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3 years ago

A large brine tank containing a solution of salt and water is being diluted with fresh water.

Mathematics

1 answer:

kirza4 [7]3 years ago

6 0

Answer:

41.04 g/L

Step-by-step explanation:

The relationship is modeled by the following function:

S(t) = 500*e^(-0.25*t)

where t is time elapsed after the dilution begins (in hours) and S(t) the concentration of salt in the tank (in g/L)

Replacing with t = 10

S(t) = 500*e^(-0.25*10)

S(t) = 41.04 g/L

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A 15-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 14 feet

Finger [1]

Answer:

Step-by-step explanation:

Well certainly friction alone will not hold it there.

c² = a² + b²

15² = 14² + b²

15² - 14² = b²

b² = 29

b = √29 = 5.385164... = 5.39 ft

6 0

3 years ago

Multiply the polynomials 3(x+7) (show work pls)

Evgen [1.6K]

Answer:

3x + 21

Step-by-step explanation:

(3)(x+7)

Now, we distribute the 3 in each term of (x+7)

So, 3*x = 3x and 3*7 = 21.

So our resulting term would be 3x+21.

8 0

3 years ago

Use the Law of Sines to solve the following triangle. Approximate your answers to the nearest tenths. c = 10.2 in, A = 45.1° B =

Sergeu [11.5K]

Law of sines says
a/sinA=b/sinB=c/SinC
where a,b,c are sides of a triangle and A,B,C are angles respectively.
a/sin45.1=c/sin59.1

(we can find angle C by sum of angles of a triangle is 180.)

a=sin(45.1) x 10.2/sin (59.1)

a=0.708 x 10.2/0.85
a=8.496
a=8.5 units

now u can find b and c sides.

4 0

3 years ago

A radar gun was used to record the speed of a runner (in meters per second) during selected times in the first 2 seconds of a ra

Pavlova-9 [17]

Answer:

Step-by-step explanation:

See image

6 0

3 years ago

What is (8-√2)(2+√8)?

siniylev [52]

Answer:

$(8 - \sqrt{2}) \cdot (2 + \sqrt{8}) = 12 + 14\; \sqrt{2}$ .

Step-by-step explanation:

Step One: Simplify the square roots.

$8 = 4 \times 2 = 2^2 \times 2$ .

The square root of 8 $\sqrt{8}$ can be simplified as the product of an integer and the square root of 2:

$\sqrt{8} = \sqrt{4 \times 2} = \sqrt{2^2 \times 2} = \sqrt{2^{2}} \times \sqrt{2} = 2 \; \sqrt{2}$ .

As a result,

$(8 - \sqrt{2}) \cdot (2 + \sqrt{8}) = (8 - \sqrt{2}) \cdot (2 + 2\; \sqrt{2})$ .

Step Two: Expand the product of the two binomials.

$(8 - \sqrt{2}) \cdot (2 + 2\; \sqrt{2})$ is the product of two binomials:

Binomial One: $8 - \sqrt{2}$ .
Binomial Two: $2 + 2\; \sqrt{2}$

Start by applying the distributive law to the first binomial. Multiply each term in the first binomial (without brackets) with the second binomial (with brackets)

$({\bf 8} - {\bf \sqrt{2}}) \cdot {(2 + 2\; \sqrt{2})}\\= [{\bf 8} \cdot {(2 + 2\; \sqrt{2})}] - [{\bf \sqrt{2}} \cdot {(2 + 2\; \sqrt{2})}]$

Now, apply the distributive law once again to terms in the second binomial.

$[8 \cdot ({\bf 2} + {\bf 2\; \sqrt{2}})] - [\sqrt{2} \cdot ({\bf 2} + {\bf 2\; \sqrt{2}})]\\= [8 \times {\bf 2} + 8 \times {\bf 2\;\sqrt{2}}] - [\sqrt{2} \times {\bf 2} + \sqrt{2} \times {\bf 2\; \sqrt{2}}]$ .

Step Three: Simplify the expression.

The square of a square root is the same as the number under the square root. For example, $\sqrt{2} \times \sqrt{2} = (\sqrt{2})^{2} = 2$ .

$[8 \times 2 + 8 \times 2\;\sqrt{2}] - [\sqrt{2} \times 2 + 2 \sqrt{2} \times \sqrt{2}]\\ =[16 + 16 \;\sqrt{2}] - [2 \;\sqrt{2} + 4]\\= 16 + 16\;\sqrt{2} - 2\; \sqrt{2} - 4$ .

Combine the terms with the square root of two and those without the square root of two:

$16 + 16\;\sqrt{2} - 2\; \sqrt{2} - 4\\= (16 - 4) + (16 \; \sqrt{2} - 2\; \sqrt{2})$ .

Factor the square root of two out of the second term:

$(16 - 4) + (16 \; \sqrt{2} - 2\; \sqrt{2})\\= (16 - 4) + (16 - 2) \; \sqrt{2} \\= 12 - 14 \; \sqrt{2}$ .

Combining the steps:

$(8 - \sqrt{2}) \cdot (2 + 2\; \sqrt{2})\\= [8 \cdot (2 + 2\; \sqrt{2})] - [\sqrt{2} \cdot (2 + 2\; \sqrt{2})]\\= [8 \times 2 + 8 \times 2\;\sqrt{2}] - [\sqrt{2} \times 2 + \sqrt{2} \times 2 \;\sqrt{2}]\\= [16 + 16 \;\sqrt{2}] - [2 \;\sqrt{2} + 2 \times (\sqrt{2})^{2}]\\= [16 + 16 \;\sqrt{2}] - [2 \;\sqrt{2} + 2 \times 2]\\= [16 + 16 \;\sqrt{2}] - [2 \;\sqrt{2} + 4]\\= 16 + 16\;\sqrt{2} - 2\; \sqrt{2} - 4\\= (16 - 4) + (16 \; \sqrt{2} - 2\; \sqrt{2})\\$

$= (16 - 4) + (16 - 2) \; \sqrt{2}\\= 12 - 14 \; \sqrt{2}$ .

3 0

3 years ago