Answer:
<h3>cosθ = c/√1+c²</h3>
Step-by-step explanation:
Given cot θ = c and 0 < θ < π/2
In trigonometry identity:
cotθ = 1/tanθ = c
1/tanθ = c
cross multiply
tanθ = 1/c
According to SOH, CAH, TOA:
Tanθ = opposite/adjacent = 1/c
cosθ = adjacent/hypotenuse
To get the hypotenuse, we will use the pythagoras theorem:
hyp² = opp²+adj²
hyp² = 1²+c²
hyp = √1+c²
Find cosθ in terms of c
cosθ = c/√1+c²
Hence the formula for cos θ in terms of c is cosθ = c/√1+c²
Answer:
Length: 12 cm
Width: 8 cm
Height; 7 cm
Step-by-step explanation:
We are told that the areas of 2 of the faces are 84cm² and 56cm².
Now, the side faces are 4 in total with 2 each having same areas.
Thus, it means they would have the same height.
Let's find the highest common factor between 84cm² and 56cm².
The highest number that can be divide each equally is 7.
Thus;
12 × 7 = 84 cm²
8 × 7 = 56 cm²
This means, the bottom part will measure 12 cm by 8 cm.
Thus, the complete measurement is;
Length: 12 cm
Width: 8 cm
Height; 7 cm
Let's check if it will give us a Volume equal to that given.
Thus;
Volume = 12 × 8 × 7 = 672 cm²
This is same as that given and so our dimensions are correct.
If youre solving for x i think its -1/7
slope is undefined
Answer:
There is no significant evidence to conclude that the mean waiting time is less than 3.8 minutes
Step-by-step explanation:
H0 : μ = 3.8
H1 : μ < 3.8
Test statistic :
(x - μ) ÷ s/sqrt(n)
(3.7 - 3.8) ÷ 0.6/sqrt(60)
Test statistic = - 1.29
The Pvalue from test statistic :
P(z < -1.29) = 0.0985
Reject Null if
Pvalue < α
0.0986 > 0.01 ; Hence, we fail to reject the null ;
There is no significant evidence to conclude that the mean waiting time is less than 3.8 minutes
Answer:
RELATED
How to Solve a Hexagon
Updated October 23, 2018
By Chris Deziel
A polygon is any closed two-dimensional figure with 3 or more straight (not curved) sides, and a 12-sided polygon is known as a dodecagon. A regular dodecagon is one with equal sides and angles, and it's possible to derive a formula for calculating its area. An irregular dodecagon has sides of different lengths and different angles. A six-pointed star is an example. There's no easy way to calculate the area of an irregular 12-sided figure unless you happen to have it plotted on a graph and can read the coordinates of each of the vertices. If not, the best strategy is to divide the figure into regular shapes for which you can calculate the area.
Calculating the Area of a Regular 12-Sided Polygon
To calculate the area of a regular dodecagon, you have to find its center, and the best way to do that is to scribe a circle around it that just touches each of its vertices. The center of the circle is the center of the dodecagon, and the distance from the center of the figure to each of its vertices is simply the radius of the circle (r). Each of the 12 sides of the figure is the same length, so denote this by s.
You need one more measurement, and that's the length of a perpendicular line drawn from the midpoint of each side to the center of the 12-sided shape. This line is known as the apothem. Denote its length by m. It divides each section formed by the radius lines into two right-angled triangles. You don't know m, but you can find it using the Pythagorean theorem.
The 12 radius lines divide the circle you scribed around the dodecagon into 12 equal sections, so at the center of the figure, the angle each line makes with the one next to it is 30 degrees. Each of the 12 sections formed by the radius lines is made up of a pair of right-angled triangles with hypotenuse r and one angle of 15 degrees. The side adjacent to the angle is m, so you can find it using r and the sine of the angle.
Step-by-step explanation: