Answer:
25km/hr (take the word train as bus )
Step-by-step explanation:
Answer
Let x km/hr be the constant speed of the train,
Then Time taken to cover 300km=
x
300
hrs
Time taken to cover 300km when the speed is increased by 5km/hr=
x+5
300
hours
It is given that the time to cover 300km is reduced by 2 hours
∴
x
300
−
x+5
300
=2
⇒
x(x+5)
300(x+5)−300x
=2⇒2x
2
+10x=1500
⇒x
2
+5x−750=0⇒x
2
+30x−25x−750=0
⇒(x+30)(x−25)=0⇒x=25orx=−30
But x cannot be negative. Therefore x=25
Hence, the original speed of the train is 25km/hr
Initially, Charlotte owes $7680. She finishes her payments after a total of 6 + 36 = 42 months. Using a simple compounding formula, the amount she owes is worth P at the end of 42 months, where P is:
P = 7680 * (1 + .2045/12)^42 = 15616.67379
Now, the first installment she pays (at the end of six months) is paid 35 months in advance of the end, so it is worth x * (1 + .2375/12)^35 at the end of her loan period.
Similarly, the second installment is worth x * (1 + .2375/12)^34 at the end of the loan period.
Continuing, this way, the last installment is worth exactly x at the end of the loan period.
So, the total amount she paid equals:
x [(1 + .2375/12)^35 + (1 + .2375/12)^34 + ... + (1 + .2375/12)^0]
To calculate this, assume that 1+.2045/12 = a. Then the amount Charlotte pays is:
x (a^35 + a^34 + ... + a^0) = x (a^36 - 1)/(a - 1)
Clearly, this value must equal P, so we have:
x (a^36 - 1)/(a - 1) = P = 15616.67379
Substituting, a = 1 + .2045/12 and solving, we get
x = 317.82
Area of the figure is 42 in²
Step-by-step explanation:
- Step 1: The area of the figure can be found by calculating the sum of the areas of the rectangle and the right angled triangle.
⇒ Area of the rectangle = length × width = 6 × 5 = 30 in²
⇒ Area of the triangle = 1/2 × base × height = 1/2 × 4 × 6 = 12 in²
∴ Area of the figure = 30 + 12 = 42 in²
Answer:
4,2
Step-by-step explanation:
720 divided by 72 is 80
7 tens divided by 9 is 8
