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natali 33 [55]
3 years ago
7

Help needed for this question.

Mathematics
1 answer:
alukav5142 [94]3 years ago
8 0

Try this option:

1) for the given function 'f': the the axis of its symmetry is x= -2;

2) for the function 'g':

g(x)=4x²-16x+12; ⇔ g(x)=4(x²-4x+3); ⇔ g(x)=4(x-1)(x-3).

It means the axis of its symmetry is x=2.

Answer: -2 and 2

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Let F⃗ =2(x+y)i⃗ +8sin(y)j⃗ .
Alik [6]

Answer:

-42

Step-by-step explanation:

The objective is to find the line integral of F around the perimeter of the rectangle with corners (4,0), (4,3), (−3,3), (−3,0), traversed in that order.

We will use <em>the Green's Theorem </em>to evaluate this integral. The rectangle is presented below.

We have that

           F(x,y) = 2(x+y)i + 8j \sin y = \langle 2(x+y), 8\sin y \rangle

Therefore,

                  P(x,y) = 2(x+y) \quad \wedge \quad Q(x,y) = 8\sin y

Let's calculate the needed partial derivatives.

                              P_y = \frac{\partial P}{\partial y} (x,y) = (2(x+y))'_y = 2\\Q_x =\frac{\partial Q}{\partial x} (x,y) = (8\sin y)'_x = 0

Thus,

                                    Q_x -P_y = 0 -2 = - 2

Now, by the Green's theorem, we have

\oint_C F \,dr = \iint_D (Q_x-P_y)\,dA = \int \limits_{-3}^{4} \int \limits_{0}^{3} (-2)\,dy\, dx \\ \\\phantom{\oint_C F \,dr = \iint_D (Q_x-P_y)\,dA}= \int \limits_{-3}^{4} (-2y) \Big|_{0}^{3} \; dx\\ \phantom{\oint_C F \,dr = \iint_D (Q_x-P_y)\,dA}= \int \limits_{-3}^{4} (-6)\; dx = -6x  \Big|_{-3}^{4} = -42

4 0
3 years ago
Anyone know the right answer? I need to finish this before tomorrow
neonofarm [45]
A) 6.50 or 6.5
b) 0.26
3 0
3 years ago
I have 8 pennies and some quarters, nickels, and dimes. The number of pennies plus nickels equals the number of dimes. I have 3
Darina [25.2K]

There are five nickels.

Let <em>w</em> = the number of pennies; <em>x</em> = the number of nickels; <em>y</em> = the number of dimes; <em>z </em>= the number of quarters.

Then, we have three equations with four unknowns:

(1) <em>w</em> + <em>x = y </em>

(2) 3<em>w</em> = 2<em>z</em>

(3) 2<em>y</em> = 3<em>z</em>

However, there is a fourth <em>unstated </em>condition: <em>w</em>, <em>x</em>, y, and <em>z</em> must all be integers.

Assume that z = 6 (to avoid fractions).

From Equation (2), w = 4.

From Equation (3), y = 9.

Insert the values for <em>w</em> and <em>y</em> into equation (1).

4 + <em>x</em> = 9

x = 9 – 4 = 5

Thus, there are 4 pennies, 5 nickels, 9 dimes, and 6 quarters.

<em>Check</em>: 4 pennies + 5 nickels = 9 dimes

6 quarters + 4 pennies = 3 quarters for every 2 pennies

9 dimes + 6 quarters = 3 dimes for every 2 quarters

5 0
3 years ago
Read 2 more answers
Solve for n.<br> Q=5n+5z
kirill115 [55]
q=5n+5z\ \ \ \ \ \ \ |subract\ 5z\\\\q-5z=5n\ \ \ \ \ \ \ |divide\ by\ 5\\\\n=\frac{q-5z}{5}\\\\Answer\ is\ n=\frac{q-5z}{5}
5 0
3 years ago
Read 2 more answers
Triangle- interior angle<br> Please help !
sp2606 [1]

Answer:

x = 25

<B = 120 degrees

<C = 30 degrees

Step-by-step explanation:

Total angle measure of a triangle - 180 degrees

Add all the angles together to find the value of x

30 + 4x + 20 + x + 5 = 180

55 + 5x = 180

55 - 55 + 5x = 180 - 55

5x = 125

\frac{5x}{5} = \frac{125}{5}

x = 25

<B = 4(25) + 20

<B = 100 + 20

<B = 120

<C = 25 + 5

<C = 30

7 0
3 years ago
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