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4 years ago

HELP PLZ

Mathematics

2 answers:

Alexxandr [17]4 years ago

7 0

Answer:

$x=\frac{-7-\sqrt{17}}{2}\textrm{ or }x=\frac{-7+\sqrt{17}}{2}$

Step-by-step explanation:

Given:

The equation is given as:

$x^2=-7x-8$

Rearrange the above equation in standard quadratic equation of the form $ax^2+bx+c=0$

Adding $7x + 8$ on both sides, we get

$x^2+7x+8=0$

Here, $a=1,b=7,c=8$

Now, we solve this using quadratic formula,

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\x=\frac{-7\pm \sqrt{7^2-4(1)(8)}}{2(1)}\\x=\frac{-7\pm \sqrt{49-32}}{2}\\x=\frac{-7\pm \sqrt{17}}{2}\\\\\\\therefore x=\frac{-7-\sqrt{17}}{2}\textrm{ or }x=\frac{-7+\sqrt{17}}{2}$

iVinArrow [24]4 years ago

3 0

Answer: option D.

Step-by-step explanation:got a 100 on it

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Consider F and C below. F(x, y, z) = 2xz + y2 i + 2xy j + x2 + 9z2 k C: x = t2, y = t + 3, z = 3t − 1, 0 ≤ t ≤ 1 (a) Find a func

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Answer:

a)∇f = 2y + 2x + 18z

b) $\int\limits^._C {F} \, dr$ =108

Step-by-step explanation:

Given:

f (x,y,z ) = $(2xz+ y^{2})i + (2xy) j +(x^{2} + 9z^{2})k$

The curve C :

$x=t^{2} ,\\y= t+3\\z= 3t-1$

where 0 ≤ t ≤ 1

Required:

(a) F = ∇f =? (F is a vector here)

(b) $\int\limits^._C {F} \, dr$ =?

Solution

First we will find the directional derivative F = ∇f

for that , we will use the formula :

∇f = $F_{x}i+ F_{y} j+F_{z}k$

Fx= δf/δx = δ/δx $(2xz+ y^{2})i$ = 2z i

Fy= δf/δy=δ/δy (2xy)j = 2x j

Fz= δf/δz=δ/δz $(x^{2} + 9z^{2})k$ = 18z k

∇f = (2z) i .i + (2x) j.j + (18z) k.k

∇f = 2z + 2x + 18z

<em>we will use line integral formula:</em>

$\int\limits^._C {F} \, dr$

to calculate dr, we will need the curve C:

r = x(t)+y(t)+z(t)

r= $(t^{2})i + (t+3) j +(3t-1) k$

$\frac{dr}{dt}=\frac{dx}{dt} +\frac{dy}{dt} + \frac{dz}{dt}$

$\frac{dx}{dt} = 2t$

$\frac{dy}{dt} = 1$

$\frac{dz}{dt} = 3$

$\int\limits^._C {F} \, dr$ = $\int\limits^1_0 {F_{x} } \, dx+ F_{y} dy +F_{z} dz$

= $\int\limits^1_0 {(2z(2t) + 2x(1) + 18z (3)} \, )$

put values of y, x and z

= $\int\limits^1_0 {2(3t-1) + 2(t^{2}) +18 (3) (3t-1)} \,$

= ${2t^{2} + 6t+162t -54-2}\, |^1_0$

= ${ 2t^{2}+ 168t - 56} \,|^1_0$ (Note : f(1)-f(0))

=2(1)+162(1)+2(0)+162(0)-56

= 2+162 -56

$\int\limits^._C {F} \, dr$ =108

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Step-by-step explanation:

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Each of a sample of four home mortgages is classified as fixed rate (F) or variable rate (V). (Enter your answers in set notatio

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Answer:

a) FFFF, FVFF, FFVF, FFFV,

FVFV, FFVV,FVVF,VVFF,

VFVF, VFFF,VFFV,FFVV

VVVV, VFVV, VVFV, VVVF

b) FVFF, FFVF, FFFV,VFFF

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d) FFFF, FVFF, FFVF, FFFV, VFFF

e) FFFF, FVFF, FFVF, FFFV ,VFFF, VVVV

Step-by-step explanation:

For this case we define some notation:

F= mortgage classified as fixed rate

V= mortgage classified as variable rate

We select a sample of 4 mortgages.

Part a

We have 2*2*2*2= 16 possible combinations defined below:

FFFF, FVFF, FFVF, FFFV,

FVFV, FFVV,FVVF,VVFF,

VFVF, VVFF,VFFV,FFVV

VVVV, VFVV, VVFV, VVVF

Part b

Which outcomes are in the event that exactly three of the selected mortgages are fixed rate

We need to see in the possible outcomes from part a) how many we have exactly three F's .If we analyze the possible options the possible combinations are:

FVFF, FFVF, FFFV, VFFF

Part c

Which outcomes are in the event that all four mortgages are of the same type?

For this case we have just two possible values: VVVV or FFFF

Part d

Which outcomes are in the event that at most one of the four is a variable rate mortgage?

We need to see in the possible outcomes from part a) how many have at least one V. After analyze we see that the possible values:

FFFF, FVFF, FFVF, FFFV, VFFF

Part e

The union represent all four mortgages are of the same type or outcomes are in the event that at most one of the four is a variable rate. So we are looking for the possible outcomes VVVV and FFFF and the outcomes with just one V ( FVFF, FFVF, FFFV ,VFFF) so then the union would be:

FFFF, FVFF, FFVF, FFFV ,VFFF, VVVV

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