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zhannawk [14.2K]
3 years ago
14

What is the volume of the figure?

Mathematics
1 answer:
FromTheMoon [43]3 years ago
7 0
It’s going to be the area of the triangle on the side times the length, so 0.5 x 36 x 15 x 48 = 12960
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A small island is 3 kilometers from the nearest point p on the straight shoreline of a large lake. if a woman on the island can
yKpoI14uk [10]
The distance walked will be (12-x) km
the distance rowed will be (9+x²) km
A] The function T(x) will be given by:
Time=distance/speed
thus we shall have:
T(x)=[√(9+x²)]/2.5+(12-x)/4

B] To get the distance x=c that minimizes the time travel, we differentiate the above.
T'(x)=(1/2.5)[1/(2.5√9+x²)*2x-1/4]
this should give us 0 for x=c, thus
c/[2.5*√(9+c²)]-1/4=0
⇒c/[2.5*√(9+c²)]=1/4
c/√(9+c²)=2.5/4
squaring both sides we get:
c²/(9+c²)=5/8
8c²=5(9+c²)
8c²=45+5c²
3c²=45
c²=15
c=3.87 km

c] The least travel time is
T(c)=[√(9+c²)]/2.5+(12-c)/4
this will give us:
T(c)=[√(9+3.87²)]/2.5+(12-3.87)/4
T(c)=3.9999209~4 hours

d] The second derivative will be:
T"(x)=1/[2.5√(9+x²)]-x²/[2.5(9+x²)^(3/2)]
but
x=c=3.87
T"(x)=0.01668 hours/ mile²
Given that T(c)=0, while T(x)<0 for x<c and T(x)>0 for x>c proves that T(x)  decreases for x<c and increases for x>c, so there is a minimum at x=c


4 0
3 years ago
It has been estimated that the population of Indianapolis is growing at a rate of 0.9% per year. Assuming that the population gr
sweet [91]

Hi there!

Ok, so, here are the important facts:

Yearly population growing rate : 0.9%

Population in January 2016 : 1 988 817

Population in January 2019 (3 years later) : x


First off, you need to calculate 0.9% of the population in January 2016 to figure out the number of people it represents :

Saying 0.9% of 1 988 817 is like saying 0.9% times 1 988 817!


\frac{0.9}{100} = \frac{?}{1 988 817}


To solve this, you can use the cross product method :

(1 988 817 × 0.9) ÷ 100 = ?

1 789 935.3 ÷ 100 = ?

17 899.353 = ?


So 0.9% represents a growing rate of 17 899.353 people (we'll keep the decimals just to be more precise in the end).


Now, since you want to know the expected population in January 2019, 3 years later, you need to multiply 17 899.353 by 3 and then add the result to the population number in 2016 :


(17 899.353 × 3) + 1 988 817 = x

53 698.059 + 1 988 817 = x

2 042 515.059 = x

2 042 515 ≅ x (Since we are talking about a population, which represents a certain amout of people, you need to round the number)


Your answer is : The expected population of Indianapolis in January 2019 would be of 2,042,515 people.


There you go! I really hope this helped, if there's anything just let me know! :)

8 0
3 years ago
A point at (4,6) is reflected across the x-axis.What is the y-coordinate of the reflected point?
iren [92.7K]
I believe the ansr would be (-6,-4) I say this becuase if it's positive on the y axis the X axis will be negative and if it's being reflected the coordinates will be backwards. If this answer is wrong I'm truly sorry, but I hope this helps!
7 0
3 years ago
<img src="https://tex.z-dn.net/?f=4%5E%7B%5Cfrac%7B-5%7D%7B2%7D%20%7D" id="TexFormula1" title="4^{\frac{-5}{2} }" alt="4^{\frac{
photoshop1234 [79]

Answer:

Given expression is equal to  1/32

Step-by-step explanation:

Given that:

= 4^(-5/2)

To eliminate "-" sign we will invert the fraction as follows:

= (1/4)^ 5/2

Or it can be written as:

= =\sqrt{(1/4)^5} \\=\sqrt{1/1024} \\=1/32

This is the simplified expression.

i hope it will help you!

8 0
3 years ago
If j= 14, find the value of 1/2j.
Yakvenalex [24]

Answer:7

Step-by-step explanation:

1/2 of j is the same as j ÷ 2

14 ÷ 2 = 7

8 0
3 years ago
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