write an equation in point slope form for the line through the given point with the given slope (-4, -3); m=8
1 answer:
Answer:
An equation in point-slope form for the line will be:
Please check the attached line graph also.
Step-by-step explanation:
Given
The point (-4, -3)
The slope m = 8
To determine
Write an equation in point slope form for the line.
Using the point-slope form of the line equation
where
- m is the slope of the line
- (x₁, y₁) is the point
In our case,
- (x₁, y₁) = (-4, -3)
- The slope m = 8
substituting the values m = 8 and the point (-4, -3)
Therefore, an equation in point-slope form for the line will be:
Please check the attached line graph also.
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Height of the tower = 101.9 m
Solution:
Given data:
Angle θ = 27°
Adjacent side = 200 m
Opposite side = Height
Let height be taken as h.
The given image shows it is a right triangle.
Using basic trigonometric ratio formulas,
The value of tan 27° = 0.5095
Do cross multiplication, we get
0.5095 × 200 = h
101.9 = h
Height of the tower = 101.9 m
The answer is 6.7 mi.
Since the right triangle is present, to calculate this we will use the Pythagorean theorem. According to the Pythagorean theorem, the square of the hypotenuse (c²) is equal to the sum of the squares of two other sides (a² + b²)<span>:
c</span>² = a² + b²<span>
First, we need to express symbols:
b - side of the right triangle (distance </span><span>between police department and Freeport High School).
a1 - </span>side of the first right triangle (distance between library and Freeport High School).<span>
a2 - </span><span>side of the second right triangle (distance between park and Freeport High School).
c1 - hypotenuse of the first triangle (distance between </span>police<span> department and library).
c2 - </span>hypotenuse of the second triangle (distance between police<span> department and park).
Therefore, we need to calculate c2.
It is given:
a2 = 6 mi
a1 = 4 mi
c1 = 5 mi
First, let's calculate b, which is a common side for two triangles:
</span>c1<span>² = a1² + b²
</span>b² = c1<span>² - a1²
</span>b² = 5<span>² - 4²
</span>b² = 25<span> - 16
</span>b² = 9
√b² = √9
b = 3.
We know b, now we can calculate c2:
c2<span>² = a2² + b²
</span>c2<span>² = 6² + 3²
</span>c2<span>² = 36 + 9
</span>c2<span>² = 45
</span>√c2<span>² = </span>√45
c2 = 6.7
The distance between police department and park is 6.7 miles.
Since the right triangle is present, to calculate this we will use the Pythagorean theorem. According to the Pythagorean theorem, the square of the hypotenuse (c²) is equal to the sum of the squares of two other sides (a² + b²)<span>:
c</span>² = a² + b²<span>
First, we need to express symbols:
b - side of the right triangle (distance </span><span>between police department and Freeport High School).
a1 - </span>side of the first right triangle (distance between library and Freeport High School).<span>
a2 - </span><span>side of the second right triangle (distance between park and Freeport High School).
c1 - hypotenuse of the first triangle (distance between </span>police<span> department and library).
c2 - </span>hypotenuse of the second triangle (distance between police<span> department and park).
Therefore, we need to calculate c2.
It is given:
a2 = 6 mi
a1 = 4 mi
c1 = 5 mi
First, let's calculate b, which is a common side for two triangles:
</span>c1<span>² = a1² + b²
</span>b² = c1<span>² - a1²
</span>b² = 5<span>² - 4²
</span>b² = 25<span> - 16
</span>b² = 9
√b² = √9
b = 3.
We know b, now we can calculate c2:
c2<span>² = a2² + b²
</span>c2<span>² = 6² + 3²
</span>c2<span>² = 36 + 9
</span>c2<span>² = 45
</span>√c2<span>² = </span>√45
c2 = 6.7
The distance between police department and park is 6.7 miles.