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valkas [14]
3 years ago
8

Given: 4d=1/3(c-d) Proof= c=13d

Mathematics
1 answer:
Reika [66]3 years ago
8 0

Proof:

Multiply both of the sides by 3. You would get 12d = c - d. Add d on both sides, and you would get c = 12d

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can someone pls help me? i have no idea what to do. pls show the work steps for the questions. i will mark u as
tiny-mole [99]

Ok, so the question is based on geometric progression. Remember, the formula for calculating the nth-term of a geometric progression is: a*r^{n-1}. The a in the expression stands for the 1st term of the sequence, and r is the common ratio of the elements of the sequence. Now let's take a look at the problem.

"A ping pong ball has a 75% rebound ration". We can infer that our common ratio, r, is 75% which is 0.75.

"When you drop it from a height of k feet...", this means the first height you drop it from, a.k.a, the first term.

Now going back to the expression, the nth-term = a*r^{n-1}, we can substitute our common ration, 0.75 with r, and our 1st term, k, with a. This becomes: k * 0.75^{n-1}. This becomes our expression.

a. The highest height achieved by the ball after six bounces. Our nth-term here is 6, so let's use our expression to find the 6th term. n_{6} = 235 * 0.75^{6-1} = 235*0.75^{5} = 235*0.2373 = 55.7655ft

b. The total distance travelled by the ball when it strikes the ground for the 12th time. This involves the use of the sum of elements in the geometric progression. The formula for that is \frac{a(1 - r^{n})}{1-r}, provided that r is less than 1, which it is in this case, since 0.75 is less than one. Our nth-term here is 12, so we substitute.

\frac{235(1-0.75^{12})}{(1-0.75)} = 910.2242ft

6 0
2 years ago
The radius of a circle is 4.53 in. What is the length of the circumference of the circle?
Inessa05 [86]

Answer:

28.4484

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Starlight tree farms sells douglas firs and noble first one December they sold 139 more douglas first than noble firs the total
Aloiza [94]
Part A:

Given that <span>Starlight tree farms sells Douglas Firs and Noble First.

Let </span>n be the number of Noble Fir trees sold, then<span> if they sold 139 more Douglas First than Noble Firs, this means that the number of Douglas First trees sold is n + 139.

Given that the total number of trees sold was 377, then we have, n + n + 139 = 377, which means that 2n + 139 = 377

Therefore, the equation that could be used to solve for n, the number of Noble Fir trees sold is 2n + 139 = 377.


Part B:

</span><span>Given that you are driving 55 miles per hour and you must drive a total of 440 miles. If you already driven 275 miles, then, the equation representing the number of hours, h, it will take to reach your destination is given by 55h + 275 = 440.

Subtracting 275 from both sides of the equation gives:

</span>55h+275-275=440-275 \\  \\ \Rightarrow55h=165
<span>
Dividing both sides by 55 gives:

</span>\frac{55h}{55} = \frac{165}{55}  \\  \\ \Rightarrow h=3
<span>
Therefore, the time it will take you to reach your destination is 3 hours.</span>
6 0
3 years ago
Traveling with the current, a boat covers a distance 1.5 times greater than traveling against the current in the same amount of
jeka94
Let the speed of the current equal c
and the speed of the boat in still water equal b.

b + c = 1.5 (b - c)
b + c = 1.5b - 1.5c
0.5b = 2.5c
b = 5c

The speed of the current is 1.5 mph so
b = 5 * 1.5 = 7.5 mph
4 0
3 years ago
Lettuce is packed four to a box . If there are 3.5 boxes of Lettuce in the cooler , how many bags of Lettuce would there be
Tanya [424]
3.5 x 4 = 14 lettuces
8 0
3 years ago
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