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xz_007 [3.2K]
3 years ago
10

An environmentalist is studying a certain microorganism in a sample of city lake water. The function h(x) = 146(1.16)ˣ gives the

number of the microorganisms present in the water sample at the end of x weeks. Which statement is the best interpretation of one of the values of the function? *
F. After 1 week, there will be 146 microorganisms in the water sample.
G. The initial number of microorganisms in the water sample was 16.
H. The number of microorganisms decreases by 84% each week.
J. The number of microorganisms increases by 16% each week.
Mathematics
1 answer:
Sever21 [200]3 years ago
6 0

Answer:

j

Step-by-step explanation:

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Find a point on the curve x^3+y^3=11xy other than the origin at which the tangent line is horizontal.
attashe74 [19]

Compute the derivative dy/dx using the power, product, and chain rules. Given

x³ + y³ = 11xy

differentiate both sides with respect to x to get

3x² + 3y² dy/dx = 11y + 11x dy/dx

Solve for dy/dx :

(3y² - 11x) dy/dx = 11y - 3x²

dy/dx = (11y - 3x²)/(3y² - 11x)

The tangent line to the curve is horizontal when the slope dy/dx = 0; this happens when

11y - 3x² = 0

or

y = 3/11 x²

(provided that 3y² - 11x ≠ 0)

Substitute y into into the original equation:

x³ + (3/11 x²)³ = 11x (3/11 x²)

x³ + (3/11)³ x⁶ = 3x³

(3/11)³ x⁶ - 2x³ = 0

x³ ((3/11)³ x³ - 2) = 0

One (actually three) of the solutions is x = 0, which corresponds to the origin (0,0). This leaves us with

(3/11)³ x³ - 2 = 0

(3/11 x)³ - 2 = 0

(3/11 x)³ = 2

3/11 x = ³√2

x = (11•³√2)/3

Solving for y gives

y = 3/11 x²

y = 3/11 ((11•³√2)/3)²

y = (11•³√4)/3

So the only other point where the tangent line is horizontal is ((11•³√2)/3, (11•³√4)/3).

3 0
2 years ago
Question 1 WRONG With what number must 3.475817 be multiplied in order to obtain the number 34,758.17? A 100 1,000 10,000 D 100,
lbvjy [14]

Answer:

1 - Option C - 10,000

2 - 3x+5 will be 12 more than 3x-7.

Step-by-step explanation:

1) To find : With what number must 3.475817 be multiplied in order to obtain the number 34,758.17?

Solution :

The number 3.475817 is multiplied by number to obtain 34,758.17.

As we see that, the decimal is moved four places to the right.

Which means the number is multiplied by 10000.

i.e. 3.475817\times 10000=34,758.17

Therefore, option C is correct.

2) To find : How much greater is the value of 3x+5 than the value of 3x−7?

Solution ;

Assuming that x is the same value in each equation,

In order to determine the difference between the two values,

We ignore the 3x part as it is the same on both of the equations.

So, from 5 to -7 i.e. 7+5=12.

Therefore, 3x+5 will be 12 more than 3x-7.

5 0
3 years ago
In one day, a book store earned $253 in sales for 4 copies of a new cookbook and 5 copies of a new science fiction novel. On the
Aloiza [94]

Answer: cookbook $40 and science $15

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
A car drives with an average velocity of 20.1 m/s . After some time, it has traveled 34.2 km. How long has the car been travelin
exis [7]

Answer:

time = distance / velocity

time = 34,200 meters / 20.1 meters per second

time = 1,701.4925373134 seconds

time = 28.36 minutes

 

Step-by-step explanation:

3 0
3 years ago
After a storm, 135 trees out of 180 were left standing. What is the percentage loss of the number of trees?
beks73 [17]

Answer:

Percentage loss of the number of trees is 25\%.

Step-by-step explanation:

Given: After a storm, 135 trees out of 180 were left standing.

To find: What is the percentage loss of the number of trees?

Solution:

We have,

Total number of trees =180

Number of trees left standing =135

Therefore, loss of trees=180-135=45

We now that \text {Loss\%}=\frac{\text{Number of trees left}}{\text{Total number of trees}}\times 100 \%

\implies \text {Loss\%}=\frac{45}{180}\times 100 \%

\implies \text {Loss\%}=\frac{450}{18} \%

\implies \text {Loss\%}=25 \%

Hence, the percentage loss of the number of trees is 25\%.

6 0
3 years ago
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