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ELEN [110]
3 years ago
6

A pharmacist has 30% and 60% iodine solutions on hand. How many liters of each iodine solution will be required to produce 6 lit

ers of a 50% iodine.

Mathematics
1 answer:
kkurt [141]3 years ago
6 0

Answer:

4 liters of 60% solution; 2 liters of 30% solution

Step-by-step explanation:

I like to use a simple, but effective, tool for most mixture problems. It is a kind of "X" diagram as in the attachment.

The ratios of solution concentrations are 3:6:5, so I've used those numbers in the diagram. The constituent solutions are on the left; the desired mixture is in the middle, and the numbers on the other legs of the X are the differences along the diagonals: 6 - 5 = 1; 5 - 3 = 2. This tells you the ratio of 60% solution to 30% solution is 2 : 1.

These ratio units (2, 1) add to 3. We want 6 liters of mixture, so we need to multiply these ratio units by 2 liters to get the amounts of constituents needed. The result is 4 liters of 60% solution and 2 liters of 30% solution.

_____

If you're writing equations, it often works well to let the variable represent the quantity of the greatest contributor—the 60% solution. Let the volume of that (in liters) be represented by v. Then the total volume of iodine in the mixture is ...

... 0.60·v + 0.30·(6 -v) = 0.50·6

... 0.30v = 0.20·6 . . . . subtract 0.30·6, collect terms

... v = 6·(0.20/0.30) = 4 . . . . divide by the coefficient of v

4 liters of 60% solution are needed. The other 2 liters are 30% solution.

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When juggling a ball travels in a complete circle every 10 seconds how many circle does it make in a minute.Please Help and expl
WITCHER [35]

Answer:

It make 6 circles in a minute.

Step-by-step explanation:

Given:

a ball travels in a complete circle every 10 seconds

i.e

one complete circle = time taken 10 seconds.

Two complete circle = time taken 20 seconds.

Three complete circle = time taken 30 seconds.

Four complete circle = time taken 40 seconds.

Five complete circle = time taken 50 seconds.

Six complete circle = time taken 60 seconds.

60 seconds =  one minute.

∴ Six complete circle  in one minute.

8 0
3 years ago
Use spherical coordinates. Find the volume of the solid that lies within the sphere x^2 + y^2 + z^2 = 81, above the xy-plane, an
Natasha_Volkova [10]

Answer:

The volume of the solid is 243\sqrt{2} \ \pi

Step-by-step explanation:

From the information given:

BY applying sphere coordinates:

0 ≤ x² + y² + z² ≤ 81

0  ≤ ρ²   ≤   81

0  ≤ ρ   ≤  9

The intersection that takes place in the sphere and the cone is:

x^2 +y^2 ( \sqrt{x^2 +y^2 })^2  = 81

2(x^2 + y^2) =81

x^2 +y^2 = \dfrac{81}{2}

Thus; the region bounded is: 0 ≤ θ ≤ 2π

This implies that:

z = \sqrt{x^2+y^2}

ρcosФ = ρsinФ

tanФ = 1

Ф = π/4

Similarly; in the X-Y plane;

z = 0

ρcosФ = 0

cosФ = 0

Ф = π/2

So here; \dfrac{\pi}{4} \leq \phi \le \dfrac{\pi}{2}

Thus, volume: V  = \iiint_E \ d V = \int \limits^{\pi/2}_{\pi/4}  \int \limits ^{2\pi}_{0} \int \limits^9_0 \rho   ^2 \ sin \phi \ d\rho \   d \theta \  d \phi

V  = \int \limits^{\pi/2}_{\pi/4} \ sin \phi  \ d \phi  \int \limits ^{2\pi}_{0} d \theta \int \limits^9_0 \rho   ^2 d\rho

V = \bigg [-cos \phi  \bigg]^{\pi/2}_{\pi/4}  \bigg [\theta  \bigg]^{2 \pi}_{0} \bigg [\dfrac{\rho^3}{3}  \bigg ]^{9}_{0}

V = [ -0+ \dfrac{1}{\sqrt{2}}][2 \pi -0] [\dfrac{9^3}{3}- 0 ]

V = 243\sqrt{2} \ \pi

4 0
3 years ago
on the left side of the triangle, it says 10 cm, on the right side of the triangle, it says 18 cm, below the triangle, it says 1
stira [4]
Area formula for a triangle is 1/2BxH

B=15
H=10

1/2(15)= 7.5

7.5 x 10= 75

So the area is 75 square cm :)
8 0
3 years ago
I Need Help With 9 And 10Please Help
Burka [1]
9: the answer is 4 to 13
10: the answer is 6 to 13
5 0
3 years ago
While exercising, a person’s recommended target heart rate is a function of age. The recommended number of beats per minute, y ,
Deffense [45]

Answer:

170 heart beat per minute.

Step-by-step explanation:

While exercising, a person’s recommended target heart rate is a function of age. The recommended number of beats per minute, y, is given by the function y = f(x) = − 0.85x + 187 where x represents a person’s age in years.

So, if my age is 21 years i.e. x = 21, then the number of recommended heart beats per minute for my age will be

y = f(21) = - 0.85(21) + 187 = - 17.85 + 187 = 169.15 ≈ 170. (Answer)

{Taking the larger integer value}

8 0
3 years ago
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