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Katen [24]
2 years ago
11

A scientist had a bottle that contains 56.6 ML of a solution. she used 3.2 ML of the solution for an experiment then she poured

half of the solution remaining in the bottle into a beaker. finally, she poured to six ML of the solution remaining in the bottle into a test tube how many milliliters of a solution remain in the bottle
Mathematics
1 answer:
hjlf2 years ago
3 0
1. 56.6 - 3.2 = 53.4
2. 53.4 divided by 2 = 26.7
3. 26.7 - 6 = 20.7
Answer: 20.7 mL
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A small island is 4 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a
True [87]

Answer:

a) t(x)  = [ √ (4)² + (x)²]/ 4    +   7/5  - x/5

b) x = 0,97 miles

c) t (min)  = 1,24 hours

Step-by-step explanation: See Annex

Figure in annex shows a clear description of the situation

Let  x be distance in miles between point P and where boat lands

A woman has to row  a distance L

L = √ (4)² + (x)²

and the part to get to the town (which she has to walk)

d = ( 7 -  x)

But we are required to give time as a function of x

distance   =  speed * time     ⇒   t  = distance / speed

Therefore

t(x)  = [ √ (4)² + (x)²]/ 4   +   ( 7  -  x  ) / 5

t(x)  = [ √ (4)² + (x)²]/ 4    +   7/5  - x/5

Taking derivatives both sides of the equation

t¨(x)   = ( 2x)*4 / 16√ (4)² + (x)²]   -  5/25  

t¨(x)   = x/  2√ (4)² + (x)²]  - 1/5

t¨(x)   = 0      x/  2√ (4)² + (x)²]  - 1/5   =  0

[ 5 x  -  2√ (4)² + (x)²]  =  0       ⇒   5x    =  2√ (4)² + (x)²]   or

   25 x² =  4  (  4 +   x²)

   25 x² = 16  +   8x²

  17x²   =   16

  x²  =   16/17      

   x²   =  0,941

  x = 0,97 miles  

And the distance walking to get to town

d =  7  -  x       d =   7  -  0,97

d  = 6,03 miles

The least travel time  is   t(x)  = [ √ (4)² + (x)²]/ 4    +   7/5  - x/5  

t (min)  =  √ 16 +  0,94) /4   +  1,4  - 0,97/5

t (min)  = 1,03  +  1,4  - 0,194

t (min)  = 1,24 hours

7 0
1 year ago
Describe in words the surface whose equation is given. (assume that r is not negative.) θ = π/4
Delvig [45]
An equation in the form \theta=\dfrac{\pi}{4} is the line 
that goes through the origins and whose tangent equates \dfrac{\pi}{4}. In general, any equation in the form \theta=\theta_0
is the equation of a line. 
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2 years ago
Stu hiked a trail at an average rate of 3 miles per hour. He ran back on the same trail at an average rate of 5 miles per hour.
Andrews [41]
3t = 5(3-t)
3t = 15 - 5t
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8t = 15
t = 15/8
t = 1 7/8 

7/8 * 60 mins = 52.50 minutes

t = 1 hour and 52.5 minutes

It took Stu 1 hour and 52.5 minutes to hike the trail one way.
3 0
2 years ago
Read 2 more answers
there is 4/5 lb of sand in the class science supplies. if one scoop of sand weighs 1/20 lb, how many scoops of sand can maria ge
Harman [31]
<span>With the bag having 4/5 lb currently in it, this can be translated to 16/20 lb. Maria wants to scoop out sand until the bag has 1/2 lb, which is 10/20 lb. The scoop that Maria uses is 1/20 lb, so using the equation of 16-10 = 6, Maria can get 6 scoops of sand before the bag contains 1/2 lb.</span>
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2 years ago
D(-3+x)=kx+9 solve for x
Gnesinka [82]

d(-3 + x) = kx + 9

  • Distribute d inside the parentheses.

-3d + dx = kx + 9

  • Subtract kx from both sides.

-3d + dx - kx = 9

  • Add 3d to both sides.

dx - kx = 9 + 3d

  • Factor x out of dx - kx.

x(d - k) = 9 + 3d

  • Divide both sides by d - k.

x = \frac{9+3d}{d-k}

  • If you want to simplify this even more, factor 3 out of the numerator.
<h3>x = \frac{3(d + 3)}{d-k}</h3>
5 0
2 years ago
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