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2 years ago

9

Susan made 2 identical necklaces, each having beads and a pendent. The total cost of the beads and pendents for both necklaces w

as $9.80. If the beads cost a total of 3.40, how much did each pendant cost?

2 answers:

Charra [1.4K]2 years ago

7 0

Step-by-step explanation:

$ 3.15 each pendents .......

pogonyaev2 years ago

5 0

$3.15 each pendent.

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In a right triangle, the side opposite a 33 degree angle is 17 units. What is the length of the side adjacent to that angle to t

AnnyKZ [126]

Answer:

The length of the side adjacent to that angle is 26 units

Step-by-step explanation:

We are given

In a right triangle, the side opposite a 33 degree angle is 17 units

Firstly, we will draw diagram

we can use trig

$cot(33)=\frac{x}{17}$

now, we can solve for x

$x=17\times cot(33)$

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So,

The length of the side adjacent to that angle is 26 units

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The volume of the region R bounded by the x-axis is: $\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}$

<h3>What is the volume of the solid (R) on the X-axis?</h3>

If the axis of revolution is the boundary of the plane region and the cross-sections are parallel to the line of revolution, we may use the polar coordinate approach to calculate the volume of the solid.

From the given graph:

The given straight line passes through two points (0,0) and (2,8). Thus, the equation of the straight line becomes:

$\mathbf{y-y_1 = \dfrac{y_2-y_1}{x_2-x_1}(x-x_1)}$

here:

(x₁, y₁) and (x₂, y₂) are two points on the straight line

Suppose we assign (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 8) from the graph, we have:

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Now, our region bounded by the three lines are:

y = 0
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Similarly, the change in polar coordinates is:

x = rcosθ,
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Therefore;

rsinθ = 0 i.e. r = 0 or θ = 0
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rsinθ = 4(rcosθ) ⇒ tan θ = 4; θ = tan⁻¹ (4)

⇒ r = 0 to r = 2/cosθ
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Then:

$\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^2 (rdr d\theta )}$

$\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}$

Learn more about the determining the volume of solids bounded by region R here:

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2 years ago

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