When I see "at what rate", I know this question must come from
pre-Calculus, so I won't feel bad using a little Calculus to solve it.
-- The runner, first-base, and second-base form a right triangle.
The right angle is at first-base.
-- One leg of the triangle is the line from first- to second-base.
It's 90-ft long, and it doesn't change.
-- The other leg of the triangle is the line from the runner to first-base.
Its length is 90-24T. ('T' is the seconds since the runner left home plate.)
-- The hypotenuse of the right triangle is
square root of [ 90² + (90-24T)² ] =
square root of [ 8100 + 8100 - 4320T + 576 T² ] =
square root of [ 576 T² - 4320 T + 16,200 ]
We want to know how fast this distance is changing
when the runner is half-way to first base.
Before we figure out when that will be, we know that since
the question is asking about how fast this quantity is changing,
sooner or later we're going to need its derivative. Let's bite the
bullet and do that now, so we won't have to worry about it.
Derivative of [ 576 T² - 4320 T + 16,200 ] ^ 1/2 =
(1/2) [ 576 T² - 4320 T + 16,200 ] ^ -1/2 times (576T - 4320) .
There it is. Ugly but manageable.
How fast is this quantity changing when the runner is halfway to first-base ?
Well, we need to know when that is ... how many seconds after he leaves
the plate.
Total time it takes him to reach first-base = (90 ft)/(24 ft/sec) = 3.75 sec .
He's halfway there when T = (3.75 / 2) = 1.875 seconds. (Seems fast.)
Now all we have to do is plug in 1.875 wherever we see 'T' in the big derivative,
and we'll know the rate at which that hypotenuse is changing at that time.
Here goes. Take a deep breath:
(1/2) [ 576 T² - 4320 T + 16,200 ] ^ -1/2 times (576T - 4320) =
[ 576 T² - 4320 T + 16,200 ] ^ -1/2 times (1152T - 8640) =
[576(1.875)² - 4320(1.875) + 16,200]^-1/2 times [1152(1.875)-8640] =
[ 2,025 - 8,100 + 16,200 ] ^ -1/2 times [ 2,160 - 8640 ] =
- 6480 / √10,125 = - 64.4 ft/sec.
I have a strong hunch that this answer is absurd, but I'm not going to waste
any more time on it, (especially not for 5 points, if you'll forgive me).
I've outlined a method of analysis and an approach to the solution, and
I believe both of them are reasonable. I'm sure you can take it from there,
and I hope you have better luck with your arithmetic than I've had with mine.
Answer:
a) $26.4
b) $324
Step-by-step explanation:
Hire purchase is the purchase of an item which can be paid instalmentally.
The bicycle costs $300 for an instant purchase.
For a hire purchase, a $60 deposit must be made and the rest paid instalmentally over 10 months. An interest of 10% is included in the outstanding balance
The outstanding balance after paying deposit= $300 - $60 = $240
Hence, 10% of 240 = 10/100 × 240 = 24
An interest of $24 is added.
Therefore, a total of $240 + $24 = $264 will be paid for the next 10 months.
a) Hence, the amount to be paid in instalment each month is $264/10 = $26.4
b) the total cost of buying the bicycle by hire purchase= deposit amount + instalment price
= $60 + $264
= $324
Hence, a total of $324 will be paid for the bicycle by hire purchase.
N.B: $300 is the sale price + $24 interest
Yo me voy con c) 9
porque c is igual a ax3= 5x3
pienso que d deveria ser igual a bx3= 3x3
espero te ayude yo no lo estudie en espanol y pienso que cada pais nos ensena differente y perdon por mi espanol pero mi teclado es differente. :)
Answer:
624 square inches of cardboard were used to make the box.
Step-by-step explanation:
Slant height of the box = l = 20 inches
Side of the base of the box = s = 12 inch
Area of the base = 
Area of triangular face = 
There are 4 triangle faces, and single square base , so the total area is :
624 square inches of cardboard were used to make the box.
