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Andrej [43]
3 years ago
6

Mountain officials want to know the length of a new ski lift from A to C , as shown in the figure below. They measure angle DAC

to be 32° . They then move 960 feet to point B and measure angle DBC to be 18° . What is the length of the new ski lift from A to C ? Round your answer to the nearest tenth of a foot.
Mathematics
1 answer:
Ede4ka [16]3 years ago
4 0
We assume that the hill is represented by points ACD  and the ski lift is represented by points BCD. From the description above, points CDB would have an angle of 90 degrees. Then, we would have:

sin (32) = CD / 960
CD = 508.72

tan 32 = 508.72 / AD
AD = 814.13

Therefore, the distance would be 814.13 - 508.72 = 305.4 ft.

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sdas [7]

Draw out a number line with the values 0, 5, 10, 15, 20, 25, 30, etc (basically multiples of 5)

Then plot a point at 25

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

Or you can draw out a number line with the multiples of 10, so with the values 0, 10, 20, 30, ...

Then plot a point at the exact midway point between 20 and 30 to represent the value 25

3 0
3 years ago
Solve for x.
Nonamiya [84]

-\dfrac{2}{3}(3x-4)+3x=\dfrac{5}{6}\ \ \ \ |\text{use distributive property}\\\\-\dfrac{2}{\not3_1}\cdot\not3^1x+\dfrac{8}{3}+3x=\dfrac{5}{6}\\\\-2x+3x+\dfrac{8}{3}=\dfrac{5}{6}\ \ \ \ |-\dfrac{8}{3}\\\\x=\dfrac{5}{6}-\dfrac{8}{3}\\\\x=\dfrac{5}{6}-\dfrac{8\cdot2}{3\cdot2}\\\\x=\dfrac{5}{6}-\dfrac{16}{6}\\\\\boxed{x=-\dfrac{11}{6}}

Other method:

-\dfrac{2}{3}(3x-4)+3x=\dfrac{5}{6}\ \ \ \ |\cdot6\\\\2(-2)(3x-4)+18x=5\\\\-4(3x-4)+18x=5\ \ \ \ |\text{use distributive property}\\\\-12x+16+18x=5\ \ \ \ |-16\\\\6x=-11\ \ \ \ |:6\\\\\boxed{x=-\dfrac{11}{6}}

7 0
3 years ago
Read 2 more answers
A metal hollow bar whose cross section and dimension are shown below weighs 8x10^3 kg/m^3 and measure 2m in length ..determine t
devlian [24]
1) We calculate the volume of a metal bar (without the hole).

volume=area of hexagon x length
area of hexagon=(3√3 Side²)/2=(3√3(60 cm)²) / 2=9353.07 cm²
9353.07 cm²=9353.07 cm²(1 m² / 10000 cm²)=0.935 m²

Volume=(0.935 m²)(2 m)=1.871 m³

2) we calculate the volume of the parallelepiped

Volume of a parallelepiped= area of the section  x length
area of the section=side²=(40 cm)²=1600 cm²
1600 cm²=(1600 cm²)(1 m² / 10000 cm²=0.16 m²
Volume of a parallelepiped=(0.16 m²)(2 m)=0.32 m³

3) we calculate the volume of a metal hollow bar:
volume of a metal hollow bar=volume of a metal bar -  volume of a parallelepiped

Volume of a metal hollow bar=1.871 m³ - 0.32 m³=1.551 m³

4) we calculate the mass of the metal bar

density=mass/ volume  ⇒ mass=density *volume

Data:
density=8.10³ kg/m³
volume=1.551 m³

mass=(8x10³ Kg/m³ )12. * (1.551 m³)=12.408x10³ Kg

answer: The mas of the metal bar is 12.408x10³ kg  or   12408 kg  


4 0
3 years ago
6.5/v = 3/11.7 <br> I need help help finding v
viva [34]

Answer:   =25.35

im sure its right

7 0
3 years ago
Read 2 more answers
A pair of reading glasses shows you an image of an object that is 3.1 times the object's actual size. So the scale factor of the
KiRa [710]

When given the scale factor and the factored size of the object, to find the original size, divide the factored size by the scale factor:


0.8 / 3.1 = 0.258 inches



3 0
4 years ago
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