Answer:
Step-by-step explanation:
Given two upward facing parabolas with equations
The two intersect at
=
x=
area enclosed by them is given by
A=![\int_{-\sqrt{\frac{2}{5}}}^{\sqrt{\frac{2}{5}}}\left [ \left ( x^2+2\right )-\left ( 6x^2\right ) \right ]dx](https://tex.z-dn.net/?f=%5Cint_%7B-%5Csqrt%7B%5Cfrac%7B2%7D%7B5%7D%7D%7D%5E%7B%5Csqrt%7B%5Cfrac%7B2%7D%7B5%7D%7D%7D%5Cleft%20%5B%20%5Cleft%20%28%20x%5E2%2B2%5Cright%20%29-%5Cleft%20%28%206x%5E2%5Cright%20%29%20%5Cright%20%5Ddx)
A=
A=![4\left [ \sqrt{\frac{2}{5}} \right ]-\frac{5}{3}\left [ \left ( \frac{2}{5}\right )^\frac{3}{2}-\left ( -\frac{2}{5}\right )^\frac{3}{2} \right ]](https://tex.z-dn.net/?f=4%5Cleft%20%5B%20%5Csqrt%7B%5Cfrac%7B2%7D%7B5%7D%7D%20%5Cright%20%5D-%5Cfrac%7B5%7D%7B3%7D%5Cleft%20%5B%20%5Cleft%20%28%20%5Cfrac%7B2%7D%7B5%7D%5Cright%20%29%5E%5Cfrac%7B3%7D%7B2%7D-%5Cleft%20%28%20-%5Cfrac%7B2%7D%7B5%7D%5Cright%20%29%5E%5Cfrac%7B3%7D%7B2%7D%20%5Cright%20%5D)
A=
<span>6s^2 = 294
Solve for s
Solve for s:
6 s^2 = 294
Divide both sides by 6:
s^2 = 49
Take the square root of both sides:
Answer: s = 7 m
</span>
The measure of the unknown angle are; a) x = 89 degrees, b) p = 92 degrees.
<h3>What is the sum of all the angles of a regular polygon?</h3>
For a regular polygon of any number of sides, the sum of its exterior angle is 360°.
We already know that a 4-sided polygon's angles add up to 360 degrees.
So to find the value of x:
69 + 118 + 84 + x = 360
x = 360 - (69 + 118 + 84)
x = 89 degrees
b)
For a 4-sided polygon, we also know that the outside angles add up to 360 degrees.
So to find the value of p:
100 + 62 + 106 + p = 360
p = 360 - (100 + 62 + 106)
p = 92 degrees
Learn more about interior angles of a regular polygon here:
brainly.com/question/14173422
#SPJ1
Answer:
This is 0.14 to the nearest hundredth
Step-by-step explanation:
Firstly we list the parameters;
Drive to school = 40
Take the bus = 50
Walk = 10
Sophomore = 30
Junior = 35
Senior = 35
Total number of students in sample is 100
Let W be the event that a student walked to school
So P(w) = 10/100 = 0.1
Let S be the event that a student is a senior
P(S) = 35/100 = 0.35
The probability we want to calculate can be said to be;
Probability that a student walked to school given that he is a senior
This can be represented and calculated as follows;
P( w| s) = P( w n s) / P(s)
w n s is the probability that a student walked to school and he is a senior
We need to know the number of seniors who walked to school
From the table, this is 5/100 = 0.05
So the Conditional probability is as follows;
P(W | S ) = 0.05/0.35 = 0.1429
To the nearest hundredth, that is 0.14
