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4 years ago

A table of values of a linear function is shown below. Find the output when the input is n

Mathematics

1 answer:

lesya692 [45]4 years ago

5 0

y = 6 - n

Step-by-step explanation:

Step 1 :

Given ,

input: 1, 2, 3, 4 ,5 Output: 5, 4, 3, 2, 1

Let y = m x + c be the linear function

Step 2 :

When we take the input as 1, the output is 5, and when input is 2 the output is 4

so we have x,y as (1,5) and (2,4)

Hence substituting this in the linear function we get,

5 = m (1) + c and 4 = m (2) + c

=> m + c = 5 and 2 m + c = 4

Step 3 :

Solving for m and c with these 2 equations , we have

m = -1 and c = 6

so we have the equation as y= (-1) x + 6

When the input is n, x = n

so output is y = (-1) n + 6

y = 6 - n

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Calculate the flux of the vector field F⃗ (x,y,z)=(exy+9z+4)i⃗ +(exy+4z+9)j⃗ +(9z+exy)k⃗ through the square of side length 3 wit

ikadub [295]

The square (call it $S$ ) has one vertex at the origin (0, 0, 0) and one edge on the y-axis, which tells us another vertex is (0, 3, 0). The normal vector to the plane is $\vec n=\vec\imath-\vec k$ , which is enough information to figure out the equation of the plane containing $S$ :

$(x\,\vec\imath+y\,\vec\jmath+z\,\vec k)\cdot(\vec\imath-\vec k)=0\implies x-z=0\implies z=x$

We can parameterize this surface by

$\vec s(x,y)=x\,\vec\imath+y\,\vec\jmath+x\,\vec k$

for $0\le x\le\frac3{\sqrt2}$ and $0\le y\le3$ . Then the flux of $\vec F$ , assumed to be

$\vec F(x,y,z)=(e^{xy}+9z+4)\,\vec\imath+(e^{xy}+4z+9)\,\vec\jmath+(9ze^{xy})\,\vec k$ ,

$\displaystyle\iint_S\vec F(x,y,z)\cdot\mathrm d\vec S=\iint_S\vec F(\vec s(x,y))\cdot\vec n\,\mathrm dx\,\mathrm dy$

$=\displaystyle\int_0^3\int_0^{3/\sqrt2}\left((4+e^{xy}+9x)\,\vec\imath+(9+e^{xy}+4x)\,\vec\jmath+(e^{xy}+9x)\,\vec k\right)\cdot(\vec\imath-\vec k)\,\mathrm dx\,\mathrm dy$

$=\displaystyle\int_0^3\int_0^{3/\sqrt2}4\,\mathrm dx\,\mathrm dy=\boxed{18\sqrt2}$

3 0

3 years ago

Brad wants to buy flowers for his friend with $15. The daisies are $1 each and the roses are $3 each. He buys 3 more daisies tha

melisa1 [442]

D + 3r = 15
d = r + 3

r + 3 + 3r = 15
4r + 3 = 15
4r = 15 - 3
4r = 12
r = 12/4
r = 3 ....he bought 3 roses, at $ 3 per rose = $ 9 <==

d = r + 3
d = 3 + 3
d = 6....he bought 6 daisies, at $ 1 per daisy = $ 6

6 0

3 years ago

Read 2 more answers

Need answer ASAP will give BRAINLEST <br><br> Please put a full answer thank you

Novosadov [1.4K]

Answer:
1. It means they saved $125 in 10 months
2. y = 25/2

5 0

2 years ago

PLEASSSEEEE HELLLLP MEEEE!

Vanyuwa [196]

Answer:

1) C = 3

2) B = 5

3) C = 8

Step-by-step explanation:

Question 1)

We have:

$(2x+3)(4x-1)$

Distribute:

$=(2x+3)(4x)+(2x+3)(-1)$

Distribute:

$=8x^2+12x-2x-3$

Combine like terms:

$=8x^2+10x-(3)$

Therefore, C = 3.

Question 2)

We have:

$(x+2) (2x^2+x-1)$

Distribute:

$\displaystyle =(x+2)(2x^2)+(x+2)(x)+(x+2)( - 1)$

Distribute:

$=(2x^3+4x^2)+(x^2+2x)+(-x -2)$

Combine like terms:

$=2x^3+(5)x^2+x-2$

Therefore, B = 5.

Question 3)

We have:

$(x+2)(x^2-3x-2)$

Distribute:

$=(x+2)(x^2)+(x+2)(-3x)+(x+2)(-2)$

Distribute:

$=(x^3+2x^2)+(-3x^2-6x)+(-2x-4)$

Combine like terms:

$=x^3-x^2-(8)x-4$

So, C = 8.

6 0

2 years ago

Work out the area of this semi circle

kirill [66]

Answer:

39.27

Step-by-step explanation:

The area of a semi-circle is pi times the radius squared divided by 2. So basically standard area of a circle formula (pi times the radius squared) but then you add in the extra step of dividing it by 2.

The formula looks like this:

π × r² ÷ 2

The radius is half the diameter of the circle. So basically think of it as a line to the middle of the circle. Our diameter is 10, (the diameter is the entire length of the circle. It gives us this already. If you need diameter and only have the radius add the radius together twice or multiply it by 2 to get the diameter. Fun fact..?)

and it tells us to substitute pi for 3.142.

So, plugging our numbers in we get:

3.142 x 5^2 ÷ 2 = 39.275.

Cut out the 3rd decimal place (5) as it tells us to only include the first 2 decimal places, and we finally end up with 39.27.

<u>Hope this helps and have a nice day!</u>

5 0

2 years ago