If f(x)=x-1/3and g(x)=3x+1, what is (f o g)(x)?
3x + 1
x – 3
3x
x

Answers

Answer 1

Answer: (f o g) means f(g(x))
f(g(x)) means put g(x) for x in f(x)
f(g(x))=(3x+1)-1/3
simplified
f(g(x))=3x+2 and 2/3

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A rectangle with an area of 24 square units has length x+1 and width 4x-6. find the value of x.

Answers

$area = length \cdot width \n \nA = 24 s^2 \n \n l=x+1 , \ \ w=4x-6 \n \n A=lw\n \n24 =(x+1)(4x-6)$

$24 =4x^2-6x+4x-6 \n \n4x^2-6x+4x-6 -24=0\n \n4x^2-2x-30=0 \ \ / :2\n \n2x^2-x-15=0 \n \na=2, \ b=-1 , c= -15$

$\Delta =b^2-4ac = (-1)^2 -4\cdot2\cdot (-15) = 1+120=121\n \nx_(1)=(-b-√(\Delta) )/(2a)=(1-√(121))/(2*2 )=( 1-11)/(4)=(-10)/(4)=- (5)/(2) \n \nx_(2)=(-b+√(\Delta) )/(2a)=(1+√(121))/(2*2 )=( 1+11)/(4)=(12)/(4)=3 \n \nUse \ positive \ value \ of \ x : \n \n x =3$

whats the lateral area of a right circular cone if the diameter of the base is 4m and the slant height of the cone is 15m? round your anwser the the nearest whole number.

Answers

Answer:

94 m ^2

Step-by-step explanation:

Answer for Penn

Answer:

94 m²

Step-by-step explanation:

The lateral area of a right circular cone if the diameter of the base is 4m and the slant height of the cone is 15m. Solution: Lateral Area = pi*r ( h²+r²) r = 4/2 r = 2 meters Lateral Area = 3.14*2 ( 15²+2²) Lateral Area = 94 m²

Identify each expression that represents the slope of a tangent to the curve y= -x^3+17x^2-x+3 at any point (x,y).

Answers

This is seriously so long I'm not sure it will even fit on a single line. The formula for the derivative using the limiting process is $\lim_(h \to 0) (f(x+h)-f(x))/(h)$ . And of course this is a problem because if h approaches 0, we would have a 0 in the denominator of that fraction and that is definitely not allowed! Every x in the function will be replaced with (x+h) to give us this: $\lim_(h \to 0) (-(x+h)^3+17(x+h)^2-(x+h)+3)/(h)$ . When we expand that we will get this very long numerator (I'm purposely leaving out the limit as h approaches 0 part to save space): $(-(x^3+2x^2h+xh^2+x^2h+2xh^2+h^3)+17x^2+34xh+17h^2-x-h+3-(-x^3+17x^2-x+3))/(h)$ . Simplifying that leaves us with this: $(-x^3-2x^2h-xh^2-x^2h-2xh^2-h^3+17x^2+34xh+17h^2-x-h+3+x^3-17x^2+x-3)/(h)$ . We have a lot of terms that cancel each other out so when we do that we are left with $\lim_(h \to 0) (-3x^2h-3xh^2-h^3+34xh+17h^2-h)/(h)$ . That is one of your choices for answers, the third one down on the left to be specific. Now we can factor out an h: $\lim_(h \to 0) (h(-3x^2-3xh-h^2+34x+17h-1))/(h)$ . That h on the top outside the parenthesis cancels with the h on the bottom. Now, as h approaches 0 we have no problems! Yay! That means when we now replace h with 0, we have this: $-3x^2-0-0+34x+0-1$ , or simplified we have $-3x^2+34x-1$ which is also a choice for your answers, top one on the right. Those are your 2 answers for that dertivative. It's much simpler when you learn the rules!

Of the following numbers, which one is prime: 32, 42, 29, 15?

Answers

The answer is 29 I think

29 because 1*29........................

Maria bought several post stamps and paid one dollar. There are stamps costing five cents, two cents, and one cent in the post office. She bought 10 times as many one-cent stamps as two-cent stamps, while the rest of the stamps she bought were five-cent stamps. How many one-cent stamps did Maria buy?