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2 years ago

Mei and Anju are sitting next to each other on different horses on a carousel. Mei's horse is 3 meters from the center of the

Mathematics

2 answers:

Law Incorporation [45]2 years ago

6 0

Answer:

The answer below me is correct, He just didnt have answers to go off, of the answer is 2pi because 2 x 3.14 is 6.28

Post answers next time

SOVA2 [1]2 years ago

5 0

Answer:

$2\pi \approx 6.28\ meters$

Step-by-step explanation:

Mei's horse is 3 meters from the center of the carousel. After one rotation, Mei travelled

$l_M=2\pi r=2\pi \cdot 3=6\pi\ meters$

Anju's horse is 2 meters from the center. After one rotation, Mei travelled

$l_A=2\pi r=2\pi \cdot 2=4\pi\ meters$

The difference in their travelled distances is

$l_M-l_A=6\pi -4\pi =2\pi \approx 6.28\ meters$

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A wild animal generally stays at least x mi from the edge of a forest. For a rectangular forest preserve that is 2 mi

Butoxors [25]

Answer:

$Area = 4x^2 - 14x + 10$

Step-by-step explanation:

See Attachment for Complete Question

Given

$Width = 5mi$ --- For the forest

$Length = 2mi$ -- --- For the forest

Required

Determine the area of the habitat

Since the distance between the animal's habitat is x mi on both sides;

The length and width of the habitat is:

$Width = 5 - (x + x)$

$Width = 5 - 2x$

$Height = 2 - (x +x)$

$Height = 2 - 2x$

The area is then calculated as follows;

$Area = Width * Height$

$Area = (5 - 2x) * (2 - 2x)$

Expand

$Area = 5(2 - 2x) -2x(2 - 2x)$

Open Brackets

$Area = 10 - 10x - 4x + 4x^2$

$Area = 10 - 14x + 4x^2$

Reorder

$Area = 4x^2 - 14x + 10$

Hence; the required polynomial for the habitat area is:

$Area = 4x^2 - 14x + 10$

3 0

2 years ago

The cost function for a certain company is C = 20x + 700 and the revenue is given by R = 100x − 0.5x2. Recall that profit is rev

Brilliant_brown [7]

Answer:

x = 20

x = 140

Step-by-step explanation:

Find the equation for profit P

P = R - C

Substitute the equations for R and C then simplify.

P = 100x − 0.5x² - (20x + 700)

P = -0.5x² + 80x - 700

Find the values of x when profit is $700

P = -0.5x² + 80x - 700

700 = -0.5x² + 80x - 700

0 = -0.5x² + 80x - 1400

This is in the standard form 0 = ax² + bx + c

Use the quadratic formula to find values of x

$x = \frac{-b±\sqrt{b^{2}-4ac} }{2a}$

(Ignore Â)

Substitute a b and c.

a = -0.5

b = 80

c = -1400

$x = \frac{-(80)±\sqrt{80^{2}-4(-0.5)(-1400)} }{2(-0.5)}$

$x = \frac{-80±60}{-1}$

Split the formula at the ± so that there are two to get the two x values.

$x = \frac{-80+60}{-1}$

$x = \frac{-80-60}{-1}$

x = 20

x = 140

The profit will be $700 when x is 20 or when x is 140.

5 0

2 years ago

Complete the following two-column proof that proves the Congruent Supplements Theorem. HELP ME ASAPPPP BRO PLEASE DUED BY TONIGH

LiRa [457]

Answer:

21 savae just relased an album

Step-by-step explanation:

So get off math a listen 2 it make me brainly daddy

4 0

2 years ago

The center of a circle is at the origin on a coordinate grid. The vertex of a parabola that opens upward is at (0, 9). If the ci

zhannawk [14.2K]

Answer:

"The maximum number of solutions is one."

Step-by-step explanation:

Hopefully the drawing helps visualize the problem.

The circle has a radius of 9 because the vertex is 9 units above the center of the circle.

The circle the parabola intersect only once and cannot intercept more than once.

The solution is "The maximum number of solutions is one."

Let's see if we can find an algebraic way:

The equation for the circle given as we know from the problem without further analysis is so far $x^2+y^2=r^2$ .

The equation for the parabola without further analysis is $y=ax^2+9$ .

We are going to plug $ax^2+9$ into $x^2+y^2=r^2$ for $y$ .

$x^2+y^2=r^2$

$x^2+(ax^2+9)^2=r^2$

To expand $(ax^2+9)^2$ , I'm going to use the following formula:

$(u+v)^2=u^2+2uv+v^2$ .

$(ax^2+9)^2=a^2x^4+18ax^2+81$ .

$x^2+y^2=r^2$

$x^2+(ax^2+9)^2=r^2$

$x^2+a^2x^4+18ax^2+81=r^2$

So this is a quadratic in terms of $x^2$

Let's put everything to one side.

Subtract $r^2$ on both sides.

$x^2+a^2x^4+18ax^2+81-r^2=0$

Reorder in standard form in terms of x:

$a^2x^4+(18a+1)x^2+(81-r^2)=0$

The discriminant of the left hand side will tell us how many solutions we will have to the equation in terms of $x^2$ .

The discriminant is $B^2-4AC$ .

