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lana66690 [7]
2 years ago
10

A Ferris wheel car moves from point C to point D on the circle shown below: Circle A is shown with points C and D on the circle

and the central angle C A D marked 42 degrees. The diameter is 30 feet. What is the arc length the car traveled, to the nearest hundredth?
Mathematics
1 answer:
natali 33 [55]2 years ago
7 0

Answer:

10.99 feet

Step-by-step explanation:

The arc length when an angle of 360° is made is the perimeter of the circle.

Perimeter = π*Diameter = π*30 = 94.25 ft

To know the arc length when an angle of 42° is made, we need to use the following proportion

94.25 ft / x ft = 360° / 42°

x = 42/360*94.25

x = 10.99 ft

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Please answer this as fast as you can In the graphic above, ΔABC ≅ ΔEDC by: HL. AAS. AAA. SSS.
Masja [62]

Answer:

Step-by-step explanation:

Triangles by definition have 3 sides. If the sides are corresponding then it is beneficial to us if they are the same length as well. If all 3 sides in one triangle are equal in length to the corresponding sides in another triangle, then the triangles are congruent by SSS (side-side-side).  This is the case for us. Side EC is corresponding and congruent to side AC; side CD is corresponding and congruent to side CB; side ED is corresponding and congruent to side AB.

4 0
2 years ago
The path traveled by a bottlenose dolphin as it jumps out of water is modeled by the equation y = −0.4x2 + 3x, where y is the he
Tamiku [17]

Answer:

5 feet

Step-by-step explanation:

The path traveled by a bottlenose dolphin as it jumps out of water is modeled by the equation,

y=-0.4x^2+3x

where y is the height above water and x is the horizontal distance in feet.

If a beam of light is shone upward at an angle modeled by the equation

x+y=10

A beam of light hit the dolphin.

So, line must be intersect path of dolphin.

Using substation method,

Substitute y=10-x into dolphin equation.

10-x=-0.4x^2+3x

-0.4x^2+4x-10=0

x=\dfrac{-4\pm\sqrt{4^2-4(-10)(-0.4)}}{2(-0.4)}

x=5\text{ feet }

y=5\text{ feet }

Hence, The beam hit dolphin at 5 feet.

8 0
2 years ago
PLEASE HELP ME  Which of the following is the correct graph of the compound inequality 4p + 1 > −7 or 6p + 3 < 33? (1 poin
nikitadnepr [17]
The first inequality has solution
  4p > -8 . . . . . . subtract 1
  p > -2 . . . . . . . divide by 4
This is graphed as an open dot at -2, with shading to the right.

Neither inequality symbol includes "or equal to", so both dots are open dots. The appropriate choice is the first one:
  a number line with open circles at negative 2 and 5 with shading in between
4 0
2 years ago
Read 2 more answers
Darren invests $4,500 into an account that earns 5% annual interests. How much will be in the account after 10 years if the inte
xz_007 [3.2K]

We have been given that Darren invests $4,500 into an account that earns 5% annual interests. We are asked to find the amount in his account after 10 years, if the interest rate is compounded annually, quarterly, monthly, or daily.

We will use compound interest formula to solve our given problem.  

A=P(1+\frac{r}{n})^{nt}, where,

A = Final amount,

P = Principal amount,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year,

t = Time in years.

5\%=\frac{5}{100}=0.05  

When compounded annually, n=1:

A=4500(1+\frac{0.05}{1})^{1\cdot 10}

A=4500(1.05)^{10}

A=4500(1.6288946267774414)

A=7330.025820498\approx 7330.03

When compounded quarterly, n=4:

A=4500(1+\frac{0.05}{4})^{4\cdot 10}

A=4500(1.0125)^{40}

A=4500(1.6436194634870132)

A=7396.28758569\approx 7396.29

When compounded monthly, n=12:

A=4500(1+\frac{0.05}{12})^{12\cdot 10}

A=4500(1.00416666)^{120}

A=4500(1.64700949769)

A=7411.542739605\approx 7411.54

When compounded daily, n=365:

A=4500(1+\frac{0.05}{365})^{365\cdot 10}

A=4500(1.0001369863013699)^{3650}

A=4500(1.6486648137656943695)

A=7418.9916619456\approx 7419.00

Since amount earned will be maximum, when interest is compounded daily, therefore, Darren should use compounded daily interest rate.

4 0
2 years ago
Brody has his computer repaired at store A. His bill was:
PIT_PIT [208]

Initial repair cost = $1200

Gratuity = 15% of the initial repair cost

= 15% of 1200

=\frac{15}{100} (1200)

= 15 × 12

= 180

Hence, the gratuity for the service is $180.

4 0
2 years ago
Read 2 more answers
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