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Guest asker, 

If you want some clarification, please ask. 

Thanks asinus,  

I got the same answser as you but my answer invlolved some calculus.

       To find the minimum distance between the points   \((12,0)\;\; and \;\;(x, \sqrt{49-x^2}+5)\)

I also graphed it to as a second way to solve it.

Here is my gaphical solution.  If you right click on the point C you can drag it and see what difference it makes to the distance CD.

Simplified to:

\(-i + 1\over4i - 1\)

Simplified with the difference of squares:

\((-i + 1)(4i + 1)\over(4i)^2 - 1\)

Simplified to:

\(-4i^2 + 4i - i + 1\over16i^2 - 1\)

Substituted to:

\(3i + 5\over-17\)

Thus, the expression is simplified to:

\(3i + 5\over-17\)

3x^2 + 10x + 8 =

3x^2 + 6x + 4x + 8 =

2(3x + 4) + x(3x + 4) = (3x + 4)(x + 2)

so (3x + A)(x + B) = (3x + 4)(x + 2).

4 - 2 = 2,

thus our answer is 2.

First we can see that the sum of the first n terms ends with a denominator of 32.

If the denominator multiplies by 2 every time, then we know the last term has a denominator of 32.

Thus n = 4.

This is true because the first term can be 8/32, second term is 4/32, third term is 2/32, and the fourth term is 1/32,

adding up the four terms is 15/32, so there are 4 terms, and that is the explanation why n = 4.

3 * (1) + 1 * (5) + 2 * (10) + 1 * (25) = 3 + 5 + 20 + 25 = 53 cents.

You have 53 cents or 0.53$.

What is the minimum distance between C and D?

Hello Guest!

The sensor describes an arc of a circle:

\(f(x)=\sqrt{7^2-x^2}+9-4\)

The point of closest distance from the sensor to D is on the line (0,5) --> D:

\(g(x)= -\frac{5}{12}x+5\\ f(x)=g(x)\)

\(\sqrt{7^2-x^2}+5=-\frac{5}{12}x+5\\ 49-x^2=\frac{25x^2}{144}\\ \frac{169x^2}{144}=49\\ x=\frac{7\cdot 12}{13}\\ x=6.\overline{461538}\\ y=-\frac{5}{12}\cdot x+5\\ y=2.\overline{307692}\)

What is the minimum distance between C and D?

\(\overline{CD}_{min}=\sqrt{(12-x)^2+y^2}=\sqrt{(12-6.4615)^2+2.3077^2}\\ \color{blue}\overline{CD}_{min}=6\)

  !

answered

thank u so much that u helped me out, u really made my day😁

a) Finance option: The monthly payments will be==$183.67

     Credit card option: The monthly payments will be: $199.96

b) Finance option: [183.67 x 6 months - 1,150 - 100 credit]==$52.02 - interest charge.

     Credit card option: [199.96  x  6 months - 1,150 ]==$49.76 - interest charge.

c) Finance option will cost him: 183.67 x 6 ==$1,102.02 - total cost

    Credit card option will cost him: 199.96 x 6 ==$1,199.76 - total cost

Conclusion: Finance option is a better deal because he gets $100 credit up front.

would be nice!!

Excess = 15 × 3 = 45
3u + 6u = 9u
9u = 153 - 45 = 108
1u = 108÷ 9 = 12
Elmo = 3u + 45 = 3 × 12 + 45 = 81 plates

thanks!!

You must convert the interest rate of 9.8% from weekly compound to monthly compound.

9.8% compounded weekly==9.83082720035% compounded monthly

PV=2240; FV=0; PMT=80;R=0.0983082720035/12; N=Log((PMT-FV*R) /(PMT-R*PV)) / Log(R+1)

N==31.94 ==~32 months to pay off her line of credit loan.

thank u so much!

PV ==12,000 / [1  +  0.075/4]^(3*4)

PV ==12,000 / [1  +  0.01875]^12

PV ==12,000 / 1.2497163766

PV ==$9,602.18 - maximum amount that Andy can borrow.

So, the correct answer is 24.

That's not right. It's 21%. Not 12%

Use the fact that 12% of 121 = 121 * 0.12. (Commutative property) 121 * 0.12 = 14.52.

Use the fact that

\((x+y+z)^2=x^2+y^2+z^2+2(xy +xz+yz)\)

The possible values of f(3) are 3, 0, and -3, so the answer is 3*0 = 0.

You must roll at least 8 dice.