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Veronika [31]
3 years ago
9

Assume that k and V0 are constant and are, respectively, 0.02, and 7. The parameter CA varies from an initial value CA0 = 100 to

a final value of CA = 7. What is the value of V given the following equation and assuming that the integral of dV equals V. Express your answer rounded to one decimal place.
dCA/dV = -kCA/V0
Mathematics
1 answer:
julia-pushkina [17]3 years ago
7 0

Answer:

V = 929.7

Step-by-step explanation:

Given the equation:

\frac{dCA}{dV} = \frac{-kCA}{V0}

The integral of the above equation is:

\int\limits {\frac{dCA}{dV} } = \int\limits{\frac{-kCA}{V0} }

Re-organizing the integrals:

\int\limits  {\frac{dCA}{CA} } = \int\limits {\frac{-kdV}{V0} }

Integrating:

ln(CA) - ln(CA0) = \frac{-kV}{V0}

Inputting the initial conditions of CA and the values of k and V0:

ln(7) - ln(100) = \frac{-0.02V}{7}

1.946 - 4.605 = -0.00286V

-2.659 = -0.00286V

=> V = \frac{2.659}{0.00286}

V = 929.720

Approximating to one decimal place,

V = 929.7

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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
Kryger [21]

Answer:

The first, second, and fifth statements are correct.

Step-by-step explanation:

We are given a circle with the equation:

x^2+y^2-2x-8=0

And we want to select the statements that are true.

First, we can convert the equation into standard form. We can group each variable:

(x^2-2x)+(y^2)=8

And complete the square for the first term:

(x^2-2x+1)+(y^2)=8+1

Factor and simplify:

(x-1)^2+y^2=9

We can rewrite our equation as:

(x-(1))^2+(y-(0))^2=(3)^2

So, this tells us that we have a circle centered on (1, 0) with a radius of 3 units.

In this case, the first statement, second statement (the point (1,0) is on the x-axis), and fifth statements are correct (the square root of 9 is also 3).

8 0
3 years ago
Read 2 more answers
Can someone help me in question #5 please
Tamiku [17]

Answer:

62 degrees

Step-by-step explanation:

Since lines i and k are parallel, angle b and h are interior angles and are equal to each other. Set up the equation by setting the two equal to each other.

8x-34=5x+2

Subtract 5x from both sides. (it cancels on the right side)

3x-34=2

Add 34 to both sides. (cancels on the left side)

3x=36

Divide both sides by 3.

x=12

Now plug it into either equation since they are equal. I'm gonna use the one for angle h so that it's less confusing.

5(12)+2

60+2

62

The measure of angle h is 62 degrees.

6 0
3 years ago
Find the number of tiles required to be put in a floor with dimensions 25 m x 20 m. Each tile is a rhombus with side 25 cm altit
Romashka-Z-Leto [24]

Answer:

8000

Step-by-step explanation:

Area of floor=25×20m

=500²

Area of each tile=area if each rhombus

=25×25=625cm²

No. of tiles required= area of floor/ area of each tile

=500×104⁴/ 625

=4/5 ×10×1000

=8000

hope it helps!

6 0
3 years ago
Express in simplified exponential notation.<br> x3 • x5 =
Darya [45]
x^3 \times x^5 = x^{3+5} =\boxed{\bf{x^8}}}
5 0
3 years ago
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Graph the function f(x) = (x + 1)(x - 5). Use the drop-
hodyreva [135]

Answer:

3) (2,-9)

4) (0,-5)

5) (1,-8)

Step-by-step explanation:

3)

The vertex will occur between you x-intercepts.

You already found that happens at x=2.

To find the corresponding y-coordinate, replace x in

f(x)=(x+1)(x-5) with 2:

f(2)=(2+1)(2-5)

f(2)=(3)(-3)

f(2)=-9

So the vertex is (2,-9).

4)

The y-intercept is when x=0.

So in f(x)=(x+1)(x-5) replace x with 0:

f(0)=(0+1)(0-5)

f(0)=(1)(-5)

f(0)=-5

So the y-intercept is (0,-5).

5)

To find another point just plug in anything besides any x already used.

We preferably want to use a value of x that will keep us on their grid however far up,down,left, or right their grid goes out. So I'm going to choose something close to the vertex which is at x=2. Let's go with x=1.

So replace x in f(x)=(x+1)(x-5) with x=1:

f(1)=(1+1)(1-5)

f(1)=(2)(-4)

f(1)=-8

So another point to graph is (1,-8).

7 0
4 years ago
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