The volume of the original cylinder is
... V = π·r²·h
For r=1 and h=1, this is
... V = π·1²·1 = π
For the new cylinder, the volume is 1.089 times that amount.
... V = 1.089π = π·1.1²·(1-k)
... 1.089/1.21 = 1-k
... k = 1 - 1.089/1.21 = 1 - 0.9 = 0.1 = 10%
The appropriate choice is (B) 10.
Answers:1)Tthe first answer is that as x increases the value of p(x) approaches a number that is greater than q (x).
2) the y-intercept of the function p is greater than the y-intercept of the function q.
Explanation:1) Value of the functions as x increases.Function p:
![p(x)= ( \frac{2}{5} )^{x} -3](https://tex.z-dn.net/?f=p%28x%29%3D%20%20%28%20%5Cfrac%7B2%7D%7B5%7D%20%29%5E%7Bx%7D%20-3)
As x increases, the value of the function is the limit when x → ∞.
Since [2/5] is less than 1,
the limit of [2/5]ˣ when x → ∞ is 0, and the limit of p(x) is 0 - 3 = -3.While in the graph you see that the function
q has a horizontal asymptote that shows that the
limit of q (x) when x → ∞ is - 4.Then, the first answer is that
as x increases the value of p(x) approaches a number that is greater than q (x).2) y - intercepts.i) To determine the y-intercept of the function p(x), just replace x = 0 in the equation:
p(x) = [ 2 / 5]⁰ - 3 = 1 - 3 = - 2ii) The y-intercept of q(x) is read in the
graph. It is - 3.
Then the answer is that
the y-intercept of the function p is greater than the y-intercept of the function q.
A quadratic equation is in the form of ax²+bx+c. The time at which the height of the ball is 16 feets is 0.717 seconds and 1.221 seconds.
<h3>What is a quadratic equation?</h3>
A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
The complete question is:
A ball is thrown from an initial height of 2 feet with an initial upward velocity of 31 ft/s. The ball's height h (in feet) after 7 seconds is given by the following, h=2+31t-16t². Find all values of t for which the ball's height is 16 feet. Round your answer(s) to the nearest hundredth.
The time at which the height of the ball is 16 feet can be found by,
h = 2 + 31t - 16t²
16 = 2 + 31t - 16t²
16 - 2 - 31t + 16t² = 0
16t² - 31t + 14 = 0
![t = \dfrac{-(-31)\pm \sqrt{(-31)^2-4(16)(14)}}{2(16)}\\\\](https://tex.z-dn.net/?f=t%20%3D%20%5Cdfrac%7B-%28-31%29%5Cpm%20%5Csqrt%7B%28-31%29%5E2-4%2816%29%2814%29%7D%7D%7B2%2816%29%7D%5C%5C%5C%5C)
t = 0.717 , 1.221
Hence, the time at which the height of the ball is 16 feets is 0.717 seconds and 1.221 seconds.
Learn more about Quadratic Equations:
brainly.com/question/2263981
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Answer:
400 meters
Step-by-step explanation:
We are told in the question that:
Jake runs the 100-meter dash in
track.
Erika runs a race 400% the distance of Jake's race.
Hence, the length of
Erika's race is calculated as:
400% × 100 - meter
= 4 × 100- meter
= 400 meters
Therefore, Erika's race was 400 meters long.