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3 years ago

There are 225 calories in a 45 gram candy bar what is the unit rate

Mathematics

1 answer:

Genrish500 [490]3 years ago

4 0

Answer:

5 calories per gram

Step-by-step explanation:

Take the number of calories and divide by the number of grams

225/45

5 calories per gram

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M/9+2/3=7/3 Solve for m.

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3 years ago

If y varies inversely as x and y 27 when x 40 find y when x 10

Iteru [2.4K]

When y varies inversely as x ⇒ y*x=k

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3 years ago

A swimming pool with a volume of 30,000 liters originally contains water that is 0.01% chlorine (i.e. it contains 0.1 mL of chlo

SpyIntel [72]

Answer:

$R_{in}=0.2\dfrac{mL}{min}$

$C(t)=\dfrac{A(t)}{30000}$

$R_{out}= \dfrac{A(t)}{1500} \dfrac{mL}{min}$

$A(t)=300+2700e^{-\dfrac{t}{1500}},$ A(0)=3000$

Step-by-step explanation:

The volume of the swimming pool = 30,000 liters

(a) Amount of chlorine initially in the tank.

It originally contains water that is 0.01% chlorine.

0.01% of 30000=3000 mL of chlorine per liter

A(0)= 3000 mL of chlorine per liter

(b) Rate at which the chlorine is entering the pool.

City water containing 0.001%(0.01 mL of chlorine per liter) chlorine is pumped into the pool at a rate of 20 liters/min.

$R_{in}=$ (concentration of chlorine in inflow)(input rate of the water)

$=(0.01\dfrac{mL}{liter}) (20\dfrac{liter}{min})\\R_{in}=0.2\dfrac{mL}{min}$

Volume of the pool =30,000 Liter

$Concentration, C(t)= \dfrac{Amount}{Volume}\\C(t)=\dfrac{A(t)}{30000}$

(d) Rate at which the chlorine is leaving the pool

$R_{out}=$ (concentration of chlorine in outflow)(output rate of the water)

$= (\dfrac{A(t)}{30000})(20\dfrac{liter}{min})\\R_{out}= \dfrac{A(t)}{1500} \dfrac{mL}{min}$

(e) Differential equation representing the rate at which the amount of sugar in the tank is changing at time t.

$\dfrac{dA}{dt}=R_{in}-R_{out}\\\dfrac{dA}{dt}=0.2- \dfrac{A(t)}{1500}$

We then solve the resulting differential equation by separation of variables.

$\dfrac{dA}{dt}+\dfrac{A}{1500}=0.2\\$The integrating factor: e^{\int \frac{1}{1500}dt} =e^{\frac{t}{1500}}\\$Multiplying by the integrating factor all through\\\dfrac{dA}{dt}e^{\frac{t}{1500}}+\dfrac{A}{1500}e^{\frac{t}{1500}}=0.2e^{\frac{t}{1500}}\\(Ae^{\frac{t}{1500}})'=0.2e^{\frac{t}{1500}}$

Taking the integral of both sides

$\int(Ae^{\frac{t}{1500}})'=\int 0.2e^{\frac{t}{1500}} dt\\Ae^{\frac{t}{1500}}=0.2*1500e^{\frac{t}{1500}}+C, $(C a constant of integration)\\Ae^{\frac{t}{1500}}=300e^{\frac{t}{1500}}+C\\$Divide all through by e^{\frac{t}{1500}}\\A(t)=300+Ce^{-\frac{t}{1500}}$

Recall that when t=0, A(t)=3000 (our initial condition)

$3000=300+Ce^{0}\\C=2700\\$Therefore:\\A(t)=300+2700e^{-\dfrac{t}{1500}}$

3 0

3 years ago

leonhard wants to place a triangular-based cabinet in the corner of his rectangle-shaped living room. the triangular base has a

Georgia [21]

The answer is $x = \frac{-7+ \sqrt{193} }{4}$ .

There is very similar question on Brainly, in which dimensions of the living room are given (20 feet, 30 feet).
So, knowing this, we first need to calculate how much 6% of the living room is.
The area of the living room is 600 square feet, since it is rectangle-shaped:
P = a * b = 200 feet * 30 feet = 600 square feet.

6% of 600 square feet is 36 square feet:
600 square feet : 100% = A : 6%
A = 600 * 6 / 100 = 36 square feet

The area of the triangular-based cabinet (A) is $A = \frac{a*h}{2}$ , where a is the base, and h is the height of the triangle.
It is given:
A = 36
a = 2x + 3
h = 3x + 6

Now, let's implement this to the formula $A = \frac{a*h}{2}$ :
$36 = \frac{(2x+3)(3x+6)}{2}$
⇒ $36*2=6 x^{2} +12x+9x+18$
$72=6 x^{2} +21x+18$

Let's both sides divide by 3:
$24=2 x^{2} +7x+6$
⇒ $2 x^{2} +7x-18=0$

This is the quadratic formula ( $a x^{2} +bx+c=0$ ) for which
$x = \frac{-b+\sqrt{b^{2} -4ac} }{2a}$ or
 $x = \frac{-b-\sqrt{b^{2} -4ac} }{2a}$ .
We will use only $x = \frac{-b+\sqrt{b^{2} -4ac} }{2a}$ , because the length cannot have negative value.

From the equation $2 x^{2} +7x-18=0$ , we know that
a = 2
b = 7
c = -18

Thus, $x = \frac{-7+ \sqrt{193} }{4}$ :
 $x= \frac{-b+ \sqrt{ b^{2} -4ac} }{2a} = \frac{-7+ \sqrt{ (7)^{2} -4*2*(-18)} }{2*2} = \frac{-7+ \sqrt{49+144} }{4} = \frac{-7+ \sqrt{193} }{4}$

4 0

3 years ago

There are 225 calories in a 45 gram candy bar what is the unit rate​

There are 225 calories in a 45 gram candy bar what is the unit rate