As soon as I read this, the words "law of cosines" popped
into my head. I don't have a good intuitive feeling for the
law of cosines, but I went and looked it up (you probably
could have done that), and I found that it's exactly what
you need for this problem.
The "law of cosines" relates the lengths of the sides of any
triangle to the cosine of one of its angles ... just what we need,
since we know all the sides, and we want to find one of the angles.
To find angle-B, the law of cosines says
b² = a² + c² - 2 a c cosine(B)
B = angle-B
b = the side opposite angle-B = 1.4
a, c = the other 2 sides = 1 and 1.9
(1.4)² = (1)² + (1.9)² - (2 x 1 x 1.9) cos(B)
1.96 = (1) + (3.61) - (3.8) cos(B)
Add 3.8 cos(B) from each side:
1.96 + 3.8 cos(B) = 4.61
Subtract 1.96 from each side:
3.8 cos(B) = 2.65
Divide each side by 3.8 :
cos(B) = 0.69737 (rounded)
Whipping out the
trusty calculator:
B = the angle whose cosine is 0.69737
= 45.784° .
Now, for the first time, I'll take a deep breath, then hold it
while I look back at the question and see whether this is
anywhere near one of the choices ...
By gosh ! Choice 'B' is 45.8° ! yay !
I'll bet that's it !
Answer: 
Step-by-step explanation:
Given
The area is bounded by 
and x-axis from [0,2]
The volume generated for 
when rotated about the x-axis in the interval [a,b] is
Insert the values
![\Rightarrow V=\int_0^2\pi x^4dx\\\\\Rightarrow V=\pi \int_0^2x^4dx\\\\\Rightarrow V=\pi \left[ \dfrac{x^5}{5}\right]_0^2\\\\\Rightarrow V=\dfrac{2^5\pi }{5}\\\\\Rightarrow V=\dfrac{32\pi }{5}\ \text{unit}^3](https://tex.z-dn.net/?f=%5CRightarrow%20V%3D%5Cint_0%5E2%5Cpi%20x%5E4dx%5C%5C%5C%5C%5CRightarrow%20V%3D%5Cpi%20%5Cint_0%5E2x%5E4dx%5C%5C%5C%5C%5CRightarrow%20V%3D%5Cpi%20%5Cleft%5B%20%5Cdfrac%7Bx%5E5%7D%7B5%7D%5Cright%5D_0%5E2%5C%5C%5C%5C%5CRightarrow%20V%3D%5Cdfrac%7B2%5E5%5Cpi%20%7D%7B5%7D%5C%5C%5C%5C%5CRightarrow%20V%3D%5Cdfrac%7B32%5Cpi%20%7D%7B5%7D%5C%20%5Ctext%7Bunit%7D%5E3)
Line plots are used to display data elements using markers
The total growth, in inches, of Isabella's plant is 
inches
<h3>How to determine the total growth</h3>
From the line plot, the total growth can be represented as:
Evaluate the products
Evaluate the sum
Evaluate the numerator
Evaluate the quotient
Hence, the total growth, in inches, of Isabella's plant is inches
Read more about line plots at:
brainly.com/question/15853311
Side DF is congruent (the = and ~ symbol) to side DE
Answer:
60 miles
Step-by-step explanation:
let d = distance to the lake
Using: time = distance ÷ speed
Create expressions for the time it takes for each journey:
Drive: 
Walk: 
If total time = 17 hours
Therefore she walked 60 miles
