Answer:
2/3 of her glasses
Step-by-step explanation:
If 1/2 liter apple juice fills 1/3 of her glasses, then twice that volume will fill twice as many glasses: 2/3 of her glasses.
Answer: 4.5 miles
Explanation:
When you draw the situation you find two triangles.
1) Triangle to the east of the helicopter
a) elevation angle from the high school to the helicopter = depression angle from the helicopter to the high school = 20°
b) hypotensue = distance between the high school and the helicopter
c) opposite-leg to angle 20° = heigth of the helicopter
d) adyacent leg to the angle 20° = horizontal distance between the high school and the helicopter = x
2) triangle to the west of the helicopter
a) elevation angle from elementary school to the helicopter = depression angle from helicopter to the elementary school = 62°
b) distance between the helicopter and the elementary school = hypotenuse
c) opposite-leg to angle 62° = height of the helicopter
d) adyacent-leg to angle 62° = horizontal distance between the elementary school and the helicopter = 5 - x
3) tangent ratios
a) triangle with the helicpoter and the high school
tan 20° = Height / x ⇒ height = x tan 20°
b) triangle with the helicopter and the elementary school
tan 62° = Height / (5 - x) ⇒ height = (5 - x) tan 62°
c) equal the height from both triangles:
x tan 20° = (5 - x) tan 62°
x tan 20° = 5 tan 62° - x tan 62°
x tan 20° + x tan 62° = 5 tan 62°
x (tan 20° + tan 62°) = 5 tan 62°
⇒ x = 5 tant 62° / ( tan 20° + tan 62°)
⇒ x = 4,19 miles
=> height = x tan 20° = 4,19 tan 20° = 1,525 miles
4) Calculate the hypotenuse of this triangle:
hipotenuese ² = x² + height ² = (4.19)² + (1.525)² = 19.88 miles²
hipotenuse = 4.46 miles
Rounded to the nearest tenth = 4.5 miles
That is the distance between the helicopter and the high school.
Answer:
60
Step-by-step explanation:
Cot is the same as 1/tan so:
By rearranging the equation, we get:
By taking the inverse tan, we get:
Answer:
The answer is 7
Step-by-step explanation:
an easier way to think of it is 21 divided by 3, which again, is 7.
Hope That Helps!
Answer: Hello mate!
we know that p(x,y) means "Student x has taken class y"
and the used symbols are:
∃: this means "existence", you use this symbol to say that there exists at least one object that makes true the sentence.
∀: this means "for all", you use this symbol to say that the sentence is true for all the elements, then:
a) ∃x∃yP (x, y)
"exist at least one student x, that took at least one class y"
b) ∃x∀yP (x, y)
"exist at least one student x, that took all the classes y"
c) ∀x∃yP (x, y)
"every student x, took at least one class y"
d) ∃y∀xP (x, y)
"exist at least one class y, that has been taken by all the students x"
e) ∀y∃xP (x, y)
"for every class y, there is at least one student x that took the class"
f) ∀x∀yP (x, y)
"all the students x took all the classes y"
