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3 years ago

I will give brainliest to whoever gets it right

Mathematics

1 answer:

lorasvet [3.4K]3 years ago

7 0

Answer:

give me brainliest plz

Step-by-step explanation:

(a+d)/a = (a+4d)/(a+d)

d = 2a

so, (a+d)/a = 3

You might be interested in

The measure of the largest angle of a triangle is 80º more than the measure of the smallest angle, and the measure of the remain

Korolek [52]

L = S + 80
180 - L - S = S + 10 simplify: L = 180 - 2S - 10
L = 170 - 2S = S + 80
3S = 90
S = 30 L = 110 3rd angle = 40

4 0

3 years ago

For each vector field f⃗ (x,y,z), compute the curl of f⃗ and, if possible, find a function f(x,y,z) so that f⃗ =∇f. if no such f

butalik [34]

$\vec f(x,y,z)=(2yze^{2xyz}+4z^2\cos(xz^2))\,\vec\imath+2xze^{2xyz}\,\vec\jmath+(2xye^{2xyz}+8xz\cos(xz^2))\,\vec k$

Let

$\vec f=f_1\,\vec\imath+f_2\,\vec\jmath+f_3\,\vec k$

The curl is

$\nabla\cdot\vec f=(\partial_x\,\vec\imath+\partial_y\,\vec\jmath+\partial_z\,\vec k)\times(f_1\,\vec\imath+f_2\,\vec\jmath+f_3\,\vec k)$

where $\partial_\xi$ denotes the partial derivative operator with respect to $\xi$ . Recall that

$\vec\imath\times\vec\jmath=\vec k$

$\vec\jmath\times\vec k=\vec i$

$\vec k\times\vec\imath=\vec\jmath$

and that for any two vectors $\vec a$ and $\vec b$ , $\vec a\times\vec b=-\vec b\times\vec a$ , and $\vec a\times\vec a=\vec0$ .

The cross product reduces to

$\nabla\times\vec f=(\partial_yf_3-\partial_zf_2)\,\vec\imath+(\partial_xf_3-\partial_zf_1)\,\vec\jmath+(\partial_xf_2-\partial_yf_1)\,\vec k$

When you compute the partial derivatives, you'll find that all the components reduce to 0 and

$\nabla\times\vec f=\vec0$

which means $\vec f$ is indeed conservative and we can find $f$ .

Integrate both sides of

$\dfrac{\partial f}{\partial y}=2xze^{2xyz}$

with respect to $y$ and

$\implies f(x,y,z)=e^{2xyz}+g(x,z)$

Differentiate both sides with respect to $x$ and

$\dfrac{\partial f}{\partial x}=\dfrac{\partial(e^{2xyz})}{\partial x}+\dfrac{\partial g}{\partial x}$

$2yze^{2xyz}+4z^2\cos(xz^2)=2yze^{2xyz}+\dfrac{\partial g}{\partial x}$

$4z^2\cos(xz^2)=\dfrac{\partial g}{\partial x}$

$\implies g(x,z)=4\sin(xz^2)+h(z)$

Now

$f(x,y,z)=e^{2xyz}+4\sin(xz^2)+h(z)$

and differentiating with respect to $z$ gives

$\dfrac{\partial f}{\partial z}=\dfrac{\partial(e^{2xyz}+4\sin(xz^2))}{\partial z}+\dfrac{\mathrm dh}{\mathrm dz}$

$2xye^{2xyz}+8xz\cos(xz^2)=2xye^{2xyz}+8xz\cos(xz^2)+\dfrac{\mathrm dh}{\mathrm dz}$

$\dfrac{\mathrm dh}{\mathrm dz}=0$

$\implies h(z)=C$

for some constant $C$ . So

$f(x,y,z)=e^{2xyz}+4\sin(xz^2)+C$

3 0

4 years ago

Given the function f(x) = 4x^2 - 17, find f (h+2).

forsale [732]

Answer:

Step-by-step explanation:

Substitute x = h + 2 into f(x), that is

f(h + 2)

= 4(h + 2)² - 17 ← expand factor using FOIL

= 4(h² + 4h + 4) - 17 ← distribute parenthesis and simplify

= 4h² + 16h + 16 - 17

= 4h² + 16h - 1 → B

6 0

3 years ago

Read 2 more answers

2. What is the 50th term in the sequence t(n) = 2 + 8n?

kap26 [50]

Answer:

402?

2+ 8(50)?

not sure

Step-by-step explanation:

if so mark the brainliest!

3 0

3 years ago

♦HURRY PLEASE!!! ♦<br><br> ↓<br> Don't worry about the answer choice that is highlighted : )

tatiyna

Answer:

It's 3

Step-by-step explanation:

Bc it's placed before and it's multiplying the variable in the algebraic expression

4 0

3 years ago