In the diagram below , tan theta =square root 3. What is the value of m?

Mathematics

1 answer:

vova2212 [387]3 years ago

7 0

Answer:

$m=\frac{\sqrt{3}}{2}$

Step-by-step explanation:

we know that

In the diagram

$tan(\theta)=\frac{m}{1/2}=2m$

$tan(\theta)=\sqrt{3}$

Equate

$2m=\sqrt{3}$

$m=\frac{\sqrt{3}}{2}$

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Below is a drawing of a wall that is to be covered with either wallpaper or paint. The wall is 8 ft. high and

Snowcat [4.5K]

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 × width

Area 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 wallpaper

Area of the wall to be covered with paint or wallpaper = 128 - (21 + 15 + 8)

= 128 - 44

= 84 ft²

5 0

3 years ago

Read 2 more answers

Sketch the region enclosed by y=3x and y=x^2 . Then find the area of the region.

kolezko [41]

Answer:

$A=4.5u^2$

Step-by-step explanation:

The integral of a function gives you the area under the curve, the subtraction of one of the areas from the other will give you the area in between.

The limits of integration are the points where the curves intersect each other(take the curves has a system of equation and solve for x and y):

$y=3x, y=x^2\\3x=x^2\\x^2-3x=0\\x(x-3)=0\\x_1=0\\x-3=0\\x_2=3$

$y_1=3x_1=3(0)=0\\y_2=3x_2=3(3)=9$

The integral will be the subtraction of the curve $y=3x$ and $y=x^2$ (In the graph you can see y=3x is the upper curve):

$\int\limits^3_0 {3x-x^2} \, dx =\left\frac{3x^2}{2}-\frac{x^3}{3}\right|^3_0=\frac{3(3)^2}{2}-\frac{(3)^3}{3}-\left(\frac{3(0)^2}{2}-\frac{(0)^3}{3}\right)\\\int\limits^3_0 {3x-x^2} \, dx =\frac{27}{2}-\frac{27}{3} =13.5-9=4.5u^2$