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torisob [31]
3 years ago
12

5th grade math. Correct answer will be marked brainliest.

Mathematics
1 answer:
Nutka1998 [239]3 years ago
6 0

Answer:

407.4

Step-by-step explanation:

Answer:

Partial product 1: 194

Partial product 2: 388

Answer: 407.4

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Evaluate the line integral, where c is the given curve. (x + 9y) dx + x2 dy, c c consists of line segments from (0, 0) to (9, 1)
viktelen [127]
\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=\int_C\langle x+9y,x^2\rangle\cdot\underbrace{\langle\mathrm dx,\mathrm dy\rangle}_{\mathrm d\mathbf r}

The first line segment can be parameterized by \mathbf r_1(t)=\langle0,0\rangle(1-t)+\langle9,1\rangle t=\langle9t,t\rangle with 0\le t\le1. Denote this first segment by C_1. Then

\displaystyle\int_{C_1}\langle x+9y,x^2\rangle\cdot\mathbf dr_1=\int_{t=0}^{t=1}\langle9t+9t,81t^2\rangle\cdot\langle9,1\rangle\,\mathrm dt
=\displaystyle\int_0^1(162t+81t^2)\,\mathrm dt
=108

The second line segment (C_2) can be described by \mathbf r_2(t)=\langle9,1\rangle(1-t)+\langle10,0\rangle t=\langle9+t,1-t\rangle, again with 0\le t\le1. Then

\displaystyle\int_{C_2}\langle x+9y,x^2\rangle\cdot\mathrm d\mathbf r_2=\int_{t=0}^{t=1}\langle9+t+9-9t,(9+t)^2\rangle\cdot\langle1,-1\rangle\,\mathrm dt
=\displaystyle\int_0^1(18-8t-(9+t)^2)\,\mathrm dt
=-\dfrac{229}3

Finally,

\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=108-\dfrac{229}3=\dfrac{95}3
5 0
3 years ago
there are 30 students in mr. Holland music class. If 30% of the students play in the school band, how many students in the class
MA_775_DIABLO [31]
9 students 30% ends up being .3%, multiply .3% by 30 students which equals 9.
3 0
3 years ago
Read 2 more answers
The diameter of a circle is 4 kilometers. What is the circle's circumference?
scZoUnD [109]

Answer:

12.57 km

Step-by-step explanation:

Radius = 4 / 2 = 2 km

Circumference = 2πr = 2π(2) = 4π = 12.57 km

6 0
2 years ago
Read 2 more answers
Barney's Book Store currently has 2000 books in stock. There are 3 times as many non-fiction books as fiction books. Determine t
xxMikexx [17]

Answer:

There are 1500 non fiction books and 500 fiction books currently in the store.

Step-by-step explanation:

Given:

Total Number of books = 2000

Let the number of fiction books be 'x'.

Now given:

There are 3 times as many non-fiction books as fiction books.

Number of non fiction books = 3x

We need to find the number of non-fiction and fiction books.

Solution:

Now we know that;

Total Number of books is equal to sum of the number of non-fiction and fiction books.

framing in equation form we get;

x+3x=2000\\\\4x=2000

Dividing both side by 4 we get;

\frac{4x}{4}=\frac{2000}{4}\\\\x= 500\ books

Number of fiction books = 500

Number of non fiction books = 3x=3\times 500 =1500

Hence There are 1500 non fiction books and 500 fiction books currently in the store.

8 0
3 years ago
5 pounds of tomatoes cost $15.50. How much does one pound of tomatoes cost?
Tanzania [10]

Answer:

C 3.10

Step-by-step explanation:

15.50 divide by 5 is 3.10

Brainliest?

3 0
3 years ago
Read 2 more answers
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