Answer:
-
Step-by-step explanation:
cos(87° + 33°) = cos(120°) = -
Use point slope form to write the lines with the given slope and point in slope intercept form.m= -1(-5,-4)
1 answer:
The slope point form is
m is the slope
x1, y1 are the coordinates of a point on the line
The slope of the line is -1
m = -1
point (-5, -4) lies on the line
x1 = -5 and y1 = -4
Let us substitute them in the form above
Remember (-)(-) = (+)
The equation of the line in the slope-point form is y + 4 = -1(x + 5)
You might be interested in
Answer:
The answer to your question is below
Step-by-step explanation:
Data
Center = (0, 0)
Vertex = (13, 0)
Focus = (12, 0)
Process
From the data we know that it is a horizontal ellipse.
1.- Calculate "a", the distance from the center to the vertex.
a = 13
2.- Calculate "c", the distance from the center to the focus
c = 12
3.- Calculate b
Use the Pythagorean theorem to find it
a² = b² + c²
-Solve for b
b² = a² - c²
-Substitution
b² = 13² - 12²
-Simplification
b² = 169 - 144
b² = 25
b = 5
4.- Find the equation of the ellipse
or
Answer:
7. 183 in^2
8. 192.42 m^2
9. 239.4 ft^2
Step-by-step explanation:
7. The figure seems most easily seen as a trapezoid with a triangle removed. The trapezoid has bases of 26 and 14, and a height of 15. So, its area is ...
A = (1/2)(b1 +b2)(h) = (1/2)(26+14)(15) = 300 . . . . . . square inches
The triangle has a base of 26 and a height of 9, so an area of ...
A = (1/2)bh = (1/2)(26)(9) = 117 . . . . . . square inches
Then the shaded area is ...
300 in^2 -117 in^2 = 183 in^2
__
8. The area of the donut can be found different ways. One way is to multiply the width of the shaded area (3.5 m) by the circumference of its centerline.
The centerline diameter is 21 m - 3.5 m = 17.5 m, so the circumference of that circle is ...
C = πd = π(17.5 m) = 17.5π m
Then the area of the shaded part is ...
(3.5 m)(17.5π m) = 61.25π m^2 ≈ 192.42 m^2
__
9. As in problem 7, this can be treated as a parallelogram less a triangle. Here, we need to do a little work to find the area of the triangle.
The triangle of interest is a right triangle with hypotenuse 23.8 ft and one leg 21 ft. The Pythagorean theorem can be used to find the other leg:
h = √(23.8^2 -21^2) = √125.44 = 11.2
Then the area of the triangle is ...
A = (1/2)bh = (1/2)(21)(11.2) = 117.6 . . . ft^2
The area of the parallelogram (including the triangle) is ...
A = bh = (23.8 ft)(15 ft) = 357 ft^2
So, the shaded area is the difference ...
357 ft^2 -117.6 ft^2 = 239.4 ft^2
_____
<em>Comment on significant digits</em>
The area in problem 8 may be considered to be 192.325 m^2 if you are required to use 3.14 as the value for pi. Since that value is only good to 3 significant digits, it is quite pointless to report the answer to 6 significant digits when using that value. It is quite reasonable to use 192 m^2 for the answer, especially if you're required to round to whole numbers.
