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densk [106]
3 years ago
11

How do you do this question?

Mathematics
1 answer:
tensa zangetsu [6.8K]3 years ago
3 0

Answer:

18 ln(9) − ¹⁰⁴/₉

Step-by-step explanation:

∫₁⁹ √y ln(y) dy

If u = ln(y), then du = dy/y.

If dv = √y dy, then v = ⅔ (y)^³/₂.

∫ u dv = uv − ∫ v du

= ln(y) (⅔ (y)^³/₂) − ∫ (⅔ (y)^³/₂) (dy/y)

= ln(y) (⅔ (y)^³/₂) − ∫ (⅔ (y)^½) dy

= ln(y) (⅔ (y)^³/₂) − ⁴/₉ (y)^³/₂ + C

= (⅔ (y)^³/₂) (ln(y) − ⅔) + C

Evaluate between y=1 and y=9.

[(⅔ (9)^³/₂) (ln(9) − ⅔)] − [(⅔ (1)^³/₂) (ln(1) − ⅔)]

[18 (ln(9) − ⅔)] − [(⅔) (-⅔)]

18 ln(9) − 12 + ⁴/₉

18 ln(9) − ¹⁰⁴/₉

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Bridget, Jim and Krutika share some sweets in the ratio 4:5:1. Bridget gets 39 more sweets than Krutika. How many sweets does Ji
Yakvenalex [24]

Step-by-step explanation:

Let Bridget, Jim and Krutika's shares be 4x, 5x and x respectively.

According to the given information:

4x = x + 39

4x - x = 39

3x = 39

x = 39/3

x = 13

5x = 5*13 = 65

Hence, Jim got 65 sweets.

8 0
3 years ago
Write the equation of a slope intercept form with a slope of 9 and a y-intercept of -3
Usimov [2.4K]

Answer:

y = 9x-3

Step-by-step explanation:

since the slope intercept form is in the y=mx+b form, you just have to plug in the slope for m and the y-intercept for b.

3 0
4 years ago
What is the outlier in the following data set:<br> 15,11,10,8,9,1,8,7,5,4,2,3, and 37?
NeTakaya

Step-by-step explanation:

The steps to find an outlier:

1. Put the data in numerical order.

2. Find the median.

3. Find the medians for the top and bottom parts of the data. This divides the data into 4 equal parts.

The median with the smallest value is called Q1. The median for all the values - usually just called the median is also called Q2. The median with the largest value is Q3.

4. Subtract...Q3 - Q1. This value is the InterQuartileRange or IQR. Remember that the range means taking the largest minus the smallest. This is a special range having to do with the quartiles.

5. Multiply...1.5 * IQR

6. Take your answer from #5 and do 2 things with it. A). Subtract it from Q1 and B) Additional to Q3.

7. Look at all your data points. If any are SMALLER than Q1 - 1.5 *IQR, they are outliers. If any are LARGER than Q3 + 1.5 *IQR, they are also outliers.

For your data....the median, Q2 is

(43+38)/2 = 40.5.

Q1 = (30+26)/2 = 28.

Q3 = (54+52)/2 = 53

The IQR is 53 - 28 = 25

1.5 * IQR = 37.5

Q1 - 37.5 = 28 - 37.5 = -9.5. There is no data value less than -9.5.

Q3 + 37.5 = 53 + 37.5 = 90.5. there is no data value greater than 90.5.

My conclusion is that there are no outliers in this data.

I hope this helps!

4 0
3 years ago
What's the slope of (-4,7)(-2,17)
yaroslaw [1]
Given two points (x₁,y₁) and (x₂,y₂) the slope of the line passes through these points will be:

m=(y₂-y₁)/(x₂-x₁)

Data:
The points are (-4,7) and (-2,17), then the slope will be:
m=(17-7)/(-2+4)=7/2

Answer: the slope of the line passes through these points would be 7/2
7 0
3 years ago
Read 2 more answers
Three times a number, subtracted from two equals twice the number, added to 27.find the number
timofeeve [1]

Answer:

-5

Step-by-step explanation:

Let the number be n

Three times the number: 3n

Subtracted from 2: 2-3n

Twice the number: 2n

Added to 27: 27+2n

2-3n = 27+2n

-25 = 5n

n = -5

6 0
4 years ago
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