A) cylinder
b) triangular pyramid
Answer:
Step-by-step explanation:
add 4 on both sides
leaves you with 15 on the right side
you then divide by negative 2
since you divide by a negative you have to switch the sign
Answer:
y = 2*x^2 - 2*x - 24
Step-by-step explanation:
If we have a quadratic function with roots a and b, we can write the equation for that function as:
y = f(x) = A*(x - a)*(x - b)
Where A is the leading coefficient.
In this case, we know that the roots are: 4 and -3
Then the function will be something like:
f(x) = A*(x - 4)*(x - (-3) )
f(x) = A*(x - 4)*(x + 3)
Now we need to determine the value of A.
We also know that the graph of the function passes through the point (3, -12)
This means that:
f(3) = -12
Then:
-12 = A*(3 - 4)*(3 + 3)
-12 = A*(-1)*(6)
-12 = A*(-6)
-12/-6 = A
2 = A
Then the equation is:
y = f(x) = 2*(x - 4)*(x + 3)
Now we need to write this in standard form, so we just need to expand the equation:
y = f(x) = 2*(x^2 + x*3 - x*4 - 4*3)
y = f(x) = 2*(x^2 - x - 12)
y = f(x) = 2*x^2 - 2*x - 24
Then the relation is:
y = 2*x^2 - 2*x - 24
This is the future value quadrupled in t years at an annual interest rate of 6.5% compounded daily. We need to find t.
1*(1+0.065/365)^(365t)t=4
take log on both sides,
365t(log(1+0.065/365)=log(4)
=>
365t=log(4)/log(1+0.065/365)
t=(log(4)/log(1+0.065/365))/365
=(1.38629/.000178066)/365
=21.33 years
Check with the rule of 69, applicable to continuous compounding (an approximation to current problem) to double money, it take 69/interest rate in % years.
=69/6.5
=10.62 years
To double twice (quadruple), it takes twice 10.62
=21.24 years, not that far from 21.33 that we got earlier.
Answer:12
Step-by-step explanation:
Given
Balthazar,Rudy,Jebediah and Ezekiel in a single-File line to pull sleigh
Jebediah and Ezekiel Stay together
i.e. we need to arrange three person considering Ezekiel and jebediah as Single person
therefore 3 person can be arrange in 3! ways =6
and also Ezekiel and Jebediah can be arranged in 2 ways
Therefore a total of 
ways are possible
