Does anyone have answers to the Parametric Functions Test? Pre-Calc

Answer:

12.16 years

Step-by-step explanation:

Continuous Compounding Formula

[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for t:

[tex]\sf \implies 5000=2500e^{0.0570t}[/tex]

[tex]\sf \implies \dfrac{5000}{2500}=\dfrac{2500e^{0.0570t}}{2500}[/tex]

[tex]\sf \implies 2=e^{0.0570t}[/tex]

Take natural logs of both sides:

[tex]\sf \implies \ln 2=\ln e^{0.0570t}[/tex]

[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]

[tex]\sf \implies \ln 2=0.0570t\ln e[/tex]

As ln e = 1:

[tex]\sf \implies \ln 2=0.0570t[/tex]

[tex]\sf \implies \dfrac{\ln 2}{0.0570}=\dfrac{0.0570t}{0.0570}[/tex]

[tex]\sf \implies t=\dfrac{ \ln 2}{0.0570}[/tex]

[tex]\implies \sf t=12.16047685...[/tex]

Therefore, the time required for the amount to double is 12.16 years (2 d.p.).

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Step-by-step explanation:

would you still like me to help you with this question

Angle of depression of the slope is 24. degree.

Angle of depression is equal to the angle of elevation.

sine = the vertical drop/ the ski slope

sine = 100/250

      = 2/5 = 0.4.

sine - 1 (0.4) = 23.57 which is about 24 degree.

Therefore, the correct angle of depression of the slope is approximately 24 degree.

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Answer:

370

Step-by-step explanation:

Area of the entire thing is 20*20 = 400

You need to remove the triangle since it's not shaded, so find the area of the triangle and subtract it from the total (total = 400)

Area of triangle:

First find the height using pythagorean theorem

5*12 = 156

Then divide by two: 60/2= 30

400-30 = 370

Answer:

In mathematics, the intersection of two sets A and B, denoted by A ∩ B, is the set containing all elements of A that also belong to B (or equivalently, all elements of B that also belong to A).

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

6g = 48

/6 /6

divide 6 by both sides

g = 8

hope this helped!

Answer:

A) .8 x.6 = .48

Step-by-step explanation:

B, C, and D are all answered incorrect

Answer:

5 dogs

1 1/4 cups per bottle

Step-by-step explanation:

10/3 ÷ 2/3 get solved by 10/3 x 3/2, which gives you 30/6 or 5

45/8 ÷ 9/2 is 45/8 x 2/9 which is 5/4 or 1 1/4

Answer:

x = 16

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

x + (3x - 4) = 5 - (-7 - 3x)

Step 2: Solve for x

The number of coloured papers as per the given problem is 18.

A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.

Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.

Given that,

The ratio of coloured papers to white papers is 3/8.

And, the number of white papers is 48.

Suppose, the number of coloured papers be x.

Then, as per the question the following equation can be obtained,

3/8 = x/48

=> x = 3/8 × 48

=> x = 18

Hence, the number of coloured papers is 18.

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Answer:

∠A = 30

Step-by-step explanation:

Look at attachment:

Hope this helps! :)

The exact value of cot A will be 0.857.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The co-secant of angle A is √85 / 6. And that angle A is in Quadrant I.

Then the value of angle A will be

csc A = √85 / 6

1 / cos A = √85 / 6

cos A = 6 / √85

A = 49.4°

Then the exact value of cot A will be

cot A = cot 49.4°

cot A = 0.857

The exact value of cot A will be 0.857.

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Answer:

4

Step-by-step explanation:

Using the rule of exponents

[tex]a^{0}[/tex] = 1

Then

4[tex](57ab)^{0}[/tex] = 1 and

4[tex](57ab)^{0}[/tex] = 4 × 1 = 4

Answer:

4

Step-by-step explanation:

since 57ab has power 0 it is equal to 1

1×4 is 4

Answer:

3710.67 mm

Step-by-step explanation:

The formula is a^2 h/3

a = 22  h = 23

First, do 22 squared which is 484.

Now do 23 divided by 3 which is 7.666666667

Now multiply 484 and 7.666666667 together to get

3710.666667 or 3710.67 mm

Answer:

you have to tell us the question honey

Answer:

The correct answer is "4.5 liters". A further explanation is provided below.

