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3 years ago

Please help me I don’t understand how to do it. If you can please use a data table to explain how to do it.

Mathematics

1 answer:

Ksivusya [100]3 years ago

4 0

Answer:

The 70% mixture makes up 0.7 liters of the solution whereas the 60% mixture makes up 2.8 liters of the solution.

Step-by-step explanation:

Let us have x liters of the .7 mixture and y liters of the .6 mixture.

We want total liters to be 3.5 which means we need x+y=3.5 . I don't like the decimal in the equation so I'm going to multiply both sides by 10: 10x+10y=35

We also need the .7x+.6y=.62(3.5) . I hate the decimal business going on in this question so I'm going to multiply by 1000 which gives 700x+600y=62(35) .

So we have the system

700x+600y=62(35)

10x+10y=35

I'm going to setup this up for linear combination/elimination.

Multiply bottom equation by 60.

700x+600y=62(35)

600x+600y=60(35)

Subtract equations (bottom from top):

(700-600)x+(600-600)y=35(62-60)

Simplify:

100x+0y=35(2)

100x=70

Divide both sides by 100:

x=70/100

x=7/10

Going back to x+y=3.5 along with x=7/10 or .7 liters to find y.

y=3.5-x with x=.7

y=3.5-0.7

y=2.8

The 70% mixture makes up 0.7 liters of the solution whereas the 60% mixture makes up 2.8 liters of the solution.

Pic added.

Another way to do problem:

.7x+.6(3.5-x)=.62(3.5)

Multiply and distribute:

.7x+2.1-.6x=2.17

Combine like terms on left:

.1x+2.1=2.17

Subtract 2.1 on both sides:

.1x=.07

Multiply both sides by 10:

x=0.7 liters

Now the other acid solution is 3.5-0.7 which is 2.8 litera.

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each of the variables a, b, c, d, e and f represents a different positive real number. given the equations below, which variable

slega [8]

Answer:

The greatest value is "e"

Step-by-step explanation:

We have the following equations:

a. 1.31 a = f

b. 1.12b=f

c. 1.01c=f

d. 0.98d=f

e. 0.31e =f

Then solving for "a", "b", "c", "d" and "e" we have:

a. a = f /1.31

b. b=f/1.12

c. c=f /1.01

d. d=f / 0.98

e. e=f / 0.31

Now, given that in all the equations "f" represents the same number, the gratest value it's going to be the option in which "f" is divided by the smaller number.

The option in which f is divided by the less number is option e because, in this case, f is divided by 0.31.

8 0

4 years ago

Find all points on the curve x=4cos(t),y=4sin(t) that have the slope of 12.

Marianna [84]

Answer:

$\left (-\dfrac{4}{\sqrt{5}},\dfrac{8}{\sqrt{5}}\right )\text{ and }\left (\dfrac{4}{\sqrt{5}},-\dfrac{8}{\sqrt{5}}\right )$ .

Step-by-step explanation:

We need to find all the points on the curve x=4cos(t),y=4sin(t) that have the slope of 1/2.

$x=4cos (t)$

$\dfrac{dx}{dt}=-4sin (t)$

$y=4sin (t)$

$\dfrac{dy}{dt}=4cos (t)$

Now,

$\dfrac{dy}{dx}=\dfrac{dy}{dt}\times \dfrac{dt}{dx}$

$\dfrac{dy}{dx}=4cos (t)\times \dfrac{1}{-4sin (t)}$

$\dfrac{dy}{dx}=-\cot t$

So, slope of the curve is $-\cot t$ .

$-\cot t=\dfrac{1}{2}$

$-\tan t=2$

$\tan t=-2$ ...(1)

Using $\sec^2t=1+\tan^2t$ , we get

$\sec^2t=1+(-2)^2$

$\sec^2t=1+4$

$\sec t=\pm \sqrt{5}$

$\cos t=\pm \dfrac{1}{\sqrt{5}}$

Now,

$\sin^2t=1-cos^2t$

$\sin t=\pm \sqrt{1-\dfrac{1}{5}}$

$\sin t=\pm \sqrt{\dfrac{4}{5}}$

$\sin t=\pm \dfrac{2}{\sqrt{5}}$

It equation (1), tan(t) is negative. So, sin and cos have different signs.

If $\sin t= \dfrac{2}{\sqrt{5}}$ , then $\cos t=- \dfrac{1}{\sqrt{5}}$ .

$x=4cos (t)=-\dfrac{4}{\sqrt{5}}$

$y=4sin (t)=\dfrac{8}{\sqrt{5}}$

If $\sin t=- \dfrac{2}{\sqrt{5}}$ , then $\cos t= \dfrac{1}{\sqrt{5}}$ .

$x=4cos (t)=\dfrac{4}{\sqrt{5}}$

$y=4sin (t)=-\dfrac{8}{\sqrt{5}}$

Therefore, the two points are $\left (-\dfrac{4}{\sqrt{5}},\dfrac{8}{\sqrt{5}}\right )\text{ and }\left (\dfrac{4}{\sqrt{5}},-\dfrac{8}{\sqrt{5}}\right )$ .

5 0

3 years ago

PLEASE HELP WORTH 50 POINTS!

Scorpion4ik [409]

Jessica’s mistake is that when isolating h from b, she multiplied b instead of dividing it on both sides. The new formula for h would be A/2b=h.
Now let’s solve. 23/2(6)=h
23/12
Approx. 1.91

6 0

3 years ago

Read 2 more answers

A plane flies at 350 mph in the direction N 40° E with a wind blowing at 40 mph in the direction S 70° E. What is the plane’s dr

kozerog [31]

Answer:

The drift angle is approximately 7.65° towards the East from the plane's heading

Step-by-step explanation:

The speed of the plane = 350 mph

The direction in which the plane flies N 40° E = 50° counterclockwise from the eastern direction

The speed of the wind = 40 mph

The direction of the wind = S 70° E = 20° clockwise from the eastern direction