Answer:
[tex] { \cos}^{3} x[/tex]
Step-by-step explanation:
We want to simplify:
[tex] \frac{ \sin( \frac{\pi}{2} - x) }{ { \cot}^{2} ( \frac{\pi}{2} -1 ) + 1} [/tex]
Use the Pythagorean identity:
[tex] { \csc}^{2}x = { \cot}^{2}x + 1[/tex]
We apply this property to get:
[tex] \frac{ \sin( \frac{\pi}{2} - x) }{ { \csc}^{2} ( \frac{\pi}{2} -x) } [/tex]
This gives us:
[tex]\frac{ \sin( \frac{\pi}{2} - x) }{ \frac{1}{{ \sin}^{2} ( \frac{\pi}{2} -x)} } [/tex]
We simplify to get:
[tex]\sin^{3} ( \frac{\pi}{2} -x)[/tex]
[tex](\sin ( \frac{\pi}{2} -x))^{3}[/tex]
Apply the complementary identity;
[tex](\cos x)^{3} = { \cos}^{3} x[/tex]
Given f(x) and g(x) = k·f(x), use the graph to determine the value of k.
g(x)
The diagram for this exercise is attached below. We have two linear functions [tex]f(x) \ and \ g(x)[/tex] and the following relationship:
[tex]g(x) = kf(x)[/tex]
From the graph, we know that:
[tex]f(-3)=1 \\ \\ g(-3)=-3[/tex]
Then, substituting into the relationship:
[tex]g(-3)=kf(-3) \\ \\ -3=k(1) \\ \\ \\ Finally: \\ \\ \boxed{k=-3}[/tex]
1) Write in the formula. What equals the perimeter P of the rectangle wich is 25 cm wide. (show the length with the letter b.) 2) Calculate the perimeter of the rectangle when its length is equal to:
a) 45 cm; b) 0.25 m; c) 650 mm; d) 3 m by 9 cm; e) 3 dm.
Please I really need help
Answer:
1)P = 2 x(L+l) = 2 x (25+L)
2) Maintaing L= 25 cm
P= 2x (25+45) = 140 cm²
P= 2x (25+0,25m) =2x(25+25)= 100 cm²
P= 2x (25+650 mm) =2x(25+65)= 180 cm²
d) ambigous
P= 2x (25+3dm) = 2x (25+30)=110 cm²
Step-by-step explanation:
Below is a drawing of a wall that is to be covered with either wallpaper or paint. The wall is 8 ft. high and
16 ft wide. The window, mirror, and fireplace are not to be painted or papered. The window measures 18 in wide
and 14t. high. The fireplace is sit wide and 3 it. High while the mirror above the fireplace is 4 ft. wide and 2 ft.
high. Note: this drawing is not to scale)
How many square feet of wallpaper are needed to cover the wall?
84 sq. ft of the wall has to be covered with paint or wallpaper.
Step-by-step explanation:
Step 1: Find the area of wallpaper to be covered by calculating the area of the wall and subtracting the areas of the window, mirror and fireplace from it. All are rectangular in shape with are given by A = length × widthArea of the wall = 8 × 16 = 128 ft²
Area of the window = 18/12 × 14 = 1.5 × 14 = 21 ft² (since 1 ft = 12 in)
Area of the fireplace = 5 × 3 = 15 ft²
Area of the mirror = 4 × 2 = 8 ft²
Step 2: Calculate the area to be painted or covered with wallpaperArea of the wall to be covered with paint or wallpaper = 128 - (21 + 15 + 8)
= 128 - 44
= 84 ft²
Answer:
84 ft²
Step-by-step explanation:
Step 1: Find the area of the wall.
The wall is 8 ft high and 16 ft wide
A = LW
A = (16)(8)
A = 128 ft²
Step 2: Find the area of the window, fireplace, and mirror.
Window: The window measures 18 in wide and 14 ft high
18 in = 1.5 ft
A = LW
A = (14)(1.5)
A = 21 ft²
Fireplace: The fireplace is 5 ft wide and 3 ft high
A = LW
A = (3)(5)
A = 15 ft²
Mirror: The mirror above the fireplace is 4 ft wide and 2 ft high
A = LW
A = (2)(4)
A = 8 ft²
Step 3: Add all the areas of the three objects (window, fireplace, and mirror)
A = 21 + 15 + 8
A = 36 + 8
A = 44 ft²
Step 4: Subtract the total area of the objects from the area of the wall.
A = 128 ft² - 44 ft²
A = 84 ft²