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Alex777 [14]
4 years ago
9

PLEASE I NEED HELP WITH THIS QUESTION A.S.A.P.

Mathematics
1 answer:
Komok [63]4 years ago
6 0
#12 is 15 instructors because 145÷10= 14 with 5 left over. You need another instructor even though there are only 5 kids. 14+1=15
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A contaminant is leaking into a lake at a rate of R(t) = 1700e^0.06t gal/h. Enzymes that neutralize the contaminant have been ad
olasank [31]

Answer:

16,460 gallons

Step-by-step explanation:

This is a differential equation problem, we have a constant flow of contaminant into the lake, but also we know that only a fraction of that quantity of contaminant remains because of the enzymes. For that reason, the differential equation of contaminant's flow into the lake would be:

\frac{dQ}{dt} =1700exp(0.06t)*exp(-0.32t)\\\frac{dQ}{dt} =1700exp(-0.26t)\\

Then, we have to integrate in order to find the equation for Q(t), as the quantity of contaminant in the lake, in function of time.

\int\limits^0_t {dQ}=\int\limits^0_t {1700exp(-0.26t)dt}\\Q(t)=\frac{1700}{-0.26} exp(-0.26t)+C \\

Now, we use the given conditions to replace them in the equation, in order to solve for C

t_{0} =0\\Q_{0}=10,000\\Q_{0}=-6538exp(-0.26*0)+C\\C=10,000+6538=16538

Then, we reorganize the equation and we replace t for 17 hours, in order to determine the quantity of contaminant at that time:

Q_{t} =-6538exp(-0.26t)+16538\\Q_{17} =-6538exp(-0.26*17)+16538\\Q_{17} =16460 gallons

3 0
3 years ago
A soccer club spent $97.50 on trophies from a custom trophy company. The cost of manufacturing x custom trophies is $18.50 for t
Tomtit [17]
They bought 5 trophies total

1st trophy cost $37.50
($18.50+$12.50+$4+$2.50=$37.50)
Each additional trophy cost $15
($12.50+$2.50=$15)

They spent $97.50 total
$97.50-$37.50=$60
Additional trophies $15
$15*X=$60
4 trophies=$60+$37.50 for 1st trophy
$60+$37.50=$97.50


6 0
4 years ago
Question 4 (Fill-In-The-Blank Worth 4 points)
alexdok [17]
- The area of the club stickers is 112 square inches.

- We know this because...
1. The calculations of a triangle is... 1/2 x b(h)

2. So first, lets calculate the b(h) first, which is 16 x 14 = 224 square inches.
  - This isn't the correct answer because it is the area of a rectangle.

3. Second, lets calculate 1/2 x 224 = 112 square inches.
  - We did this calculation because we are talking about a triangle.

- So, the total square inches of the club sticker is 112 square inches.

Hope this helps! :)
7 0
3 years ago
Read 2 more answers
Help meeeeee. Ksjsjsjs:(
BaLLatris [955]

Answer:

a rule to know: a median divides the side into equal parts.

we know:

PR = -2a + 34

SR = 2a + 26

- based on the rule, SR is half of PR. in other words, PR is two times greater than SR.

so,

2SR = PR (now simply pluggin the expressions we have)

2(2a + 26) = -2a + 34 (solve the equation like any other equation prob.)

4a + 52 = -2a + 34

6a + 52 = 34

6a = -18

a = -3

- inorder to check if this is correct, simply reverse what we did. so pluggin the value of a to see if its correct.

3 0
3 years ago
Expand and simplify (2x + 1)(x + 3)​
Paul [167]

2x2 + 7x + 3 -answer

(2x + 1) (x + 3)

(2x * x) + (2x * 3) + (1 * x) + (1 * 3)

2x2 + 6x + x+3

2x2 + 7x + 3

8 0
3 years ago
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