How many solutions does the system (picture) have?

A man flies a kite at a height of 16 ft. The wind is carrying the kite horizontally from the man at a rate of 5 ft./s. How fast

Talja [164]

Answer:

4.41 feet per second.

Step-by-step explanation:

Please find the attachment.

We have been given that a man flies a kite at a height of 16 ft. The wind is carrying the kite horizontally from the man at a rate of 5 ft./s. We are asked to find how fast must he let out the string when the kite is flying on 34 ft. of string.

We will use Pythagoras theorem to solve for the length of side x as:

$x^2+16^2=34^2$

$x^2=34^2-16^2$

$x^2=900\\\\x=30$

Now, we will use Pythagorean theorem to relate x and y because we know that the vertical side (16) is always constant.

$x^2+16^2=y^2$

Let us find derivative of our equation with respect to time (t) using power rule and chain rule as:

$2x\cdot \frac{dx}{dt}+0=2y\cdot \frac{dy}{dt}$

We have been given that $\frac{dx}{dt}=5$ , $y=34$ and $x=30$ .

$2(30)\cdot 5=2(34)\cdot \frac{dy}{dt}$

$300=68\cdot \frac{dy}{dt}$

$\frac{dy}{dt}=\frac{300}{68}$

$\frac{dy}{dt}=4.4117647058823529$

$\frac{dy}{dt}\approx 4.41$

Therefore, the man must let out the string at a rate of 4.41 feet per second.

8 0

4 years ago

A vertical pole 6 feet long casts a shadow 55 inches long. Find the angle of elevation of the sun. Draw a diagram and find the a

ivolga24 [154]

A vertical pole(AB) 6 feet long casts a shadow(CB) 55 inches long as shown in the attached image. Since the angle of elevation of sun is $\angle C$ . We hav to find the value of $\angle C$ .

Firstly, we will change the dimensions of pole(in feet) to the dimension of shadow( in inches) . So, that the dimensions of pole and shadow are same.

Since, 1 feet = 12 inches.

6 feet = $6 \times 12 = 72$ inches.

Now, let us consider the triangle ABC in the attached image,

We have to find $\angle C$

$tan\Theta =\frac{Perpendicular}{base}$

$\tan C$ = $\frac{AB}{BC}= \frac{72}{55}$

= 1.309

$= 52.6^{\circ} = 53^{\circ}$

8 0

4 years ago

Read 2 more answers

What factors dose 32 and 36 have in common

Bingel [31]

One way to approach this is to look at the difference between 32 and 36, which is 4. The greatest common factor of two numbers cannot be larger than the difference between the two numbers and must be a factor of the difference. Since both 32 and 36 are divisible by 4, the greatest common factor is 4.
Another way to determine the greatest common factor is to find all the factors of the numbers and compare them. 
The factors of 32 are 1, 2, 4, 8, 16, and 32. 
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. 
The common factors are 1, 2, and 4. Therefore, the greatest common factor is 4. 

The greatest common factor can also be calculated by identifying the common prime factors and multiplying them together. 
The prime factors of 32 are 2, 2, 2, 2, and 2. 
The prime factors of 36 are 2, 2, 3, and 3. 
The prime factors in common are 2 and 2, so the greatest common factor is 2 x 2 = 4.

8 0

4 years ago

Which function has an inverse function?

Kitty [74]

F(X)=X^4/7 +27 .......

6 0

3 years ago

Read 2 more answers

Which function has a vertex on the y-axis?

Vinil7 [7]

Answer: i just took it on the unit test review and got it wrong because someone said it was (x-2)^2. it is (x-2)(x+2)

Step-by-step explanation:

8 0

3 years ago