If you compare our equation to $Au^2+Bu+C$ , you should determine $A=a^2$

$B=(18a+1)$

$C=(81-r^2)$

The discriminant is

$B^2-4AC$

$(18a+1)^2-4(a^2)(81-r^2)$

Multiply the (18a+1)^2 out using the formula I mentioned earlier which was:

$(u+v)^2=u^2+2uv+v^2$

$(324a^2+36a+1)-4a^2(81-r^2)$

Distribute the 4a^2 to the terms in the ( ) next to it:

$324a^2+36a+1-324a^2+4a^2r^2$

$36a+1+4a^2r^2$

We know that $a>0$ because the parabola is open up.

We know that $r>0$ because in order it to be a circle a radius has to exist.

So our discriminat is positive which means we have two solutions for $x^2$ .

But how many do we have for just $x$ .

We have to go further to see.

So the quadratic formula is:

$\frac{-B \pm \sqrt{B^2-4AC}}{2A}$

We already have $B^2-4AC}$

$\frac{-(18a+1) \pm \sqrt{36a+1+4a^2r^2}}{2a^2}$

This is t he solution for $x^2$ .

To find $x$ we must square root both sides.

$x=\pm \sqrt{\frac{-(18a+1) \pm \sqrt{36a+1+4a^2r^2}}{2a^2}}$

So there is only that one real solution (it actually includes 2 because of the plus or minus outside) here for x since the other one is square root of a negative number.

That is,

$x=\pm \sqrt{\frac{-(18a+1) \pm \sqrt{36a+1+4a^2r^2}}{2a^2}}$

means you have:

$x=\pm \sqrt{\frac{-(18a+1)+\sqrt{36a+1+4a^2r^2}}{2a^2}}$

$x=\pm \sqrt{\frac{-(18a+1)-\sqrt{36a+1+4a^2r^2}}{2a^2}}$ .

The second one is definitely includes a negative result in the square root.

18a+1 is positive since a is positive so -(18a+1) is negative

2a^2 is positive (a is not 0).

So you have (negative number-positive number)/positive which is a negative since the top is negative and you are dividing by a positive.

We have confirmed are max of one solution algebraically. (It is definitely not 3 solutions.)

If r=9, then there is one solution.

If r>9, then there is two solutions as this shows:

$x=\pm \sqrt{\frac{-(18a+1)+\sqrt{36a+1+4a^2r^2}}{2a^2}}$

r=9 since our circle intersects the parabola at (0,9).

Also if (0,9) is intersection, then

$0^2+9^2=r^2$ which implies r=9.

Plugging in 9 for r we get:

$x=\pm \sqrt{\frac{-(18a+1)+\sqrt{36a+1+4a^2(9)^2}}{2a^2}}$

$x=\pm \sqrt{\frac{-(18a+1)+\sqrt{36a+1+324a^2}}{2a^2}}$

$x=\pm \sqrt{\frac{-(18a+1)+\sqrt{(18a+1)^2}}{2a^2}}$

$x=\pm \sqrt{\frac{-(18a+1)+18a+1}{2a^2}}$

$x=\pm \sqrt{\frac{0}{2a^2}}$

$x=\pm 0$

$x=0$

The equations intersect at x=0. Plugging into $y=ax^2+9$ we do get $y=a(0)^2+9=9$ .

After this confirmation it would be interesting to see what happens with assume algebraically the solution should be (0,9).

This means we should have got x=0.

$0=\frac{-(18a+1)+\sqrt{36a+1+4a^2r^2}}{2a^2}$

A fraction is only 0 when it's top is 0.

$0=-(18a+1)+\sqrt{36a+1+4a^2r^2}$

Add 18a+1 on both sides:

$18a+1=\sqrt{36a+1+4a^2r^2$

Square both sides:

$324a^2+36a+1=36a+1+4a^2r^2$

Subtract 36a and 1 on both sides:

$324a^2=4a^2r^2$

Divide both sides by $4a^2$ :

$81=r^2$

Square root both sides:

$9=r$

The radius is 9 as we stated earlier.

Let's go through the radius choices.

If the radius of the circle with center (0,0) is less than 9 then the circle wouldn't intersect the parabola. So It definitely couldn't be the last two choices.

7 0

2 years ago

Read 2 more answers

An investment firm offers three types of equity investments,

Fudgin [204]

Answer:

The expected value of the total return rate for the firm's clients is C. 7.4%

Step-by-step explanation:

1. Let's review all the information given for solving the question:

Type of equity investments = A, B and C

Percentage of investment in each type of equity = 30% in A, 50% in B and 20% in C.

Rates of return of each type of equity investment = 10% for A, 6% for B and 7% for C.

2. Let's find the expected value of the total return rate for the investment firm:

Return rate for each type of investment = Percentage of investment * Rate of return

For A = 30% * 10% = 0.3 * 0.1 = 0.03

For B = 50% * 6% = 0.5 * 0.06 = 0.03

For C = 20% * 7% = 0.2 * 0.07 = 0.014

Total return rate = Return rate for A + Return rate for B + Return rate for C

Total return rate = 0.03 + 0.03 + 0.014 = 0.074

Total return rate = 0.074 * 100 = 7.4%

The expected value of the total return rate for the firm's clients is C. 7.4%

5 0

2 years ago

Read 2 more answers