1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
faust18 [17]
3 years ago
8

Clark Kent and Lois Lane were laying on a blanket, enjoying a relaxing picnic when Clark noticed a giant asteroid approaching Ea

rth. Clark calculates the angle of elevation of the asteroid's approach to be 62°. Lois' penthouse apartment is also in the pathway of the asteroid's approach, 100 feet above ground. Clark's eye is 75 feet from the base of Lois' building. Will the asteroid take out Lois' penthouse apartment?
Mathematics
1 answer:
Nezavi [6.7K]3 years ago
3 0

Answer:

The asteroid will not take out Lois' penthouse.

Step-by-step explanation:

Since the distance between Clark and the base of Lois' building is x = 75 feet and the asteroid is at an angle of elevation of Ф = 62°. These two components form a right-angled triangle with opposite side h which is the height of the asteroid above the ground.

So, by trigonometric ratios,

tanФ = h/x

h = xtanФ

h = 75 ft × tan62°

h = 75 ft × 1.8807

h = 141.1 feet

Since h = height of asteroid above the ground = 141.1 feet is greater than height of the penthouse above the ground = 100 feet, the asteroid will not take out Lois' penthouse.

You might be interested in
Add the two expressions. 8.9x−5 and −6.8x+8 Enter your answer, in simplified form, in the box.
Verizon [17]
Let's simplify step-by-step.<span><span><span><span>8.9x</span>−5</span>−<span>6.8x</span></span>+8</span><span>=<span><span><span><span><span><span>8.9x</span>+</span>−5</span>+</span>−<span>6.8x</span></span>+<span>8

</span></span></span>Combine Like Terms:<span>=<span><span><span><span>8.9x</span>+<span>−5</span></span>+<span>−<span>6.8x</span></span></span>+8</span></span><span>=<span><span>(<span><span>8.9x</span>+<span>−<span>6.8x</span></span></span>)</span>+<span>(<span><span>−5</span>+8</span>)</span></span></span><span>=<span><span>2.1x</span>+<span>3

The simplified answer is </span></span></span><span><span>2.1x</span>+<span>3</span></span>
8 0
3 years ago
Write the word sentence as an equation. Then solve.
natima [27]

Answer:25x=320=12.8

Step-by-step explanation:

a number=x

x*25=25x

25x=320

320/25=12.8

x=12.8

5 0
3 years ago
Nathan has a collection of 220 baseball cards. He lets his brother 1/4 of his collection and sells 20% of his collection to the
tatyana61 [14]

<u>Answer:</u>

The baseball cards remain in Nathan’s collection is 106 cards

<u>Explanation:</u>

Total number of cards Nathan has= 220

Number of cards he let his brother have = 1/4 of his collection

=\frac{1}{4} \times 220 = 55 cards

Number of cards he sells = 20% of his collection

=\frac{20}{100} \times 220

=44 cards

No of cards he gives to his friends=15 cards

Remaining cards = total number of cards – (no of cards he gave to his brother+ cards he sold+ cards he gave to this friends)

= 220 – ( 55+44+15)

=220-114

=106 cards

baseball cards remain in Nathan’s collection is 106 cards

4 0
3 years ago
How are factors related to prime numbers?
melomori [17]
They have some of the same numbers 

7 0
3 years ago
Solve the following equation:<br> a) 3x - 9 = 27/ 1 - 5x<br> b) 10x - 1/x = 3
mars1129 [50]

Answer:

A) x=9/2 B) x=-1/5, 1/2

Step-by-step explanation:

3x-9=27/1-5x

3x-9=27-5x

3x-(-5x)-9=27

3x+5x-9=27

8x-9=27

8x=27+9

8x=36

x=36/8

simplify

x=9/2

Answer: x=9/2

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

10x-1/x=3

(10x^2-1)/x=3

10x^2-1=3*x

10x^2-1=3x

10x^2-3x-1=0

factor out the trinomial,

find two numbers that when they multiply,

you get the third term, which is -1 in this case.

When you add those 2 numbers, you get the second term,

which is -3 in this case.

(5x+1)(2x-1)=0

apply the zero property from here,

set 5x+1=0 and 2x-1=0 and solve for x.

5x=0-1=-1, x=-1/5,

2x=0+1=1, 2x=1, x=1/2.

So x=-1/5, 1/2.

5 0
3 years ago
Other questions:
  • Mark makes commission on his sales of software. If he sells up to $20,000 in one month his commission is 10% of the total. If he
    6·1 answer
  • 310763136 in two ways
    6·1 answer
  • Please help right away
    9·1 answer
  • Ryan boards an elevator in the lobby that is headed up at 290 meters per minute. Meanwhile, 260 meters above, Connor boards an a
    6·1 answer
  • Does anyone know what goes into these blanks
    6·1 answer
  • Bunty goes 500 km from Delhi towards East direction. Bubly goes 200 km for Delhi towards
    12·1 answer
  • Question 6 10
    5·1 answer
  • Can you guys answer these questions please i have allot of work and im trying to do multiple things answer will get brainliest
    11·1 answer
  • Find the area of circle x that has a radius XY¯¯¯¯¯¯¯¯ at coordinates X=(0,3) Y=(-3,-1). Use 3.14 for pi, and round your answer
    13·1 answer
  • 32°<br> X х<br> Х<br> x =<br> degrees
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!