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mario62 [17]
2 years ago
11

If x° – 7x2 + kx + 15 is exactly divisible by (x – 3), then find the value of k.​

Mathematics
1 answer:
faltersainse [42]2 years ago
3 0

Answer:

k=4

Step-by-step explanation:

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For a certain​ drug, the rate of reaction in appropriate units is given by Upper R prime (t )equalsStartFraction 2 Over t plus 1
Tems11 [23]

Answer:

a) 8.13

b) 4.10

Step-by-step explanation:

Given the rate of reaction R'(t) = 2/t+1 + 1/√t+1

In order to get the total reaction R(t) to the drugs at this times, we need to first integrate the given function to get R(t)

On integrating R'(t)

∫ (2/t+1 + 1/√t+1)dt

In integration, k∫f'(x)/f(x) dx = 1/k ln(fx)+C where k is any constant.

∫ (2/t+1 + 1/√t+1)dt

= ∫ (2/t+1)dt+ ∫ (1/√t+1)dt

= 2∫ 1/t+1 dt +∫1/+(t+1)^1/2 dt

= 2ln(t+1) + 2(t+1)^1/2 + C

= 2ln(t+1) + 2√(t+1) + C

a) For total reactions from t = 1 to t = 12

When t = 1

R(1) = 2ln2 + 2√2

≈ 4.21

When t = 12

R(12) = 2ln13 + 2√13

≈ 12.34

R(12) - R(1) ≈ 12.34-4.21

≈ 8.13

Total reactions to the drugs over the period from t = 1 to t= 12 is approx 8.13.

b) For total reactions from t = 12 to t = 24

When t = 12

R(12) = 2ln13 + 2√13

≈ 12.34

When t = 24

R(24) = 2ln25 + 2√25

≈ 16.44

R(12) - R(1) ≈ 16.44-12.34

≈ 4.10

Total reactions to the drugs over the period from t = 12 to t= 24 is approx 4.10

3 0
2 years ago
I need some help please
Veronika [31]
The definition of the tangent function tells you
   tan(angle) = (300 ft) / (distance to mountain)
This equation can be rearranged to
   (distance to mountain) = (300 ft) / tan(angle)

For the far end of the river,
   distance to far end = (300 ft) / tan(24°) ≈ 673.8 ft

For the near end of the river
   distance to near end = (300 ft) / tan(40°) ≈ 357.5 ft

Then the width of the river can be calculated by finding the difference of these distances:
   width of river = distance to far end - distance to near end
   width of river = 673.8 ft - 357.5 ft
   width of river = 316.3 ft

The appropriate answer choice is
   316 ft.
8 0
3 years ago
The Enterprise High School girl's soccer team won 80% of their games last year if the team won 12 games how many did they play?
jasenka [17]
I gizg A Tduuiy gf dryfchv u
3 0
2 years ago
Probability involving choosing from objects that are not distinct
Sliva [168]

Step-by-step explanation:

No. of possible selections= 5+4+3= 12

Probability of selecting drama= 3÷12

= 1÷4

PLEASE MARK BRAINLIEST.

7 0
2 years ago
The following data give the prices of seven textbooks randomly selected from a university bookstore.
swat32

Answer:

a) Mean = $121

Sum of deviations = $0

b) Standard deviation = 41.19

Variance = 1696.67

Range = $120

Step-by-step explanation:

We are given the following data:

$91 , $176 , $108 , $115 , $56 , $157 , $144

a) Mean and sum of deviations

Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}

Mean =\displaystyle\frac{847}{7} = 121

Sum of deviations =

-30 + 55 - 13 - 6 - 65 + 36 + 23 = 0

The sum of deviations is zero dollars.

b) range, variance, and standard deviation

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}  

where x_i are data points, \bar{x} is the mean and n is the number of observations.

Sum of square of differences =

900 + 3025 + 169 + 36 + 4225 + 1296 + 529 = 10180

\sigma = \sqrt{\dfrac{10180}{6}} = 41.19\\\\\sigma^2 = 1696.67

Sorted data: 56, 91, 108, 115, 144, 157, 176

Range = Maximum - Minimum

Range = 176 - 56 = 120

5 0
3 years ago
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