Janet is drawing the path formed by the parametric equations x=2+3 sin t and y=1-1/2cos t. Which curve did she draw??

Answer:

Tan(b°) = 3/4, which is equivalent to three fourths (C).

Step-by-step explanation:

Triangle JKL is a right triangle with angle K being the right angle and angle L equal to b°.

We will employ SOHCAHTOA principles from trigonometry to calculate the sides' values.

For triangle ∆JKL:

Sin(b°) = opposite/hypotenuse

Sin(b°) = 3/5

Cos(b°) = adjacent/hypotenuse

Cos(b°) = 4/5

Tan(b°) = 3/4.

From the earlier information, we have the values for each side of triangle ∆JKL.

Please refer to the attached diagram for the triangle (1).

Triangle ∆JKL is scaled with a factor of 2.

This implies multiplying each side of ∆JKL by 2, resulting in:

Opposite side = 2(3) = 6

Adjacent side = 2(4) = 8

Hypotenuse = 2(5) = 10.

To find tan(b°) for the new triangle, we use the tangent ratio:

Tan(b°) = opposite/adjacent.

Tan(b°) = 6/8.

Tan(b°) = 3/4.

Find the diagram for the new triangle included (2).

Diagram 3 provides a depiction of both triangles.

As shown, the angle remains unchanged when a triangle is scaled by a factor.

Thus, we conclude that tan(b°) = three fourths (C).

Answer:

The highest number of long-sleeved shirts that can be ordered is 8

and

The lowest number of long-sleeved shirts that can be acquired is 0

Step-by-step breakdown:

Let y denote the quantity of short sleeves and x indicate the quantity of long sleeves.

According to the stipulated conditions:

Members of a school club are purchasing coordinating shirts. They understand that a minimum of 25 members will opt for a shirt.

therefore, we have;

               or

....[1]

Given that long-sleeved shirts are priced at $10 each and short-sleeved shirts at $5 each.

Thus;

The total expense for long sleeves amounts to 10x and

the total cost of short sleeves is 5y

Moreover; the club has a budget that does not exceed $165

therefore;

 

  or

......[2]

By plotting the inequality functions:

Graphing equations [1] and [2] produces a maximum at the coordinates (8, 17)

thus, x= 8.

Taking the minimum value of x =0 results in y falling between 25 and 33.

consequently, the solution space is situated between the intersecting lines to the left.

In conclusion, a maximum of 8 long-sleeved shirts can be obtained, while the minimum number of long-sleeved shirts that can be bought is 0

6 × 10 × 10 × 10 × 10 = Step-by-step breakdown: The exponent of any number reveals how many times that number is multiplied. It signifies the power applied to a number indicating how often that number is multiplied. Here, 10 is used four times, indicating an exponent of 4 for 10. Therefore, the expression can be represented as:

Let's apply the Pythagorean theorem to determine whether a triangle could be formed.

Assuming we have two wooden dowels each measuring 8 inches, we can break one dowel in half, resulting in two pieces of 4 inches each.

Now we have three wooden dowels with lengths of 4 inches, 4 inches, and 8 inches.

According to the Pythagorean theorem:

a² + b² = c²
4² + 4² = 8²
16 + 16 = 64
34 ≠ 64

To form a triangle, the length of the cut wooden dowel needs to exceed that of the uncut dowel.

I also visually attempted this exercise on paper, cutting according to the assumed dimensions. No triangle can be constructed with these pieces. 

He gives his sister 6 stones.