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vesna_86 [32]
2 years ago
11

Evaluate log12y2, given log12y = 16. 4 32 256 65,536

Mathematics
2 answers:
Ann [662]2 years ago
8 0
32 or 256 i didn’t understand exactly what you asked
Nostrana [21]2 years ago
4 0

The value of log₁₂ y² will be : 32

Explanation


log₁₂ y²

According to the property of logarithm, if there is any exponent in the number of log, then we can just take out that exponent part to the front of the log, like: log (a)ᵇ = b × log (a)

Here, the exponent in the number of log is 2. So, according to the above property, we will get: 2 log₁₂ y

Now, the value of log₁₂ y is given as 16. So,

2 log₁₂ y

⇒ 2 (16) = 32



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A curious student asks his math teacher: "I heard you have three daughters. How old are they?" The math teacher says: "Well, the
scZoUnD [109]

Answer:

There are 7 solutions.

The possible answers are:

The oldest daughter is 72 and the others are 1 and 1 and the room number is 74.

The oldest daughter is 36 and the others are 1 and 2 and the room number is 39.

The oldest daughter is 24 and the others are 1 and 3 and the room number is 28.

The oldest daughter is 18 and the others are 1 and 4 and the room number is 23.

The oldest daughter is 12 and the others are 2 and 3 and the room number is 17.

The oldest daughter is 12 and the others are 1 and 6 and the room number is 19.

The oldest daughter is 9 and the others are 1 and 8 and the room number is 18.

The first few solutions are laughable and unlikely, but all are possible.  

OR..

The clue that the sums of the daughters' ages is the room number is the sleeper.  The student's first response is that two possible age combinations meet the necessary conditions.  The teacher's reference to the "oldest daughter" resolves the ambiguity, so one of the solutions must consist of a set of ages in which at least two of the oldest daughters are the same age.

The prime factors of 72 are 2^3 *3^2.  Because one of the solutions requires the two oldest daughters to be the same age, only combination 6, 6, 2 would be admissible.  There are insufficient factors for any other combination in which the duplicate ages represent the oldest daughter.  The ages of these daughters sum to 14, which is the room number.  The other combination must therefore add to 14 and have an unique oldest age.  The combination 8, 3, 3 meets all conditions and is the answer.

4 0
2 years ago
Theo can paint a fence three times as fast as his sister can. Working together, they can paint a fence in 9 hours. How many hour
Deffense [45]

Answer:

12 hours

Step-by-step explanation:

Let Theo's siste can paint a fence in x times

Given.

Theo can paint a fence three times as fast as his sister can. Working together, they can paint a fence in 9 hours.

\frac{1}{x}+\frac{1}{3x} =\frac{1}{9}\\\frac{3+1}{3x} =\frac{1}{9} \\\frac{4}{3x}=\frac{1}{9}

Apply cross multiplication

x=\frac{9\times 4}{3}\\x=\frac{36}{3} \\x=12hours

Theo’s sister to paint the fence in 12 hours.

8 0
2 years ago
Nia wants the total weight of her luggage to be no more than 50 kilograms.she has three suitcases that weigh 15.8 kilograms,17.4
Stella [2.4K]

Answer:

The total is 49.5

Step-by-step explanation:

15.8+17.42+16.28

6 0
2 years ago
norma cut a triangle out of construction paper for an art project. the area of the triangle os 84.5 square centimeters. select t
qwelly [4]

Answer:

h = 13

Step-by-step explanation:

Given the area of a triangle as 84.5 .

The correct value to complete the formula to calculate for the height h is 13 .

Area of a triangle = 1/2 b x h

b = base

h = height

Using the above formula

84.5 = 1/2 x 13 x h

84.5 = 13/2 x h

84.5 = 6.5 x h

84.5 = 6.5h

Divide both sides by 6.5 to get h

84.5/6.5 = 6.5h /6.5

13 = h

h = 13

3 0
2 years ago
You are setting up a zip line in your yard. You map out your yard in a coordinate plane. An equation of the line representing th
Pachacha [2.7K]
Solving this problem needs the distance formula of point to a line.

The formula is:

distance = | a x + b y + c | / √  (a^2 + b^2)

 
So we are given the equation: y = 2 x + 4

Rewriting this would be: y – 2 x – 4 = 0 ->  a = -2, b = 1, c = -4

 We are also given the points:

(-4, 11) = (x, y)

 Plugging it in the distance formula at points (x, y):

distance = | -2 * -4 + 1 * 11 + -4 | / √ [(- 2)^2 + (1)^2]

= 15 / √ (5)

= 6.7

 So the tree is approximately 6.7 feet away from the zip line.
4 0
2 years ago
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