Answer:
y" - 8y' + 15y = 0
2nd order Homogeneous DE.
Solving Quadratically
k² - 8k + 15 = 0
k= 5 or k= 3.
Two real and Unequal roots.
y= Ae^5x + Be^3x.
1yr. = 3ft = 36in.
1ft = 12in.
therefore
6yr. 9ft 4in. × 2 = 12yr. 18ft 8in.
18ft = (18:3)yd. = 6yd
Answer: 18yr. 8in.
Answer:
A. The digit 8 is in the place one million position
B. The digit 3 is in the place tens position
Step-by-step explanation:
Given:
98,045,132.706
9 is in the ten million position
8 is in the one million position
0 is in the hundred-thousand position
4 is in the ten-thousand position
5 is in the one-thousand position
1 is in the hundred position
3 is in the tens position
2 is in the one position
. Decimal
7 is in the tenth position
0 is in the hundredth position
6 is in the thousandth position
Therefore,
A. The digit 8 is in the place one million position
B. The digit 3 is in the place tens position
Answer: $3.35
To solve this, let’s first write equations for each of the coins listed. Let’s start with pennies.
We know that Susan has 3 more pennies than dimes. This means that pennies is equal to dimes, plus three. This would turn into this equation:
Pennies: d+3
Now let’s move onto nickels. The question says that Susan has three times more nickels than dimes. This means that nickels is equal to dimes, times three. This would be our equation:
Nickels: n=3d
Finally, let’s write the equation for quarters. It says that Susan has four less quarters than pennies. This means that quarters are equal to pennies minus three. This would be the equation:
Quarters: q=p-4
Now time to solve. We need to solve the amount of...
Pennies: ?
Nickels: ?
Dimes: ?
Quarters: ?
The question tells us that Susan has 7 dimes, so let’s fill that in now.
Pennies: ?
Nickels: ?
Dimes: 7
Quarters: ?
We can use the dime information to solve for the other coins, using our equation. Let’s go in order and start with pennies.
Our equation for pennies is: p=d+3. We know that d is 7, so let’s fill this in and solve.
p=d+3
p=7+3
p=10
Susan has 10 pennies. Let’s fill this into the information we have.
Pennies: 10
Nickels: ?
Dimes: 7
Quarters: ?
Now let’s do nickels. Our equation says n=3d. Let’s substitute the value for d and solve
n=3d
n=3(7)
n=21
Susan has 21 nickels. Let’s fill that into the information we have.
Pennies: 10
Nickels: 21
Dimes: 7
Quarters: ?
Let’s finally do quarters. The equation we have written for quarters is: q=p-4. Let’s fill in the value of p and solve
q=p-4
q=10-4
q=6
Susan has 6 quarters. This is our final information on the coins:
Pennies: 10
Nickels: 21
Dimes: 7
Quarters: 6
Let’s now calculate how much money she has altogether. We will do this by multiplying how many coins she has by the value of each coin.
Pennies: 10 • .01= .10
Nickels: 21•.05=1.05
Dimes: 7•.10=.70
Quarters: 6•.25=1.5
Now that we know that, let’s add these all together. This will tell us the final answer of how much is the value of her money.
.10+1.05+.70+1.5= $3.35
That’s your answer! Hope this helps comment below for more questions :)
Question 1. False
Question 2:
1. C
2. A
3. B
4. D
