17, 21, 25, etc. because when you divided 4 by any of these numbers you will get your answer with a remainder of 1. For example, 17/4 is 4 R.1 because 4 times 4 is 16, then you will have one left over. (At my school you always go to a decimal not a remainder)
Answer:
a) 16.25 centimeters
b) 6.8 centimeters
Step-by-step explanation:
We can set up a proportion for both of these problems.
a) Look at the longest side of each triangle. We can set up a fraction: 7.2/18. We can also set up a fraction for XZ and PR:
6.5/x
x represents the length you're trying to find.
Since the triangles are similar, we have an equation:
7.2/18=6.5/x
Cross multiply
16.25
XZ is 16.25 centimeters long.
b)
We can do same thing:
7.2/18=x/17
Cross multiply
6.8
QR is 6.8 centimeters long.
Hope this helps!
The first step to do is to calculate first the total
household waste generate for the two years. That is:
total waste generated = 23,400,000 tons + 48,100,000 tons
total waste generated = 71,500,000 tons
Now, to write either a very big number or a very small number
in a form of scientific notation simply means to write it in a decimal form
such as: 12.5 * 10^10
Now to write 71,500,000 in scientific notation, the decimal
form is 7.15, however we still need to find out the * 10^n factor. The value of
n depends on the number of places the decimal point was moved. If the movement
was from right to left, the value of n is positive and if the movement was from
right to left, the value of n is negative. Since the decimal point was moved by
7 places, hence the complete scientific notation is:
7.15 * 10^7 tons
From the calculation, the growth rate is 0.88.
<h3>What is the growth rate?</h3>
To find the relative growth rate
P1 = Poe^rt
P2 = Poe^rt
Thus;
1920 = Poe^4r ------ (1)
1966080 =Poe^12r -------(2)
P2/P1 gives;
1966080/1920 = Poe^12r/Poe^4r
1024 = e^12r/e^4r
1024 =e^8r
1024 = (e^r)^8
2^10 = (e^r)^8
e^r = 2^1.25
e^r = 2.38
r = ln(2.38)
r = 0.88
The initial size of the culture is;
1920 = Poe^(0.88 * 4)
Po = 1920/e^(0.88 * 4)
Po = 57
The expression for the exact number of bacteria after t hours is
P(t) = 57e^0.08t
The growth (in bacteria per hour) after 9.5 hours is
P(t) = 57e^(0.88 * 9.5)
P(t) = 243544
For the number to reach 72,000;
72,000 = 57e^0.88t
72,000/57 = e^0.88t
ln 126 = ln[e^0.88t]
4.8 = 0.88t
t = 4.8/0.88
t = 5.5 hours
Learn more about exponential growth;brainly.com/question/13674608
#SPJ1
Answer:
The answer is (d) ⇒ eccentricity = 6 , hyperbola , directrix x = 3/2
Step-by-step explanation:
∵ r = ek/(1 ± ecosФ)
∵ r = 9/(1 + 6cosФ)
∴ e = 6 ⇒ eccentricity = 6
∵ e > 1
∴ The conic is hyperbola
∵ ek = 9
∴ k = 9/6 = 3/2
∴ The directrix x = 3/2