Step-by-step explanation:

Let the solution needed be "x".

then, according to the question,

⇒ [tex]4 \ percent(9)+10 \ percent(x)=6 \ percent(9+x)[/tex]

By solving the above expression, we get

⇒ [tex]0.04\times 9+0.1x=0.06\times 9+0,06\times x[/tex]

⇒                [tex]0.04 x=0.54-0.36[/tex]

⇒                [tex]0.04x=0.18[/tex]

⇒                      [tex]x=\frac{0.18}{0.04}[/tex]

⇒                         [tex]=4.5 \ liters[/tex]

Answer:

x <-2

Step-by-step explanation:

-3x+6>12

Subtract 6 from each side

-3x+6-6>12-6

-3x> 6

Divide each side by -3, remembering to flip the inequality

-3x/-3 < 6/-3

x <-2

Answer:

Step-by-step explanation:

Use right triangle trig and SohCahToa. Elevation could either mean the height of something or it could refer to an angle of elevation. Either way, these ratios can help you. Do you have an actual question?

Answer:

12 no .

x+2(4/5)=3(1/6)

x+5*2+4/5=6*3+1/6

x+14/5=19/6

5*x+14/5=19/6(do cross multiplication)

6(x+14)=19*5

6x+84=95

6x=95-84

x=11/6

Step-by-step explanation:

13 no

-0.4a+1.2=3.6

-0.4a=3.6-1.2

a=2.4/-0.4

a=-6

Answer:

a. 4

b. 5

Step-by-step explanation:

a. r = √(112/7) =√16 =4

b. 4x+8 = 28

4x = 28-8

4x = 20

x= 5

The value of X algebraically is 5 and the common difference is;4.

There are three parameters which differentiate between which geometric sequence we're talking about.

The first parameter is the initial value of the sequence.

The second parameter is the quantity by which we multiply previous term to get the next term.

We are given that  terms shown below are the first three terms of a geometric sequence whose common ratio is positive.

7, 4x+8, 112

Therefore, the common difference is;

r = √(112/7) =√16

r =4

Now, 4x+8 = 28

4x = 28-8

4x = 20

x= 5

The value of X algebraically is 5.

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Answer: 1/3piex^2

3rd one down

Step-by-step explanation:

I’m not positive sorry if I’m wrong

Answer:

-2

Step-by-step explanation:

Well since this line is parallel to y=3x-5 they must have the same slope

We are just solving for the y-intercept

We have a point (2,4) lets plug it into

y=3x+ b

4 = 3(2) +b

4= 6 +b

-2 = b

The value of b is -2

Answer:

B-value = -2

Step-by-step explanation:

In the picture below Orange line represents the line of "y = 3x - 5", since we know that the line passing through the point (2,4) is parallel to the given line, the slope of the line would be 3x as well. To find b-value or y-intercept we have to plot the point on the graph where the line passing through the points (2,4) intersects the y-axis, in this case it's at (0,-2), therefore the b-value = -2.

Hope this helps!

Here is the diagram:

Answer:

m=-4,-2

Step-by-step explanation:

Hi there!

What we need to know:

1) Rearrange the given equation into standard form

This will help us determine the a, b and c values.

[tex]m^2+6m=-8[/tex]

Add 8 to both sides

[tex]m^2+6m+8=0[/tex]

Now, we can see that a=1, b=6 and c=8.

2) Plug a, b and c into the quadratic formula

[tex]m=\frac{-b\pm\sqrt{b^2-4ac} }{2a}\\m=\frac{-6\pm\sqrt{6^2-4(1)(8)} }{2(1)}\\m=\frac{-6\pm\sqrt{4} }{2}\\m=\frac{-6\pm2 }{2}\\m=-3\pm1 \\m=-4,-2[/tex]

I hope this helps!

Answer:

About 64 Miles

Step-by-step explanation:

I think you just divide the miles by minutes which is about 1.06 then x 60 = 64

Answer:

[tex]MN = \sqrt{14[/tex]

Step-by-step explanation:

Given

[tex]NO = 12[/tex]

[tex]OP = 2.5[/tex]

[tex]OQ = 4.5[/tex]

Required

Find MN

First, we calculate QP using Pythagoras theorem

[tex]OQ^2 = OP^2 + QP^2[/tex]

[tex]4.5^2 = 2.5^2 + QP^2[/tex]

[tex]20.25 = 6.25 + QP^2[/tex]

Collect like terms

[tex]QP^2 = 20.25 - 6.25[/tex]

[tex]QP^2 = 14[/tex]

Take square roots

[tex]QP = \sqrt{14[/tex]

To solve MN, we have:

[tex]MN = OP[/tex]

So:

[tex]MN = \sqrt{14[/tex]

Answer:

3

Step-by-step explanation:

you are dividing by 3 each time