Someone plz help. s. help
2 answers:
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Answer:
8 +(3/8)√53 in² ≈ 10.73 in²
Step-by-step explanation:
Given the net of a triangular pyramid with some of the dimensions filled in, you want to find the total surface area.
<h3>Triangle base</h3>The triangle bases identified by dashed lines will have a length equal to the hypotenuse of the right triangles with legs shown as solid lines. The legs of each of those right triangles are ...
a = (3 in)/2 = 1.5 in
b = 2 in . . . . . . shown as the altitude of the triangle
Then the hypotenuse is found using the Pythagorean theorem:
c² = a² +b²
c² = 1.5² +2² = 2.25 +4 = 6.25
c = √6.25 = 2.5
The dashed lines are 2.5 inches long.
<h3>Triangle altitude</h3>The altitude from the solid horizontal line to the vertex at the bottom of the figure can be found using the fact that all of the outside edge lengths of the net are the same length. That edge length is found as the length of the hypotenuse of the right triangles in the left- and right-sides of the upper portion of the net. Each of those has a leg that is (2.5 in)/2 = 1.25 in and a leg marked as 2 in.
c² = a² +b²
c² = 1.25² +2² = 1.5625 +4 = 5.5625
c = (√89)/4 ≈ 2.358 . . . in
The unmarked altitude of the bottom triangle is then ...
b² = c² -a²
b² = 89/16 -1.5² = 53/16
b = (√53)/4 ≈ 1.820 . . . in
<h3>Surface area</h3>The surface area of the figure is the sum of the areas of the four triangles that make up the net. Each triangle has an area given by the formula ...
A = 1/2bh
The left and right triangles have b=2.5, h=2, so they each have an area of ...
A = 1/2(2.5)(2) = 2.5 . . . . in²
The center triangle has dimensions of b=3, h=2, so an area of ...
A = 1/2(3)(2) = 3 . . . . in²
The bottom triangle has dimensions of b=3, h=(√53)/4, so an area of ...
A = 1/2(3)(√53/4) = (3/8)√53 ≈ 2.730 . . . . in²
The total surface area is the sum of the areas of these triangles, so is ...
A = 2.5 in² +2.5 in² +3 in² +2.73 in² = 10.73 in²
The surface area of the triangular pyramid is (64+3√53)/8 ≈ 10.73 in².
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<em>Additional comment</em>
Often we work with pyramids that are rotationally symmetrical about a vertical line through the peak. This one is not. The altitude of the bottom triangle in the net is less than the altitude of the other triangles. This short face of the pyramid will tend to be more vertical than the other two lateral faces.
Answer:
a)
b) 69.764
Step-by-step explanation:
1) Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
2) Part a
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability on this way:
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
3) Part b
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.95 of the area on the left and 0.05 of the area on the right it's z=1.64. On this case P(Z<1.64)=0.95 and P(z>1.64)=0.05
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 95% of data from the top 5% is 69.764.
