Evaluate limit as x approaches 0 sin^2x/(1-cosx).

Answers

Answer 1

Answer: $\lim_(x \to 0) (sin ^(2)x )/(1-cos x) = ( (0)/(0) )= \n = \lim_(x \to 0) (1-cos ^(2)x )/(1-cosx)= \n = \lim_(n \to 0) ((1+cosx)(1-cosx))/((1-cosx))= \n = \lim_(x \to 0) (1+cos x) =$
= 1 + cos 0 = 1 + 1 = 2

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How many strings of eight uppercase English letters are there if no letter can be repeated?

Answers

............................3................................

What are the next 2 terms in this sequence? -5,-2,1_,_,?

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The common difference is 3 so add three to 1 and to the answer you get

how do you find the volume to the nearest cubic in of a cone whose radius is 12 in and hieght is 15 inches

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You have to know the formula for the volume of a cone.
In high school, there's no other way.

Volume of a cone = (1 / 3) π (radius)² (height)

Volume = (1 / 3) π (12 inches)² (15 inches)

Volume = 720 π = 2,261.95 cubic inches

Rounded to the nearest cubic inch, that's 2,262 cubic inches.

$V \beta = (1)/(3) \pi r^(2)h \n V \beta = (1)/(3) \pi 12^(2) * 15 \n V \beta = 2160 * (1)/(3) \pi \n V \beta = 720 \pi$

A pair of jeans are originally priced at $30.00 jeans go on sale for 20% off, what is the difference between the sale price and the original cost?

Answers

Answer:

$ 6

Step-by-step explanation:

Discount = 20% of 30

$= (20)/(100)*30$

= 2 * 3

= $ 6

Difference between the sale price and the original cost = $ 6

A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y equals negative 0.04x squared plus 8.3x plus 4.3, where x is the horizontal distance, in meters, from the starting point on the roof and y is the height, in meters, of the rocket above the ground. How far horizontally from its starting point will the rocket land? Round your answer to the nearest hundredth meter. (1 point)
208.02 m
416.03 m
0.52 m
208.19 m

Answers

ok

y=-0.04x^2+8.3x+4.3
when the rocket reaches the ground (when height=0, ie when y=0), then the rocket will land, find the x coordinate

set y=0
0=-0.04x^2+8.3x+4.3
use quadratic formula
if you have ax^2+bx+c=0, then
x= $\frac{-b+/- \sqrt{b^(2)-4ac} }{2a}$
a=-0.04
b=8.3
c=4.3
x= $\frac{-8.3+/- \sqrt{8.3^(2)-4(-0.04)(8.3)} }{2(-0.04)}$
x=208.017 or -0.516785
xrepresents horizontal distance
you cannot have a negative horizontal distance unless you fired and theh wind blew it backwards
therefor x=280.017 is the answer
208.02 m

The range of which function is (2,infinity)?y = 2x?
y = 2(5x)?
y = 5x +2?
y = 5x + 2?

Answers

For a function: y = 5^x
range is ( 0 , + ∞ )
And we have: y = 5^x + 2 , which is translated 2 units up.
So the range is ( 2, + ∞ ) or ( 2, infinity ).
Answer:
D ) y = 5^x + 2

The exponential function that has range of (2, infinity) is given by:

$y = 5^x + 2$