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3 years ago

14

The angle of elevation of a ladder leaning against a wall is 48°. If the ladder is 25 feet long, how far is the base of the ladd

er from the wall?

1 answer:

ANTONII [103]3 years ago

7 0

Answer:

The base of the ladder to the wall is 16.73 feet.

Step-by-step explanation:

cos 48° = x/25

25 cos 48° = x

16.73 feet = x

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Planes A and B intersect.

stealth61 [152]

Answer:

Point x

Step-by-step explanation:

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3 years ago

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Five times the sum of 9 and some number is 145. What is the number?

Andrews [41]

Answer:

x=20

Step-by-step explanation:

5(x+9) =145 (watch carefully)

5x + 45 = 145

5x + 45 - 45 = 145 - 45

5x = 100

5x/5 (to cancel eachother out) then --> 100/5

x=20

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4 years ago

A rectangle has a length 6 meters longer than double the width. The perimeters is i44 meters. Find the dimensions of the rectang

Oksana_A [137]

Use the information to form an equation
x = width
x + 6 = length
perimeter = length + length + width + width
x + x + x + 6 + x + 6 = 44
4x + 12 = 44
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3 years ago

Element X decays radioactively with a half life of 12 minutes. If there are 160

Salsk061 [2.6K]

Answer:

It would take 75.8 minutes for the element to decay to 2 grams.

Step-by-step explanation:

The number of grams of element x, after t minutes, is given by the following equation:

$X(t) = X(0)(1-r)^{t}$

In which X(0) is the initial amount and r is the decay rate.

There are 160 grams of Element X

This means that X(0) = 160.

So

$X(t) = X(0)(1-r)^{t}$

$X(t) = 160(1-r)^{t}$

Half life of 12 minutes.

This means that X(12) = 0.5*X(0) = 0.5*160 = 80. So

$X(t) = 160(1-r)^{t}$

$80 = 160(1-r)^{12}$

$(1 - r)^{12} = 0.5$

$\sqrt[12]{(1 - r)^{12}} = \sqrt[12]{0.5}$

$1 - r = 0.9438$

So

$X(t) = 160(1-r)^{t}$

$X(t) = 160(0.9438)^{t}$

How long would it take for the element to decay to 2 grams?

This is t for which X(t) = 2. So

$X(t) = 160(0.9438)^{t}$

$2 = 160(0.9438)^{t}$

$(0.9438)^{t} = \frac{2}{160}$

$\log{(0.9438)^{t}} = \log{\frac{2}{160}}$

$t\log{0.9438} = \log{\frac{2}{160}}$

$t = \frac{\log{\frac{2}{160}}}{\log{0.9438}}$

$t = 75.8$

It would take 75.8 minutes for the element to decay to 2 grams.

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3 years ago

Please help! it’s for 20 points

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4 years ago