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Reptile [31]
3 years ago
10

caleb and emily are standing 100 yards from each other. caleb looks up at a 45 degree angle to see a hot air balloon. Emily look

s yup at a 60 degree angle to see the same hot air ballon. approximate how far is the hot air ballon off the ground?

Mathematics
2 answers:
Sunny_sXe [5.5K]3 years ago
8 0
Check the picture below.

thus then

\bf \begin{cases}
y=100-a\\
y=a\sqrt{3}
\end{cases}\implies 100-a=a\sqrt{3}\implies 100=a+a\sqrt{3}
\\\\\\
100=a(1+\sqrt{3})\implies \boxed{\cfrac{100}{1+\sqrt{3}}=a}
\\\\\\
\textit{what is the altitude \underline{y} then?}\qquad y=100-a
\\\\\\
y=100-\cfrac{100}{1+\sqrt{3}}\implies y\approx 63.39745962156~yards

-Dominant- [34]3 years ago
8 0

Answer:

63.4 Yards

Step-by-step explanation:

B.

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ivann1987 [24]

9514 1404 393

Answer:

  • large: 55 lb
  • small: 30 lb

Step-by-step explanation:

Let x and y represent the weights of the large and small boxes, respectively. The problem statement gives rise to the system of equations ...

  x + y = 85 . . . . . combined weight of a large and small box

  70x +50y = 5350 . . . . combined weight of 70 large and 50 small boxes

We can subtract 50 times the first equation from the second to find the weight of a large box.

  (70x +50y) -50(x +y) = (5350) -50(85)

  20x = 1100 . . . . simplify

  x = 55 . . . . . . . divide by 20

Using this in the first equation, we can find the weight of a small box.

  55 +y = 85

  y = 30 . . . . . . . subtract 55

A large box weighs 55 pounds; a small box weighs 30 pounds.

4 0
2 years ago
Metal A has a density of 12.7 g/cm3.
stira [4]

Using the given information, the density of metal B is 8.58 g/cm³

<h3>Calculating density </h3>

From the question, we are to determine the density of metal B

From the given information,

55 g of metal A is combined with metal B to create an alloy with mass 90 g

∴ Mass of metal B in the alloy = 90 g - 55 g = 35 g

Now, we will determine the volume of metal A in the alloy

Using the formula,

Density = Mass / Volume

∴ Volume = Mass / Density

Volume of metal A in the alloy = 55/12.7

Volume of metal A in the alloy = 4.33 cm³

Then, we will determine the volume of the alloy

Volume of the alloy = 90/10.7

Volume of the alloy = 8.41 cm³

∴ Volume of metal B in the alloy = 8.41 cm³- 4.33 cm³

Volume of metal B in the alloy = 4.08 cm³

Now, for the density of metal B

Density = mass / volume

Density of metal B = 35 / 4.08

Density of metal B = 8.58 g/cm³

Hence, the density of metal B is 8.58 g/cm³.

Learn more on Calculating density here: brainly.com/question/13986137

#SPJ1

5 0
1 year ago
Find the area of trapezium where area=5cm base=6cm height=8cm
Jlenok [28]

Answer:

44cm2

Step-by-step explanation:

[8×(5+6)]/2

=(8×11)/2

=88/2

=44cm2

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Answer:

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