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lesya [120]
4 years ago
12

What's a quantity represented by a 3x - 4 is subtracted for the quantity 5x - 7 what is the result

Mathematics
1 answer:
DanielleElmas [232]4 years ago
5 0
(5x - 7) - (3x - 4) = 2x + 3
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2. Find the stationary points for the function
vovikov84 [41]

Answer & step-by-step explanation:

Stationary points are the points where the first derivative is equal to zero.

Let's calculate it using the power rule (exponent comes forward, decrease exponent by 1) and the fact that the derivative is a linear operation (that is D[a\ f(x) + b\ g(x)] = a Df(x) + b Dg(x))

The first derivative is then

y' = \frac13 (3x^2) - \frac12 (2x) -6 = x^2-x-6 = (x+2)(x-3)

Note that the last passage is not strictly needed, but it's really helpful to find stationary points, when in this next passage we set it equal to zero. Alternatively, you can use the quadratic formula if you can pull the factors out of your head right away.

y'=0 \rightarrow (x+2)(x-3) = 0 \implies x=-2  || x=3

These two point could be maxima, minima, or inflection points. To check them you can either see how the sign of the first derivative goes, or check the sign of the second derivative, as you're required.

The rules states that if the second derivative evaluated in that point is negative we have a maximum, if it's positive we have a minimum, and if we have a zero we keep derivating until we get a non-zero  value.

In our case, the second derivative we get by calculating the derivative again and we get y'' = 2x-1 . Evaluating it at both points we get

y''(-2) = 2(-2)-1 = -5\\y''(3) = 2(3) -1 = 5

so -2 is a maximum and 3 is a minimum.

5 0
2 years ago
Read 2 more answers
Select the correct answer. . Which value of x makes this equation true? -12x - 2(x + 9) = 5(x + 4) ОА. 13/19 OB. -1/3 OC. -2 OD.
Naya [18.7K]

Answer:

B -1/3

Step-by-step explanation:

4 0
3 years ago
One batch of walnut muffins use 1 1/3 cups of walnuts.How many cups of walnuts are needed to 3 3/4 batches of muffins
Ede4ka [16]
All you have to do is since one batch needs 1 1/3 cup of walnuts multiply 1 1/3 to 3 3/4 = 3 1/4 cups
5 0
3 years ago
Read 2 more answers
6 men can complete a job in 20 days.if the men work at the same rate.how many more are needed to complete the job in 12 days
Vlada [557]
The answer is 5 days. I hope that helped.
6 0
4 years ago
A group of college students built a self-guided rover and tested it on a plane surface. They programmed the vehicle to move alon
makkiz [27]

Answer:

B. 40 meters

Step-by-step explanation:

— Estimating

The rectangle enclosing the path has sides of length 9 m and 14 m, so its perimeter is 2(9+14) = 46 m. The distance covered will be shorter than that.

The distance from A to C is longer than the distance from D to C, so we know the distance will be longer than 2·14+9 = 37 m.

Only one answer choice fits in the range 37 < d < 46.

____

— Detailed calculation

The distance from B to C is the hypotenuse of a right triangle with sides 9 and 12. You will recognize that these side lengths are 3 times the side lengths of a 3-4-5 right triangle, so the hypotenuse distance is 3·5 = 15 meters.

The circuit length is ...

AB +BC +CD +DA = 2 + 15 + 14 + 9 = 40 . . . . meters

4 0
3 years ago
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