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4 years ago

How do i solve this system of equations

Mathematics

2 answers:

WITCHER [35]4 years ago

8 0

22, i think because 3 times 3= 9, and 9 times 3 minus 5= 22

3241004551 [841]4 years ago

8 0

I Hope This Helps. You Only Need 2 x Answers Because Of x^2

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A large tank is partially filled with 100 gallons of fluid in which 20 pounds of salt is dissolved. Brine containing 1 2 pound o

sertanlavr [38]

Answer:

Step-by-step explanation:

From the given information:

$R_{in} = ( \dfrac{1}{2} \ lb/gal) (6)\ gal /min \\ \\R_{in} = 3 \ lb/min$

Given that the solution is pumped at a slower rate of 4gal/min

Then:

$R_{out} = \dfrac{4A}{100+(6-4)t}$

$R_{out}= \dfrac{2A}{50+t}$

The differential equation can be expressed as:

$\dfrac{dA}{dt}+ \dfrac{2}{50+t}A = 3 \ \ \ ... (1)$

Integrating the linear differential equation; we have::

$\int_c \dfrac{2}{50 +t}dt = e^{2In |50+t|$

$\int_c \dfrac{2}{50 +t}dt = (50+t)^2$

multiplying above integrating factor fields; we have:

$(50 +t)^2 \dfrac{dA}{dt} + 2 (50 + t)A = 3 (50 +t)^2$

$\dfrac{d}{dt}\bigg [ (50 +t)^2 A \bigg ] = 3 (50 +t)^2$

$(50 + t)^2 A = (50 + t)^3+c$

A = (50 + t) + c(50 + t)²

Using the given conditions:

A(0) = 20

⇒ 20 = 50 + c (50)⁻²

-30 = c(50) ⁻²

c = -30 × 2500

c = -75000

A = (50+t) - 75000(50 + t)⁻²

The no. of pounds of salt in the tank after 35 minutes is:

A(35) = (50 + 35) - 75000(50 + 35)⁻²

A(35) = 85 - $\dfrac{75000}{7225}$

A(35) =69.6193 pounds

A(35) $\simeq$ 70 pounds

Thus; the number of pounds of salt in the tank after 35 minutes is 70 pounds.

6 0

3 years ago

The sum of two numbers is 44. The second number is 4 less than three times the first number. Let x represent the first number an

MakcuM [25]

Answer:

$y = 4minus3 \times$

$let x = 44 \\ \\ lety = 4 \\ \\ x + y = 44 \\ \\ 12 \times 4 - 4 = 44$

3 0

3 years ago

How long a number is chosen a random from a set of whole numbers from 1 to 30 what is the probability that shows a number is a c

LenaWriter [7]

It is a 2 out of three chance of getting a composite number because that means that it is not odd. There are 10 odd numbers between 1 and 30 (2,3,5,7,11,13,17,19,23,29) and that means that there is a 20 out of 30, or 2 out of 3 chance taht the number will be composite.

6 0

3 years ago

Find the area of a polygon with vertices at (1, 3), (7, 3), (7, 7), and (4, 7). a. 24 units2 b. 10 units2 c. 12 units2 d. 18 uni

maria [59]

Answer:

Option D

Step-by-step explanation:

Vertices of the polygon are A(1, 3), B(7, 3), C(7, 7), D(4, 7)

Measure of AB = 7 - 1 = 6 units

Measure of BC = 7 - 3 = 4 units

Measure of CD = 7 - 4 = 3 units

From the figure attached,

Area of the trapezoid = $\frac{1}{2}(AB+CD)(BC)$ [Here, AB and CD are the parallel bases and BC is the height of the trapezoid]

= $\frac{1}{2}(6+3)(4)$

= 18 square units

Therefore, Option D will be the correct option.

4 0

4 years ago

Gold in the form of solid cylinders will be molded into solid blocks. Each cylinder has a diameter of 6.18 cm and a height of 6

nordsb [41]

First we need to find out the volume of one cylinder. We already know the volume of the block of gold is 360cm3

V = Pie * radius squared* height.

Pie is 3.142

radius is 6.18/2 = 3.09 cm

height is 6cm

V = 3.142 * 3.09 * 3.09 * 6

V = 180cm3

Now we divide the volume of this cylinder with the volume of block of gold.

360/180 = 2

So it will take 2 cylinders to mold one block of gold.

6 0

3 years ago