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DerKrebs [107]
3 years ago
10

Suppose you're flying a kite, and it gets caught at the top of the tree. You've let out all 100 feet of string for the kite, and

the angle that the string makes with the ground is 75 degrees. Instead of worrying about how to get your kite back, you wonder. How tall is that tree?

Mathematics
2 answers:
12345 [234]3 years ago
6 0
Check the picture below

recall your SOH CAH TOA

\bf in(\theta)=\cfrac{opposite}{hypotenuse}
\qquad \qquad 
% cosine
cos(\theta)=\cfrac{adjacent}{hypotenuse}

\\ \quad \\
% tangent
tan(\theta)=\cfrac{opposite}{adjacent}

we have,
the angle,
the hypotenuse,
we want the opposite side

which of those fellows have only that? ahhhh it has to be Ms Sine,
so let's ask her
\bf sin(\theta)=\cfrac{opposite}{hypotenuse}\implies sin(75^o)=\cfrac{x}{100}\implies 100\cdot sin(75^o)=x

the opposite side "x", is how tall the tree is

when taking the sine function, make sure your calculator is in Degree mode, since the angle is in degrees

hichkok12 [17]3 years ago
5 0
The answer to your problem is x= 96.6 ft
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Given f (x) = 6 (1- x), what is the value of f (-5)?
natta225 [31]

Answer: 36

Step-by-step explanation:

1) substitute x for 6

get f(-5)=6(1--5)= 6+30=46

5 0
3 years ago
Read 2 more answers
The area of a rectangle is 1,036 cm and its length is 74 cm.
Nikitich [7]

Answer:

(i) Breadth = 14 cm

(ii) Perimeter = 176 cm

Step-by-step explanation:

Given,

  • Area of a rectangle = 1036 cm²
  • Length = 74 cm

(i) Breadth = ?

We know that, Area of a rectangle = length × breadth.

Then,

1036 = 74 \times Breadth\\1036  \div 74 = Breadth\\\boxed{\bf\:14 \:cm = Breadth }

(ii) Perimeter of a rectangle = 2 (length + breadth)

Then,

Perimeter = 2(74 + 14)\\Perimeter = 2(88)\\\boxed{\bf\: Perimeter = 176 \: cm}

\rule{150pt}{2pt}

8 0
2 years ago
Suppose a die is tossed 5 times. what is the probability of getting exactly 2 fours?
Tasya [4]

Answer:

the probability of getting exactly 2 fours is 0.16

Step-by-step explanation:

The probability of obtaining a number that is four = ¹/₆

The probability of obtaining a non 4 number = 1 - ¹/₆ = ⁵/₆

The number of ways 2 fours can be arrange in five numbers = ⁵C₂ = 10 ways

If the die is tossed five times, the probability of the events is calculated as;

P = 10 x (¹/₆)² x (⁵/₆)³

P = 10 x (¹/₃₆) x  (¹²⁵/₂₁₆)

P = 10 x 0.02778 x 0.5787

P = 0.16

Therefore, the probability of getting exactly 2 fours is 0.16

7 0
2 years ago
Write and graph a system of inequalities that models the situation.
liubo4ka [24]

Answer:

The feasible region in the attached figure

Step-by-step explanation:

Let

x ----> the number of shirts

y ----> the number of pants

we know that

The cost of the shirts (number of shirts multiplied by the cost of one shirt) plus the cost of the pants (number of pants multiplied by the cost of one pant) must be less than or equal to $80

so

The inequality that represent this problem is

5x+8y\leq 80

using a graphing tool

The feasible region is the triangular shaded area

see the attached figure

7 0
3 years ago
Solve these simultaneous equations.<br> 4x – 7y = – 5<br> 3x – 2y = – 7<br> Solution: x=
AlexFokin [52]

Answer:

  1. \huge{x =  -  \frac{5}{4}  +  \frac{7}{4} y}
  2. \huge{x =  -  \frac{7}{3}  +  \frac{2}{3} y}

Step-by-step explanation:

1. 4x - 7y =  - 5

4x =  - 5 + 7y

\boxed{\green{x =  -  \frac{5}{4}  +  \frac{7}{4} y}}

y E R

○○•○○

2. 3x - 2y =  - 7

3x =  - 7 + 2y

\boxed{\green{x =  -  \frac{7}{3}  +  \frac{2}{3} y}}

y E R

5 0
3 years ago
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