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Alex777 [14]
2 years ago
12

10. RECREATION In a game of kickball, Rickie has to kick the

Mathematics
1 answer:
wel2 years ago
4 0

Answer:

The angle Rick must kick the ball to score is an angle between the lines BX and BZY which is less than or equal to 32°

Step-by-step explanation:

The given measures of the of the angle formed by the tangent to the given circle at X and the secant passing through the circle at Z and Y are;

m\widehat{XZ}  = 58^{\circ}

m\widehat{XY}  = 122^{\circ}

The direction Rick must kick the ball to score is therefore, between the lines BX and BXY

The angle between the lines BX and BXY = ∠XBZ = ∠XBY

The goal is an angle between m\widehat{XY}

Let 'θ' represent the angle Rick must kick the ball to score

Therefore the angle Rick must kick the ball to score is an angle less than or equal to ∠XBZ = ∠XBY

By the Angle Outside the Circle Theorem, we have;

The angle formed outside the circle = (1/2) × The difference of the arcs intercepted by the tangent and the secant

\therefore \angle XBZ = \dfrac{1}{2} \times \left (m\widehat{XY}  -m\widehat{XZ} \right)

We get;

∠XBZ = (1/2) × (122° - 58°) = 32°

The angle Rick must kick the ball to score, θ = ∠XBZ ≤ 32°

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3 years ago
PLEASE HURRY. 55P WRONG ANSWERS GET REMOVED!!!!!!!
sertanlavr [38]
  • <em>Answer:</em>

<em>1172. 08 in²</em>

  • <em>Step-by-step explanation:</em>

<em>Hi there !</em>

<em>A(prism) = 2(lw + lh + wh) - Ab(cylinder)</em>

<em>= 2(16*11 + 16*11 + 11*11) - πr²</em>

<em>= 2(176 + 176 + 121) - 3.14*16</em>

<em>= 2*473 - 50.4</em>

<em>= 946 - 50.24</em>

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<em>= 50.24 + 226.08</em>

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<em>A(total) = 895.76in² + 276.32in² = 1172.08 in²</em>

<em>Good luck !</em>

6 0
2 years ago
A rectangle has a length that is 2 meters more than the width. The area of the rectangle is 288 square meters. Find the dimensio
Rufina [12.5K]

Answer:

L = 18 and w = 16

Step-by-step explanation:

The area of a rectangle is found by A = l*w. Since the length here is 2 more than the width or 2 + w and the width is w, substitute these values and A = 288 to solve for w.

A = l*w\\288 = w(2+w)\\288 = w^2 + 2w

To solve for w, move 288 to the other side by subtraction. Then factor and solve.

w^2 + 2w  - 288 = 0 \\(w +18)(w-16) = 0\\

Set each factor equal to 0 and solve.

w - 16 = 0 so w = 16

w + 18 = 0 so w = -18

Since w is a side length and length/distance cannot be negative, then w = 16 is the width of the rectangle.

This means the length is 16 + 2 = 18.

7 0
2 years ago
Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for the constant of integration.
trasher [3.6K]

Answer:

\frac{xe^{7x}}{7} + \frac{e^{7x}}{49}

Step-by-step explanation:

Given the integral equation

\int\limits{xe^{7x}} \, dx \\

According to integration by part;

\int\limits {u} \, dv = uv +  \int\limits {v} \, du

u = x, dv = e^7x

du/dx = 1

du = dx

v = \int\limits {e^{7x}} \, dx \\v = e^7x/7

Substitute the given values into the formula;

\int\limits {xe^{7x}} \, dx = x(e^{7x}/7) + \int\limits ({e^{7x}/7}) \, dx\\\int\limits {xe^{7x}} \, dx = \frac{xe^{7x}}{7} + \frac{e^{7x}}{7*7} \\\int\limits {xe^{7x}} \, dx = \frac{xe^{7x}}{7} + \frac{e^{7x}}{49}

3 0
2 years ago
Whitney has a sprinkler than covers a circular area with diameter 24 feet. What is the area of lawn that the sprinkler covers? (
grin007 [14]
Answer:
I think the answer is 7.64331210191

Explanation:
I divided 24 by 3.14 and got 7.6433121091
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