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3 years ago

Add - (remember only like terms can be combined when add/subtract) (3x + 5) + (2x - 8)

Mathematics

1 answer:

Afina-wow [57]3 years ago

7 0

Answer:

5x-3

Step-by-step explanation:

(3x + 5) + (2x - 8)

3x+5+2x-8

Bringing the like terms together,

3x+2x+5-8

5x-3

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The function is given by the formula f(x)=3x+2.

Naily [24]

Answer:

(a) f(7) = 23

(b) x = 13/3

Step-by-step explanation:

Step 1: Define

f(x) = 3x + 2

(a) f(7) is x = 7

(b) f(x) = 15

Step 2: Substitute and Evaluate

(a) f(7) = 3(7) + 2

f(7) = 21 + 2

f(7) = 23

(b) 15 = 3x + 2

13 = 3x

x = 13/3

3 0

3 years ago

Consider F and C below. F(x, y, z) = y2 sin(z) i + 2xy sin(z) j + xy2 cos(z) k C: r(t) = t2 i + sin(t) j + t k, 0 ≤ t ≤ π (a) Fi

Liono4ka [1.6K]

Answer:

a) $f (x,y,z)= xy^2\sin(z)$

b) $\int_C F \cdot dr =0$

Step-by-step explanation:

Recall that given a function f(x,y,z) then $\nabla f = (\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z})$ . To find f, we will assume it exists and then we will find its form by integration.

First assume that F = $\nabla f$ . This implies that

$\frac{\partial f}{\partial x} = y^2\sin(z)$ if we integrate with respect to x we get that

$f(x,y,z) = xy^2\sin(z) + g(y,z)$ for some function g(y,z). If we take the derivative of this equation with respect to y, we get

$\frac{\partial f}{\partial y} = 2xy\sin(z) + \frac{\partial g}{\partial y}$

This must be equal to the second component of F. Then

$2xy\sin(z) + \frac{\partial g}{\partial y}=2xy\sin(z)$

This implies that $\frac{\partial g}{\partial y}=0$ , which means that g depends on z only. So $f(x,y,z) = xy^2\sin(z) + g(z)$

Taking the derivative with respect to z and making it equal to the third component of F, we get

$xy^2\cos(z)+\frac{dg}{dz} = xy^2\cos(z)$

which implies that $\frac{dg}{dz}=0$ which means that g(z) = K, where K is a constant. So

$f (x,y,z)= xy^2\sin(z)$

b) To evaluate $\int_C F \cdot dr$ we can evaluate it by using f. We can calculate the value of f at the initial and final point of C and the subtract them as follows.

$\int_C F \cdot dr = f(r(\pi))-f(r(0))$

Recall that $r(\pi) = (\pi^2, 0, \pi)$ so $f(r(\pi)) = \pi^2\cdot 0 \cdot \sin(\pi) = 0$

Also $r(0) = (0, 0, 0)$ so $f(r(0)) = 0^2\cdot 0 \cdot \sin(0) = 0$

So $\int_C F \cdot dr =0$

5 0

3 years ago

The value of y varies directly with x. When y=80, x=1/2. What is the value of y when x is 2 1/4?

spin [16.1K]

Using the formula y = kx
80 = .5k
k = 160
y = 160*2.25
y = 360

4 0

3 years ago

Which quantity is proportional to 90/2?

slamgirl [31]

Answer:

45/1

Step-by-step explanation:

90/2=45/1

45*2=90

6 0

3 years ago

Segment YZ has endpoints (6, 3) and (3, 9). Find the coordinates of the point that divides the line segment directed from Y to Z

fenix001 [56]

Answer:

(4, 7)

Step-by-step explanation:

The point of interest is ...

P = (2Z +1Y)/(2+1) = ((2·3+6)/3, (2·9+3)/3)

P = (4, 7)

The point that divides the segment into the ratio a:b is the weighted average of the endpoints, with the weights being "b" and "a". The weight of the first end point corresponds to the length of the far end of the segment.

8 0

3 years ago

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