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3 years ago

A 12-foot wire supports a tree creating a 48 degreee angle. What is the closest distance up the tree that the wire reaches?

Mathematics

1 answer:

BartSMP [9]3 years ago

5 0

The closest distance up the tree where the wire reaches is 17.93 foot.

Explanation:

Given-

Length of the wire, L = 12 foot

angle, Ф= 48°

Distance upto which the wire reaches the tree, x = ?

We know,

cos Ф = base/ hypotenuse

cos 48° = 12/ x

0.669 = 12/x

x = 17.93 foot

Therefore, the closest distance up the tree where the wire reaches is 17.93 foot.

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One card is selected at random from a deck of card. Determine the probability that the card selected is not a 4

Ganezh [65]

Answer:

12/13

Step-by-step explanation:

A probability is the number of desired outcomes over the total number of outcomes.

Assuming that this is a standard deck of playing cards, there will be 52 cards, and there will be 4 "4" cards.

First, find the number of desired outcomes, and put it over the total number of outcomes.

Out of the total number of outcomes (52), there are 4 outcomes that are not wanted, hence the equation is:

52 - 4 = 48

So out of the 52 possible outcomes, 48 are desired. Set up the fraction and

simplify:

48/52

/4 /4

= 12/13

7 0

3 years ago

The ratio of the geometric mean and arithmetic mean of two numbers is 3:5, find the ratio of the smaller number to the larger nu

IgorC [24]

Answer:

$\frac{1}{9}$

Step-by-step explanation:

Let the numbers be x,y, where x>y

The geometric mean is

$\sqrt{xy}$

The Arithmetic mean is

$\frac{x + y}{2}$

The ratio of the geometric mean and arithmetic mean of two numbers is 3:5.

$\frac{ \sqrt{xy} }{ \frac{x + y}{2} } = \frac{3}{5}$

We can write the equation;

$\sqrt{xy} = 3$

$xy = 9 - - - (2)$

and

$\frac{x + y}{2} = 5$

$x + y = 10 - - - (2)$

Make y the subject in equation 2

$y = 10 - x - - - (3)$

Put equation 3 in 1

$x(10 - x) = 9$

$10x - {x}^{2} = 9$

${x}^{2} - 10x + 9 = 0$

$(x - 9)(x - 1) = 0$

$x =1 \: or \: 9$

When x=1, y=10-1=9

When x=9, y=10-9=1

Therefore x=9, and y=1

The ratio of the smaller number to the larger number is

$\frac{1}{9}$

3 0

2 years ago

A spinner used in a board game is divided into 12 equally sized sectors. Seven of these sectors indicate that the player should

forsale [732]

Answer:

9.3 inches

Step-by-step explanation:

The computation of the radius of the spinner be given below:

Let us assume the same be x

We know that

Total area of the sector = one-sixth of the total area of the spinner

Given that

45.1 = 1 ÷ 6 × π × r^2

r^2 = 45.1 × 6 ÷ π

r^2 = 86.1

r = 9.279

= 9.3 inches

3 0

3 years ago

What is the value of 7 in: a. 3.7 b. 12.07 c. 200.711

masya89 [10]

A. seven tents b. seven hundredths c. seven tents

6 0

3 years ago

If you have $2500 how many board feet can you buy if the cost per board foot is $3.217

igor_vitrenko [27]

777 when rounded, or 777.1215418091389

3 0

3 years ago