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## Keys to Chemistry, Calculus, Literature and More

### Newark, DE (19711)

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# Jack's Responses in WyzAnt Answers

#### a ladder is 22 ft long. the base of the ladder is 18 ft from the house. how high is the wall? round to the nearest tenth.

homework help

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Asked by Jeanne from Florence, MA
20

Assuming that the house is perpenidcular to the ground on which the ladder stands, use the Pythagorean Theorem for the sides of right triangles:

a2 + b2  =  c2

In this problem a = 18, b is the unknown, and c is the length of the ladder (the hypotenuse of the triangle).

182 + b2  =  222   or

b2  =  222 - 182

b2  =  484 - 324

b2  =  160

b    =  √160  =  12.6 ft.

(It would be hard to climb that ladder because it is farther away from the wall than the height of the place where it touches the house)

#### The area of a rectangle is 252 square feet. If the perimeter is 66 feet, find the length and width of a rectangle?

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Asked by Jesse from Mount Sterling, KY
10

Hello, Jesse --

You need to use your information about area and perimeter to set up two equations with two variables representing length and width of the rectangle. Then you will set up a quadratic equation. Let's use L for the length and W for the width of the rectangle:

For the perimeter:

2L + 2W = 66  or
L + W  = 33  or
W  = 33 - L

For the area:

LW =  252

Now substitute W = 33 - L from the first equation into the second one:

L(33 - L) = 252  or

33L - L2 = 252  or

L2 - 33L + 252 = 0

This can be solved by factoring, or by using the quadratic equation.

By factoring:

(L - 12)(L - 21) = 0  or

L = 12, or L = 21

In this case, let's use 21 because length is usually the longer dimension. Now we substitute L = 21 into the first equation to find W.

W = 33 - 21 or
W = 12

#### Stevens Market is selling 3 packs of toothpicks for \$0.87. How much will 10 packsof toothpicks cost at this price? Round your answer to the nearest cent.

Pre algebra help

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Asked by Brittany from Oklahoma City, OK
10

We can also set it up as a ratio:

(Original number of packs)/Original cost of those packs)  =  (New number of packs)/(New cost)

In this problem, that would be:

3/0.87  =  10/x     (where x is the cost of 10 packs)

Cross-multiplying, we get:

3x  =  8.70

x  =  2.90

Simplify. Express using exponents.

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Asked by Sarah from Boca Raton, FL
10

With instructions to use exponents, I would do it this way:

2n2(8) = 2(23)3 n2 = 2(29) n2 = 210 n2

This is exactly the same as Tamara's answer above, but with an explicit powr of 2.

#### What are all numerical solutions to the equation 2cos^2(ln(3x))+cos(ln(3x))-1=0

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Asked by Diana from Collingswood, NJ
10

Hello, Diana --

This will involve a u-substitution and a factored quadratic.

Let u = cos(ln(3x))

Then 2u+ u - 1 = 0

Factor:     (2u - 1)(u + 1) = 0

2u - 1  =  0    or   u + 1  = 0

u   =  1/2           u  =  -1

Resubstitute:

cos(ln(3x))  = 1/2      cos(ln(3x)) = -1

ln(3x)  =  pi/3                 ln(3x)  = pi

ln 3 + ln x   = pi/3          ln 3 + ln x  = pi

ln x = pi/3 - ln 3              ln x =  pi - ln 3

x  =  e(pi/3 - ln 3)              x  = e(pi - ln 3)

There may be other solutions that are integer multiples of the pi/3 and pi compnents.

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## Background Check Status for Jack M.

Jack M. passed a background check on 7/24/2012. You may run an updated background check on Jack once you send an email.