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Gekata [30.6K]
2 years ago
10

Janet used the following steps to solve

Mathematics
1 answer:
saveliy_v [14]2 years ago
6 0

Answer:

Step 2

Step-by-step explanation:

Janet replaced 43 from 12 out of nowhere, and there is nothing in the problem indicating that 43 should be changed into 12.

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The graph of the continuous function g, the derivative of the function f, is shown above. The function g is piecewise linear for
4vir4ik [10]
A) g=f' is continuous, so f is also continuous. This means if we were to integrate g, the same constant of integration would apply across its entire domain. Over 0, we have g(x)=2x. This means that


f_{0


For f to be continuous, we need the limit as x\to1^- to match f(1)=3. This means we must have


\displaystyle\lim_{x\to1}x^2+C=1+C=3\implies C=2


Now, over x, we have g(x)=-3, so f_{x, which means f(-5)=17.


b) Integrating over [1, 3] is easy; it's just the area of a 2x2 square. So,


\displaystyle\int_1^6g(x)=4+\int_3^62(x-4)^2\,\mathrm dx=4+6=10


c) f is increasing when f'=g>0, and concave upward when f''=g'>0, i.e. when g is also increasing.

We have g>0 over the intervals 0 and x>4. We can additionally see that g'>0 only on 0 and x>4.


d) Inflection points occur when f''=g'=0, and at such a point, to either side the sign of the second derivative f''=g' changes. We see this happening at x=4, for which g'=0, and to the left of x=4 we have g decreasing, then increasing along the other side.


We also have g'=0 along the interval -1, but even if we were to allow an entire interval as a "site of inflection", we can see that g'>0 to either side, so concavity would not change.
5 0
2 years ago
A 10.5-gallon aquarium is 2/3 full. How many more gallons of water does it take to fill the aquarium?
Natasha_Volkova [10]
The answer is 3.5 gallons
7 0
3 years ago
Read 2 more answers
Which graph shows the points (–3, 5) and (4, –3) plotted correctly?
Nana76 [90]

Answer:

Step-by-step explanation:

This is clearly a linear relationship.  If Alex rented the movie for 0 days, he'd owe nothing.  If he paid $6 for a 3-day rental, the slope of this line would be m = rise / run = $6/(3 days) = $2/day, which is positive.

Then the equation for this graph is C(x) = ($2/day)x, where x is the number of days for which the movie is rented.

Using this formula, we find three particular points on the graph:

(1, $2), (2, $4), (3, ($6)

8 0
3 years ago
What is the sign of the product (3) × (−3) × (−2) × (4)?
Free_Kalibri [48]

Answer:

Positive, because the products (3) × (−3) and (−2) × (4) are negative and the product of two negative numbers is positive.

Step-by-step explanation:

Since 1 * -1 = -1, and -1 * -1 = 1, the product of opposite signs produces negative numbers while the product of same signs produces positive numbers. So the product of 1 * 1 * 1 * -1 = -1, while -1 * -1 * -1 * -1 = 1.

3 0
3 years ago
Silvia was growing some plants. She measured the height, in inches, of the plants and made thisline plot to show her data:
FromTheMoon [43]

Answer:

The answer is C.

Step-by-step explanation:

The equivalents to 1/4 are 2/8, 3/12, 4/16 etc. So the fractions after 1/4 are higher than 1/4. Then you count how many 'x's are in the columns for those measurements and you will get 6.

5 0
2 years ago
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