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3 years ago

A flowchart proof

Mathematics

1 answer:

DiKsa [7]3 years ago

3 0

Answer:uses a visual representation of the logical flow of steps needed to reach a conclusion

Step-by-step explanation:

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Mary wants to make 20 gallons of a 52% acid solution by mixing together a 84% acid solution and a 4% acid solution. How much of

Setler [38]

Answer:

12 gallons 84%
8 gallons 4%

Step-by-step explanation:

I like to use an "X-diagram" to solve mixture problems. On the left side are the constituents of the mix; in the middle is the result of the mix; and on the right side are the differences between the numbers on each diagonal. These differences are the ratio numbers for the mix.

Here, that means the ratio of 84% solution to 4% solution is ...

48 : 32 = 12 : 8

Note that the last two "ratio numbers" were chosen so their sum is 20, hence they represent the number of gallons of the corresponding constituent in the mix. (The sum of the first two ratio numbers is 48+32=80, so to get a sum of 20, we divide each by 4.)

Mary must use ...

12 gallons of 84% acid solution
8 gallons of 4% acid solution

You may note that this solution takes much longer to explain than to do. The math here can all be done without a calculator.

_____

<em>Check</em>

12 × 84% + 8 × 4% = 10.40 = 20 × 52%

_____

<em>Usual Solution</em>

A more conventional approach would be to assign x to the amount of 84% solution needed. Then the number of gallons of acid in the mix is ...

0.84x + 0.04(20 -x) = 0.52(20)

0.80x + 0.8 = 10.4 . . . . simplify

0.80x = 9.6 . . . . . . . . . . subtract 0.8; next, divide by 0.8

x = 9.6/0.8 = 12 . . . . gallons of 84% acid

20-x = 8 . . . . . . . . . . gallons of 4% acid

3 0

3 years ago

Kaliska is jumping rope. The vertical height of the center of her rope off the ground R(t) (in cm) as a function of time t (in s

xz_007 [3.2K]

Answer:

R (t) = 60 - 60 cos (6t)

Step-by-step explanation:

Given that:

R(t) = acos (bt) + d

at t= 0

R(0) = 0

0 = acos (0) + d

a + d = 0 ----- (1)

After $\dfrac{\pi}{12}$ seconds it reaches a height of 60 cm from the ground.

i.e

$R ( \dfrac{\pi}{12}) = 60$

$60 = acos (\dfrac{b \pi}{12}) +d --- (2)$

Recall from the question that:

At t = 0, R(0) = 0 which is the minimum

as such it is only when a is negative can acos (bt ) + d can get to minimum at t= 0

Similarly; 60 × 2 = maximum

R'(t) = -ab sin (bt) =0

bt = k π

here;

k is the integer

making t the subject of the formula, we have:

$t = \dfrac{k \pi}{b}$

replacing the derived equation of k into R(t) = acos (bt) + d

$R (\dfrac{k \pi}{b}) = d+a cos (k \pi)$ $= \left \{ {{a+d \ for \ k \ odd} \atop {-a+d \ for k \ even}} \right.$

Since we known a < 0 (negative)

then d-a will be maximum

d-a = 60 × 2

d-a = 120 ----- (3)

Relating to equation (1) and (3)

a = -60 and d = 60

∴ R(t) = 60 - 60 cos (bt)

Similarly;

For $R ( \dfrac{\pi}{12})$

$R ( \dfrac{\pi}{12}) = 60 -60 \ cos (\dfrac{\pi b}{12}) =60$

where ;

$cos (\dfrac{\pi b}{12}) =0$

Then b = 6

∴

R (t) = 60 - 60 cos (6t)

7 0

2 years ago

Im giving free brain list just answer this question . what is 9.62 x 0.38

Sphinxa [80]

Answer:

3.6556

Step-by-step explanation:

Multiply both, can i get brainliest?

5 0

2 years ago

Read 2 more answers

If f(x)= -x+6x-1 and g(x)=3×-4x-1, find (f-g)(x)

Alex787 [66]

-x + 6x - 1 - (3x - 4x - 1)

-x + 6x - 1 - 3x + 4x + 1

5x - 3x + 4x - 1 + 1

(f-g)(x) = 6x

5 0

3 years ago

Lana has a credit card that uses the adjusted balance method. For the first 10 days of one of her 30-day billing cycles, her bal

ycow [4]

Answer:

$46.03 is the answer for APEX

Step-by-step explanation:

4 0

3 years ago