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3 years ago

Question 1

Mathematics

2 answers:

zimovet [89]3 years ago

5 0

The point of intersection of given two lines is (0,-3).

Step-by-step explanation:

Given,

Two equations are

2x-3y = 9 ------eq 1

-3x+2y = -6 ---- eq 2

To find the point if intersection of these to lines that is to find the value of x and y

Now,

6x-9y = 27 ------ eq1 ×3

-6x+4y = -12 ------ eq 2 × 2

Adding these two equations we get,

(6x-9y)+(-6x+4y) = 27+(-12)

or, -5y = 15

or, y = -3

Putting the value of y in eq 1 we get,

2x = 9 + 3×(-3)

or, 2x = 0

or, x = 0

Hence the point of intersection is (0,-3)

storchak [24]3 years ago

4 0

Answer:

(0,-3)

Step-by-step explanation:

To find the point of intersection for the two lines, we solve the two equations simultaneously

$x=0, y=-3$ $x=0 y=-3$

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Vlad1618 [11]

Answer:

that is the correct answer

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2 years ago

Consider a rabbit population P(t) satisfying the logistic equation StartFraction dP Over dt EndFraction equals aP minus bP squa

maria [59]

Solution:

Given :

$\frac{dP}{dt}= aP-bP^2$ .............(1)

where, B = aP = birth rate

D = $bP^2$ = death rate

Now initial population at t = 0, we have

$P_0$ = 220 , $B_0$ = 9 , $D_0$ = 15

Now equation (1) can be written as :

$\frac{dP}{dt}=P(a-bP)$

$\frac{dP}{dt}=bP(\frac{a}{b}-P)$ .................(2)

Now this equation is similar to the logistic differential equation which is ,

$\frac{dP}{dt}=kP(M-P)$

where M = limiting population / carrying capacity

This gives us M = a/b

Now we can find the value of a and b at t=0 and substitute for M

$a_0=\frac{B_0}{P_0}$ and $b_0=\frac{D_0}{P_0^2}$

So, $M=\frac{B_0P_0}{D_0}$

= $\frac{9 \times 220}{15}$

= 132

Now from equation (2), we get the constants

k = b = $\frac{D_0}{P_0^2} = \frac{15}{220^2}$

= $\frac{3}{9680}$

The population P(t) from logistic equation is calculated by :

$P(t)= \frac{MP_0}{P_0+(M-P_0)e^{-kMt}}$

$P(t)= \frac{132 \times 220}{220+(132-220)e^{-\frac{3}{9680} \times132t}}$

$P(t)= \frac{29040}{220-88e^{-\frac{396}{9680} t}}$

As per question, P(t) = 110% of M

$\frac{110}{100} \times 132= \frac{29040}{220-88e^{\frac{-396}{9680} t}}$

$220-88e^{\frac{-99}{2420} t}=200$

$e^{\frac{-99}{2420} t}=\frac{5}{22}$

Now taking natural logs on both the sides we get

t = 36.216

Number of months = 36.216

8 0

3 years ago

Find the distance between the points (-8, -2) and (6,-1). Round your answer to the nearest hundredth.

vitfil [10]

Answer:

distance is 14.04

Step-by-step explanation:

the distance between 2 points is the Hypotenuse of the right angled triangle of the x and y coordinate differences.

we use Pythagoras

c² = a² + b²

c = the Hypotenuse (the side of the triangle opposite to the 90 degree angle).

the x difference

-8 - 6 = -14

the y difference

-2 - -1 = -1

c² = -14² + -1² = 196 + 1 = 197

c = sqrt(197) = 14.04

7 0

2 years ago

In triangles △ABC and △DEF,

wel

Answer:

BC = 4.8
ED = 1.1
DF = 1.6

Step-by-step explanation:

Since angles A and E correspond, as well as angles C and F, we can say ...

ΔABC ~ ΔEDF

Then the ratio of side lengths of ΔABC to those of ΔEDF is ...

AC/EF = 6/2 = 3

That means ...

ED/AB = 1/3

ED = AB·(1/3) = 3.3·(1/3) = 1.1

For the remaining sides, we have the relation

3·DF = BC

3·(BC -3.2) = BC

2BC - 9.6 = 0 . . . eliminate parentheses, subtract length BC

BC -4.8 = 0 . . . . . divide by 2

BC = 4.8 . . . . . . . . add 4.8

DF = BC·(1/3) = 1.6

The unknown side lengths are BC = 4.8, DE = 1.1, DF = 1.6.

7 0

3 years ago

Find the product of A and B: A= -8+4i, B= 2-5i

Scrat [10]

A= -8 + 4i
-8 - 4i

B= 2 - 5i
2 + 5i

I hope this is correct, these ones are confusing.

4 0

3 years ago