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3 years ago

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Evie and Sophie are planning a cement patio by their swimming pool. A contractor says the cement will weigh 61/3 tons. How many

loads,will it take for Evie and Sophie to haul all of the cement in their pickup truck, which can carry 3/4 tons?

2 answers:

creativ13 [48]3 years ago

4 0

Answer: There are approximately 9 loads.

Step-by-step explanation:

Number of tons the cement weigh is given by

$6\dfrac{1}{3}\ tons\\=\dfrac{19}{3}$

Weight of each load = $\dfrac{3}{4}\ tons$

So, Number of tons is given by

$\dfrac{\text{Weight of cement}}{\text{weight of each load}}\\\\=\dfrac{\dfrac{19}{3}}{\dfrac{3}{4}}\\\\=\dfrac{19}{3}\times \dfrac{4}{3}\\\\=\dfrac{76}{9}\\\\=8.4\\\\\approx 9\ loads$

Hence, there are approximately 9 loads.

olganol [36]3 years ago

3 0

Convert the 6 1/3 tons into an improper fraction:

6 1/3 = 19/3 tons.

Divide 19/3 tons by 3/4 tons per load:

19/3 / 3/4 = 19/3 * 4/3 = 76/9 = 8.4, so it will take 9 trips.

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Step-by-step explanation:

A = LW

A = (8x - 2)(4)

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3 years ago

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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:

<u>Part a</u>

A chord is a <u>line segment</u> with endpoints on the <u>circumference</u> of the circle.

The diameter is a <u>chord</u> 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.

<u>Part b</u>

The <u>tangent</u> of a circle is always <u>perpendicular</u> to the <u>radius</u>.

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 <u>tan trigonometric ratio</u> 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.).

<u>Part c</u>

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

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).

<u>Part d</u>

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 <u>maximum height</u> of the handle from the ground before the contents start spilling out, find the <u>height from center of the wheel</u> (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)

------------------------------------------------------------------------------------------

<u>Circle Theorem vocabulary</u>

<u>Secant</u>: a straight line that intersects a circle at two points.

<u>Arc</u>: the curve between two points on the circumference of a circle

<u>Intercepted arc</u>: 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.

<u>Tangent</u>: a straight line that touches a circle at only one point.

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The length of a rectangle is 5 m less than twice the width, and the area is 33 m. Find the dimensions of the rectangle.

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Check the picture below

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A change jar contains nickels, dimes and quarters. The total amount of money in the jar is $1.90. The amount of nickels is one m

telo118 [61]

Answer:

Number of dimes = 3

Number of nickels = 7

Number of quarters = 5

Step-by-step explanation:

Let x be the number of dimes in the jar.

The amount of nickels is one more than twice the number of dimes, then the amount of nickels is $2x+1.$

The number of quarters is one half the total number of nickels and dimes, so the number of quarters is $\frac{1}{2}(x+2x+1)=\frac{1}{2}(3x+1)$

Fill in the table

$\begin{array}{ccc}&\text{Number of coins}&\text{Value in these coins in cents}\\ \\\text{Dimes}&x&10x\\\text{Nickels}&2x+1&5(2x+1)\\\text{Quarters}&\frac{1}{2}(3x+1)&25\cdot \frac{1}{2}(3x+1)\end{array}$

Thus, the total sum in cents is

$10x+5(2x+1)+\dfrac{25}{2}(3x+1)\\ \\=10x+10x+5+\dfrac{75}{2}x+\dfrac{25}{2}\\ \\=20x+37.5x+5+12.5\\ \\=57.5x+17.5$

The total amount of money in the jar is $1.90 that is 190 cents. So,

$57.5x+17.5=190\\ \\575x+175=1,900\ [\text{Multiplied by 10}]\\ \\575x=1,900-175\\ \\575x=1,725\\ \\x=3$

Number of dimes = 3

Number of nickels = 7

Number of quarters = 5

Check the total amount of money in the jar:

$3\cdot 10+7\cdot 5+5\cdot 25=30+35+125=190\ cents =\$1.90$

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3 years ago