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nlexa [21]
3 years ago
10

For which intervals the graphs of the functions f(x) = x^3 + x^2 - 4x - 4 is positive

Mathematics
1 answer:
Nookie1986 [14]3 years ago
5 0

Step-by-step explanation:

Consider a function

f

(

x

)

which is twice differentiable. The graph of such a function will be concave upwards in the intervals where the second derivative is positive and the graph will be concave downwards in the intervals where the second derivative is negative. To find these intervals we need to find the inflection points i.e. the x-values where the second derivative is 0.

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QUESTION 60 What is the mean of the following set of data? Round your answer to two decimal places. {25, 32, 16, 21, 30, 18, 37}
padilas [110]

Question 60:

The answer is B. 25.57.

Mean is calculated by adding up all the values of a data set, and then dividing that sum by the amount of values.

25, 32, 16, 21, 30, 18, 37=179

179÷7=25.57

Question 61:

The answer is A. 102.

Mode is the number in a data set that appears most often. 102 shows up twice, while the other values only appear once. So 102 is the mode.

3 0
3 years ago
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Simplify the equations:8(y-x)-2(x-y)<br> HELP ASAP!!
SVEN [57.7K]

Answer:

simplified equation is 10y-10x

Step-by-step explanation:

8(y-x) -2(x-y)

multiple 8 and 2 by the corresponding parentheses

8y-8x -2x +2y

10y -10x

5 0
3 years ago
Ben and Josh went to the roof of their 40-foot tall high school to throw their math books offthe edge.The initial velocity of Be
Taya2010 [7]

Answer

Josh's textbook reached the ground first

Josh's textbook reached the ground first by a difference of t=0.6482

Step-by-step explanation:

Before we proceed let us re write correctly the height equation which in correct form reads:

h(t)=-16t^2 +v_{o}t+s       Eqn(1).

Where:

h(t) : is the height range as a function of time

v_{o}   : is the initial velocity

s     : is the initial heightin feet and is given as 40 feet, thus Eqn(1). becomes:

h(t)=-16t^2 + v_{o}t + 40        Eqn(2).

Now let us use the given information and set up our equations for Ben and Josh.

<u>Ben:</u>

We know that v_{o}=60ft/s

Thus Eqn. (2) becomes:

h(t)=-16t^2+60t+40        Eqn.(3)

<u>Josh:</u>

We know that v_{o}=48ft/s

Thus Eqn. (2) becomes:

h(t)=-16t^2+48t+40       Eqn. (4).

<em><u>Now since we want to find whose textbook reaches the ground first and by how many seconds we need to solve each equation (i.e. Eqns. (3) and (4)) at </u></em>h(t)=0<em><u>. Now since both are quadratic equations we will solve one showing the full method which can be repeated for the other one. </u></em>

Thus we have for Ben, Eqn. (3) gives:

h(t)=0-16t^2+60t+40=0

Using the quadratic expression to find the roots of the quadratic we have:

t_{1,2}=\frac{-b+/-\sqrt{b^2-4ac} }{2a} \\t_{1,2}=\frac{-60+/-\sqrt{60^2-4(-16)(40)} }{2(-16)} \\t_{1,2}=\frac{-60+/-\sqrt{6160} }{-32} \\t_{1,2}=\frac{15+/-\sqrt{385} }{8}\\\\t_{1}=4.3276 sec\\t_{2}=-0.5776 sec

Since time can only be positive we reject the t_{2} solution and we keep that Ben's book took t=4.3276 seconds to reach the ground.

Similarly solving for Josh we obtain

t_{1}=3.6794sec\\t_{2}=-0.6794sec

Thus again we reject the negative and keep the positive solution, so Josh's book took t=3.6794 seconds to reach the ground.

Then we can find the difference between Ben and Josh times as

t_{Ben}-t_{Josh}= 4.3276 - 3.6794 = 0.6482

So to answer the original question:

<em>Whose textbook reaches the ground first and by how many seconds?</em>

  • Josh's textbook reached the ground first
  • Josh's textbook reached the ground first by a difference of t=0.6482

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How many repeating digits are in the smallest group of repeating digits in the decimal equivalent of 2/9
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Answer:

The answer is A.

Step-by-step explanation:

First, divide two by nine. The result is the decimal zero point two repeating.

Second, the digit that repeats is two. So, since two is one digit, the answer is A.

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3 years ago
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frosja888 [35]
98cm^2 - bigger triangles are 28 each, bottom one is 14. (28 x 3) + 14=98
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