + 3) = 1/7 of the numberThat isx + 3 = 1/7(10x + 3)x + 3 = (10x + 3)/77x + 21 = 10x + 33x = 18x = 6Thus the two digit number would be 63.To check1/7 of 63 = 9 (=6 + 3)
What is the derivative of f(x) =(x+3) (x-7) (x+5)?
What is the derivative of f(x) =(x+3) (x-7) (x+5)?METHOD 1: Expand the factors and then differentiate each termMETHOD 2: Instead of expanding the 3 factors, we could have used the differentiation product rule for the product of 3 functions:RegardsJames KUAAustralia > Qld > Brisbane: 2018 Feb 02 Fri 2322H
If 1+4=5, 2+5=12, and 3+6=21, how much is 5+8?
Notice that the difference between the number s before the results of each statement is 3.1+4=52+5=123+6=214+7=325+8=45The ‘=’ sign stands for ‘plus the number from the previous statement’ and and is available from 2+5=12, which actually means 2 + 5 + (1+4=5) = 12. Then:3+6 = 21, short for: 3 + 6 + (2+5=12) = 21;4+7 = 32, short for: 4 + 7 + (3+6=21) = 32;5+8 = 46, short for: 5 + 8 + (4+7=32) = 46;………and so on…..