<span>For the plane, we have z = 5x + 9y
For the region, we first find its boundary curves' points of intersection.
x = x^4 ==> x = 0, 1.
Since x > x^4 for y in [0, 1],
The volume of the solid equals
![\int\limits^1_0 { \int\limits_{x^4}^x {(5x+9y)} \, dy } \, dx = \int\limits^1_0 {\left[5xy+ \frac{9}{2} y^2\right]_{x^4}^{x}} \, dx \\ \\ =\int\limits^1_0 {\left[\left(5x(x)+ \frac{9}{2} (x)^2\right)-\left(5x(x^4)+ \frac{9}{2} (x^4)^2\right)\right]} \, dx \\ \\ =\int\limits^1_0 {\left(5x^2+ \frac{9}{2} x^2-5x^5- \frac{9}{2} x^8\right)} \, dx =\int\limits^1_0 {\left( \frac{19}{2} x^2-5x^5- \frac{9}{2} x^8\right)} \, dx \\ \\ =\left[ \frac{19}{6} x^3- \frac{5}{6} x^6- \frac{1}{2} x^9\right]^1_0](https://tex.z-dn.net/?f=%20%5Cint%5Climits%5E1_0%20%7B%20%5Cint%5Climits_%7Bx%5E4%7D%5Ex%20%7B%285x%2B9y%29%7D%20%5C%2C%20dy%20%7D%20%5C%2C%20dx%20%3D%20%5Cint%5Climits%5E1_0%20%7B%5Cleft%5B5xy%2B%20%5Cfrac%7B9%7D%7B2%7D%20y%5E2%5Cright%5D_%7Bx%5E4%7D%5E%7Bx%7D%7D%20%5C%2C%20dx%20%20%5C%5C%20%20%5C%5C%20%3D%5Cint%5Climits%5E1_0%20%7B%5Cleft%5B%5Cleft%285x%28x%29%2B%20%5Cfrac%7B9%7D%7B2%7D%20%28x%29%5E2%5Cright%29-%5Cleft%285x%28x%5E4%29%2B%20%5Cfrac%7B9%7D%7B2%7D%20%28x%5E4%29%5E2%5Cright%29%5Cright%5D%7D%20%5C%2C%20dx%20%20%5C%5C%20%20%5C%5C%20%3D%5Cint%5Climits%5E1_0%20%7B%5Cleft%285x%5E2%2B%20%5Cfrac%7B9%7D%7B2%7D%20x%5E2-5x%5E5-%20%5Cfrac%7B9%7D%7B2%7D%20x%5E8%5Cright%29%7D%20%5C%2C%20dx%20%3D%5Cint%5Climits%5E1_0%20%7B%5Cleft%28%20%5Cfrac%7B19%7D%7B2%7D%20x%5E2-5x%5E5-%20%5Cfrac%7B9%7D%7B2%7D%20x%5E8%5Cright%29%7D%20%5C%2C%20dx%20%5C%5C%20%20%5C%5C%20%3D%5Cleft%5B%20%5Cfrac%7B19%7D%7B6%7D%20x%5E3-%20%5Cfrac%7B5%7D%7B6%7D%20x%5E6-%20%5Cfrac%7B1%7D%7B2%7D%20x%5E9%5Cright%5D%5E1_0)
</span>
Answer:
Step-by-step explanation:
135 degrees
brainly plz
Answer:
V=12.167
Step-by-step explanation:
V=s^3
V=2.3x2.3x2.3
V=12.167
Since it is cubic centimeters, then it is written as 12.167cm^2
For the
writer, <span><span>there are 20
1.
</span>1
+ 39 = 40</span>
<span><span>
2.
</span>2
+ 38 = 40</span>
<span><span>3.
</span>3
+ 37 = 40</span>
<span><span>4.
</span>4
+ 36 = 40</span>
<span><span>
5.
</span>5
+ 35 = 40</span>
<span><span>
6.
</span>6
+ 34 = 40</span>
<span><span>7.
</span>7
+ 33 = 40</span>
<span><span>8.
</span>8
+ 32 = 40</span>
<span><span>
9.
</span>9
+ 31 = 40</span>
<span><span>10.
</span>10
+ 30 = 40</span>
<span><span>
11.
</span>11
+ 29 = 40</span>
<span><span>
12.
</span>12
+ 28 = 40</span>
<span><span>13.
</span>13
+ 27 = 40</span>
<span><span>
14.
</span>14
+ 26 = 40</span>
<span><span>
15.
</span>15
+ 25 = 40</span>
<span><span>
16.
</span>16
+ 24 = 40</span>
<span><span>
17.
</span>17
+ 23 = 40</span>
<span><span>
18.
</span>18
+ 22 = 40</span>
<span><span>
19.
</span>19
+ 21 = 40</span>
<span><span>
20.
</span>20
+ 20 = 40</span>
Answer:
Step-by-step explanation:
<u>Fractions</u>
They can be expressed as proper fractions, improper fractions or mixed numbers. Proper fractions are such that the numerator is less than the denominator, like 2/5, 7/11, -9/10. Improper fractions are those whose numerators are greater than the denominator, such as 5/3, 10/9, -21/8.
Mixed numbers are expressions made of whole numbers and a proper fraction, like 4 3/5, 1 1/2, -5 4/9. Mixed numbers can be transformed to improper fractions and vice-versa.
The question requires us to find the average change in field position on each run of the running back for the Bulldogs football team which carried the ball 5 times for a total loss of 11 1/4 yards.
The number 11 1/4 is mixed, to express it as an improper fraction, we add the numbers like
This improper fraction will now be divided by 5 to find the average of 5 runs:
We now need to separate the improper fraction to a mixed number, let's just divide 9 by 4 to get 2 as the quotient and 1 for the remainder, thus
