Answer:
x = 30
Step-by-step explanation:
x + 2x + 3x = 180
<u>6x</u> = <u>180</u>
6 6
x = 30
Step-by-step explanation:
let's look at the last line :
x³ + 8x - 3 = Ax³ +5Ax + Bx² + 5B + Cx + D
since we find A, B, C, and D by simply comparing the factors of the various terms in x (or constants) in both sides of the equation, we need to combine a few terms on the right hand side (so that we have one term per x exponent grade).
x³ + 8x - 3 = Ax³ + (5A + C)x + Bx² + (5B + D)
by comparing now both sides, to make both sides truly equal, the factors have to be equal.
A = 1 (the same as for x³ on the left hand side).
B = 0 (a we have no x² on the left side).
5A + C = 8 (a 8 is the factor of x in the left side).
5×1 + C = 8
5 + C = 8
C = 3
5B + D = -3 (as the constant term is -3 on the left side).
5×0 + D = -3
D = -3
so, the 4th answer option is correct.
For #11, the answer is the tall sipper thing. The formula for area in a cylinder is r squared times height. you did diameter squared, not radius squared
The derivative of the given function is f'(x) = k f(x) where 
.
<h3>What is the derivative of a function?</h3>
Let f be a function defined on a neighborhood of a real number a. Then f is said to be differentiable or derivable at 'a' if 
exists finitely. The limit is called the derivative or differential coefficient of f at 'a'. It is denoted by f'(a).
If f is differentiable at 'a', then
<h3>Calculation:</h3>
The given properties are:
(i) f(x + y) = f(x)f(y) for all real numbers x and y.
(ii) 
= k; where k is a nonzero real number.
Then, the derivative of the function f(x) is,
f'(x) = 
From property (i), f(x + h) = f(x)f(h)
On substituting,
f'(x) = 
= ![\lim_{h \to 0} \frac{f(x)[f(h) - 1]}{h}](https://tex.z-dn.net/?f=%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7Bf%28x%29%5Bf%28h%29%20-%201%5D%7D%7Bh%7D)
From property (ii), = k;
f'(x) =
= f(x).
= f(x). k
= kf(x)
Therefore, f'(x) = k f(x); where f'(x) exists for all real numbers of x.
Learn more about the derivative of a function here:
brainly.com/question/5313449
#SPJ9
Answer:
2/3
Step-by-step explanation:
given :
fraction of students that take English = 4/5 of all students
fraction of students that take composition
= 5/6 of the students that take English
= 5/6 of (4/5 of all students)
= 5/6 x 4/5
= (5 x 4) / (6 x 5)
= 20/30
= 2/3
