teh table shows a number of balls that fit into containers each container holds the same amount of balls

You work at a pioneer historical site. On this site you have handcarts. One cart has a handle that connects to the center of the

Gelneren [198K]

Answer:

a) see below

b) radius = 16.4 in (1 d.p.)

c) 18°. Yes contents will remain. No, handle will not rest on the ground.

d) Yes contents would spill. Max height of handle = 32.8 in (1 d.p.)

Step-by-step explanation:

Part a

A chord is a line segment with endpoints on the circumference of the circle.

The diameter is a chord that passes through the center of a circle.

Therefore, the spokes passing through the center of the wheel are congruent chords.

The spokes on the wheel represent the radii of the circle. Spokes on a wheel are usually evenly spaced, therefore the congruent central angles are the angles formed when two spokes meet at the center of the wheel.

Part b

The tangent of a circle is always perpendicular to the radius.

The tangent to the wheel touches the wheel at point B on the diagram. The radius is at a right angle to this tangent. Therefore, we can model this as a right triangle and use the tan trigonometric ratio to calculate the radius of the wheel (see attached diagram 1).

$\sf \tan(\theta)=\dfrac{O}{A}$

where:

$\theta$ is the angle
O is the side opposite the angle
A is the side adjacent the angle

Given:

$\theta$ = 20°
O = radius (r)
A = 45 in

Substituting the given values into the tan trig ratio:

$\implies \sf \tan(20^{\circ})=\dfrac{r}{45}$

$\implies \sf r=45\tan(20^{\circ})$

$\implies \sf r=16.37866054...$

Therefore, the radius is 16.4 in (1 d.p.).

Part c

The measure of an angle formed by a secant and a tangent from a point outside the circle is half the difference of the measures of the intercepted arcs.

If the measure of the arc AB was changed to 72°, then the other intercepted arc would be 180° - 72° = 108° (since AC is the diameter).

$\implies \sf new\: angle=\dfrac{108^{\circ}-72^{\circ}}{2}=18^{\circ}$

As the handle of the cart needs to be no more than 20° with the ground for the contents not to spill out, the contents will remain in the handcart at an angle of 18°.

The handle will not rest of the ground (see attached diagram 2).

Part d

This can be modeled as a right triangle (see diagram 3), with:

height = (48 - r) in
hypotenuse ≈ 48 in

Use the sin trig ratio to find the angle the handle makes with the horizontal:

$\implies \sf \sin (\theta)=\dfrac{O}{H}$

$\implies \sf \sin (\theta)=\dfrac{48-r}{48}$

$\implies \sf \sin (\theta)=\dfrac{48-45\tan(20^{\circ})}{48}$

$\implies \theta = 41.2^{\circ}\:\sf(1\:d.p.)$

As 41.2° > 20° the contents will spill out the back.

To find the maximum height of the handle from the ground before the contents start spilling out, find the height from center of the wheel (setting the angle to its maximum of 20°):

$\implies \sin(20^{\circ})=\dfrac{h}{48}$

$\implies h=48\sin(20^{\circ})$

Then add it to the radius:

$\implies \sf max\:height=48\sin(20^{\circ})+45\tan(20^{\circ})=32.8\:in\:(1\:d.p.)$

(see diagram 4)

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Circle Theorem vocabulary

Secant: a straight line that intersects a circle at two points.

Arc: the curve between two points on the circumference of a circle

Intercepted arc: the curve between the two points where two chords or line segments (that meet at one point on the other side of the circle) intercept the circumference of a circle.

Tangent: a straight line that touches a circle at only one point.

7 0

1 year ago

you are asked to solve for y in the equation -3=5y-2x , given that x= -4 what is the first step you will take

Genrish500 [490]

First step is replacing x with -4. => -3=5y+8 => 5y= -8-3 => y =-11/5

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2 years ago

PLS HELP ME PLS SOVLE THIS WITH THE LIKE TERMS I ONLY HAVE 25 MINS TO FINISH THIS

Basile [38]

Answer:

Step-by-step explanation:

Here are the 3 answers you needed :)!!!

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3 years ago

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The perimeter of the base of a regular quadrilateral prism is 32 cm. The height of the prism is 2 times greater than the length

horsena [70]

A regular quadrilateral prism has 12 edges. It is given perimeter of the base 32 cm. Length of each edge of base will be 32÷4=8 cm. The 4 edges at the top will also have the same number of edges that is 4 with measure 8cm each.

Given: The height of the prism is 2 times greater than the length of the base edge.Height of prism = 2(8)= 16cm. Number of edges with measure 16 cm is 4.

Sum of all the 12 edges= 8+8+8+8+16+16+16+16+8+8+8+8=128 cm.

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2 years ago

A given polygon has an area of 42 square feet. If the polygon is enlarged by a linear scale factor of 5, what is the area of the

Fittoniya [83]

Answer:

1050 ft²

Step-by-step explanation:

Enlarging the polygon by a factor of 5 has the effect of increasing the area by a factor of 5², that is 25

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teh table shows a number of balls that fit into containers each container holds the same amount of balls​

teh table shows a number of balls that fit into containers each container holds the same amount of balls