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Ray Of Light [21]
3 years ago
8

The difference of a number p and 15 is greater than -18. WRITE THE WORD SENTENCE AS AN INEQUALITY. THEN SOLVE THE INEQUALITY ALG

EBRAICALLY
Mathematics
1 answer:
tatiyna3 years ago
8 0

Answer:

P-15>18

P>33

Step-by-step explanation:

First, you need to make the equation. Knowing that deference means you need to subtract, you write it out. P-15>18 . Then to solve it, you add the 15 over to the other side. 18+15=33, therefore p>33

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How do I solve this?Help me please!!!
NISA [10]
Given:
Ship M travels E 15 km, then N35E 27 km. Its sub travels down 48° 2 km from that location.

Ship F travels S75E 20 km, then N25E 38 km. The treasure is expected to be at this location 2.18° below horizontal from the port.

Find:
1a. The distance from port to Ship M
1b. The distance from port to the sub
1c. The angle below horizontal from the port to the sub

2a. The distance from port to Ship F
2b. The depth to the expected treasure location
2c. The distance from port to the expected treasure location

Solution:
It can be helpful to draw diagrams. See the attached. The diagram for depth is not to scale.

There are several ways this problem can be worked. A calculator that handles vectors (as many graphing calculators do) can make short work of it. Here, we will use the Law of Cosines and the definitions of Tangent and Cosine.

Part 1
1a. We are given sides 15 and 27 of a triangle and the included angle of 125°. Then the distance (m) from the port to the ship is given by the Law of Cosines as
  m² = 15² +27² -2·15·27·cos(125°) ≈ 1418.60
  m ≈ 37.66
The distance from port to Ship M is 37.66 km.

1b. The distance just calculated is one side of a new triangle with other side 2 km and included angle of 132°. Then the distance from port to sub (s) is given by the Law of Cosines as
  s² = 1418.60 +2² -2·37.66·2·cos(132°) ≈ 1523.41
  s ≈ 39.03
The distance from port to the sub is 39.03 km.

1c. The Law of Sines can be used to find the angle of depression (α) from the port. That angle is opposite the side of length 2 in the triangle of 1b. The 39.03 km side is opposite the angle of 132°. So, we have the relation
  sin(α)/2 = sin(132°)/39.03
  α = arcsin(2·sin(132°)/39.03) ≈ 2.18°
The angle below horizontal from the port to the sub is 2.18°.

Part 2
2a. We are given sides 20 and 38 of a triangle and the included angle of 100°. Then the distance (f) from the port to the ship is given by the Law of Cosines as
  f² = 20² +38² -2·20·38·cos(100°) ≈ 2107.95
  f ≈ 45.91
The distance from port to Ship F is 45.91 km.

2b. The expected treasure location is at a depth that is 2.18° below the horizontal from the port. The tangent ratio for an angle is the ratio of the opposite side (depth) to the adjacent side (distance from F to port), so we have
  tan(2.18°) = depth/45.91
  depth = 45.91·tan(2.18°) ≈ 1.748
The depth to the expected treasure location is 1.748 km.

2c. The distance from port to the expected treasure location is the hypotenuse of a right triangle. The cosine ratio for an angle is the ratio of the adjacent side to the hypotenuse, so we have
  cos(2.18°) = (port to F distance)/(port to treasure distance)
  (port to treasure distance) = 45.91 km/cos(2.18°) ≈ 45.95
The distance from the port to the expected treasure is 45.95 km.

Part 3
It seems the Mach 5 Mimi is the ship most likely to have found the treasure. That one seems ripe for attack. Its crew goes to a location that is 2.18° below horizontal. The crew of the FTFF don't have any idea where they are going. (Of course, the pirate ship would have no way of knowing if it is only observing surface behavior.)

5 0
3 years ago
Can someone Please help me with this question!? If
jasenka [17]

Answer:The answer is 1 and 3

Step-by-step explanation:

4 0
3 years ago
A ladder is leaning against a building so that the distance from the ground to the top of the latter is 1 foot less than the len
masha68 [24]

Answer:

25\text{ feet}

Step-by-step explanation:

The ladder, ground, and building form a right triangle where the vertical distance between the top of the ladder and the bottom of the ground is one leg, the horizontal distance between the bottom of the ladder and the building is another leg, and the length of the ladder is the hypotenuse.

For any right triangle, the Pythagorean Theorem states that the sum of the squares of both legs is equal to the hypotenuse squared (a^2+b^2=c^2), where c is the hypotenuse.

Let the length of the ladder be \ell (hypotenuse of right triangle). The distance between the top of the ladder and the ground (vertical distance) can be represented as \ell -1.

From the Pythagorean Theorem, we then have:

7^2+(\ell-1)^2=\ell^2

Expand using (a-b)^2=a^2-2ab+b^2:

49+\ell^2-2\ell+1=\ell^2

Subtract \ell from both sides and add 2\ell to both sides:

49+1=2\ell

Combine like terms:

50=2\ell, \\2\ell =50

Divide both sides by 2:

\ell=\frac{50}{2}=\boxed{25\text{ feet}}

Therefore, the length of the ladder is 25 feet.

4 0
3 years ago
Promise Easy Points
Harman [31]

$420+$350+$432=kelsey's monthly expenses  

$700+$800=Micheal's Monthly expenses

8 0
3 years ago
I need help please and I will give u 30 points
oksian1 [2.3K]

Answer:

they are wrong because 3.59 is less than 3.6 . 3.6 is the same as 3.60 only add the 0 and it will not change the value . yes 59 is more than 6 but the student did not realize you can put a place holder to determine the comparison.

8 0
3 years ago
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