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3 years ago

Given that f(x) = x2 − 3x + 3 and g(x) = the quantity of x minus one, over four , solve for f(g(x)) when x = 5

Mathematics

1 answer:

weqwewe [10]3 years ago

6 0

Answer:

Step-by-step explanation:

To evaluate f(g(x)) when x = 5, evaluate g(5) then substitute the value obtained into f(x)

g(5) = $\frac{5-1}{4}$ = $\frac{4}{4}$ = 1, then

f(1) = 1² - 3(1) + 3 = 1 - 3 + 3 = 1

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Find the first partial derivatives of the function f(x,y,z)=4xsin(y−z)

Amanda [17]

Answer:

$f_x(x,y,z)=4\sin (y-z)$

$f_x(x,y,z)=4x\cos (y-z)$

$f_z(x,y,z)=-4x\cos (y-z)$

Step-by-step explanation:

The given function is

$f(x,y,z)=4x\sin (y-z)$

We need to find first partial derivatives of the function.

Differentiate partially w.r.t. x and y, z are constants.

$f_x(x,y,z)=4(1)\sin (y-z)$

$f_x(x,y,z)=4\sin (y-z)$

Differentiate partially w.r.t. y and x, z are constants.

$f_y(x,y,z)=4x\cos (y-z)\dfrac{\partial}{\partial y}(y-z)$

$f_y(x,y,z)=4x\cos (y-z)$

Differentiate partially w.r.t. z and x, y are constants.

$f_z(x,y,z)=4x\cos (y-z)\dfrac{\partial}{\partial z}(y-z)$

$f_z(x,y,z)=4x\cos (y-z)(-1)$

$f_z(x,y,z)=-4x\cos (y-z)$

Therefore, the first partial derivatives of the function are $f_x(x,y,z)=4\sin (y-z), f_x(x,y,z)=4x\cos (y-z)\text{ and }f_z(x,y,z)=-4x\cos (y-z)$ .

4 0

4 years ago

Rewrite using a single positive exponent. 3-6 -5

yarga [219]

Answer:

$1 \div {3}^{( 30)}$

Step-by-step explanation:

There are exponent rules I posted above that are being used here.

We have (3^-6)^-5

Since we have a power times a power, we multiply 6 and 5 to get -30. Look at the first example in the photo.

So, we're left with 3^-30.

If you look at the photo, there's a rule for negative exponents.

Take the inverse of the base number, so 3 in this case:

1 / 3

and then make the exponent positive after taking the inverse.

So, we should get 1 / 3^30

Hope this helps!

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2 years ago

PLS HELP a) -3*2-9 b) 2+ -4*-3

alekssr [168]

Answer:

hope this will help you...

Step-by-step explanation:

$a) - 3 \times 2 - 9 \\ solution \\ - 3 \times 2 - 9 \\ - 6 - 9 \\ - 15 \\ \\ b)2 + - 4 \times - 3 \\ solution \\ 2 + - 4 \times - 3 \\ 2 + 12 \\ 14$

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2 years ago

10, 12, 16, 18, 18,20, 20, 24, 28 what is the greatest variability?

Andrei [34K]

I think 28 i'm not sure

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3 years ago

Matt said 2x-7=2(x-7) has infinitley many solitions. is he correct? Justify Matts answer or show he is correct.

Flauer [41]

2x - 7 = 2x - 14
2x = 2x - 7.

Matt is incorrect, there are actually 0 correct answers to this equation.

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3 years ago