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rosijanka [135]
2 years ago
11

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the re

gion y=4x^2, y=x^2 + 3
Mathematics
1 answer:
mina [271]2 years ago
7 0

Answer:

Step-by-step explanation:

integrate with respect to x

Area is symmetric so will be twice the integral from zero to 1

( I cannot seem to figure out how to make the lower limit negative in this editor)

A = 2\int\limits^1_0 {(x^2 + 3) - 4x^2} \, dx)

A = 2\int\limits^1_0 {-3x^2 + 3} \, dx

A = 6\int\limits^1_0 {-x^2 + 1} \, dx

A = 6(-⅓x³ + x)\left \| {{x=1} \atop {x=0}} \right.

A = 6((-⅓(1)³ + (1)) - (-⅓(0)³ + (0)))

A = 6(⅔)

A = 4 units²

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Need help plsss give you brainliest plssss help me it’s rounding money cents, dime and dollar
Vladimir [108]

Answer:

Please see the attached image for solution.

Step-by-step explanation:

Cent:  Rounding to the nearest cent or multiple of 0.01.

Dime: Rounding to the nearest 10 cents or multiple of 0.10.

Dollar: Rounding to the nearest dollar or multiples of 1.

For example, in question #21:

To round $12.3456 to the nearest cent:  you must look at the hundredths place, and pay attention to the digit to its right. In this case, the digit at the hundredths place is 4, and to its right is 5. Therefore, you must round it up to 5, making it $12.3<u>5</u>.

To round $12.3456 to the nearest dime:  you must look at the tenths place, and pay attention to the digit to its right. In this case, the digit at the tenths place is 3, and to its right is 4. Since 4 is less than 5, you must round 4 down to 0, making it into $12.<u>3</u>0.

To round $12.3456 to the nearest dollar:  you must look at the ones place, and pay attention to the digit to its right. In this case, the digit at the ones place is 2, and to its right is 3. Since 3 is less than 5, you must round 3 down to 0, making it into $1<u>2</u>.00.

5 0
3 years ago
What is the y-intercept of the line shown below? <br> A. 5<br> B. -5<br> C. 2<br> D. -2
lys-0071 [83]

Answer: -2

Step-by-step explanation: The y-intercept of a line is the point where the graph crosses or intersects the y-axis.

In this case, the line crosses the y-axis 2 units down from the

origin and we can write the coordinates of the point as (0, -2).

So the answer is -2.

3 0
2 years ago
Read 2 more answers
In Applied Life Data Analysis (Wiley, 1982), Wayne Nelson presents the breakdown time of an insulating fluid between electrodes
ale4655 [162]

Answer:

The sample mean is \bar{x}=14.371 min.

The sample standard deviation is \sigma = 18.889 min.

Step-by-step explanation:

We have the following data set:

\begin{array}{cccccccc}0.15&0.82&0.81&1.44&2.70&3.28&4.00&4.70\\4.96&6.49&7.25&8.03&8.40&12.15&31.89&32.47\\33.79&36.80&72.92&&&&&\end{array}

The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values.

The formula for the mean of a sample is

\bar{x} = \frac{{\sum}x}{n}

where, n is the number of values in the data set.

\bar{x}=\frac{0.15+0.82+0.81+1.44+2.7+3.28+4+4.7+4.96+6.49+7.25+8.03+8.4+12.15+31.89+32.47+33.79+36.80+72.92}{19}\\\\\bar{x}=14.371

The standard deviation measures how close the set of data is to the mean value of the data set. If data set have high standard deviation than the values are spread out very much. If data set have small standard deviation the data points are very close to the mean.

To find standard deviation we use the following formula

\sigma = \sqrt{ \frac{ \sum{\left(x_i - \overline{x}\right)^2 }}{n-1} }

The mean of a sample is  \bar{x}=14.371.

Create the below table.

Find the sum of numbers in the last column to get.

\sum{\left(x_i - \overline{X}\right)^2} = 6422.0982

\sigma = \sqrt{ \frac{ \sum{\left(x_i - \overline{x}\right)^2 }}{n-1} }       = \sqrt{ \frac{ 6422.0982 }{ 19 - 1} } \approx 18.889

7 0
3 years ago
Enter the resulting inequality.<br> -9 ≤ -6; Add 15 to both sides<br>​
inessss [21]

Step-by-step explanation:

-9+15=6, -6+15=9

So,

6 < 9

3 0
3 years ago
A ball is thrown horizontally with a speed of 10 m/s, from the edge of the top of the building of height 19.6m, and later strike
kodGreya [7K]
1) You need to solve t - 19.6=.5(9.8)t^2
2) Then solve fvf^2=2(9.8)(19.6)
3) As it's constant it is<span> still 10m/s
4) You need to </span><span>use the</span> time from part 1 times 10m/s
5) Use Pythagorean theorem with <span>10m/s and vf

I am pretty sure it will help you.</span>
3 0
3 years ago
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