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jolli1 [7]
3 years ago
15

Which option is correct and how would one solve for it?

Mathematics
1 answer:
Harlamova29_29 [7]3 years ago
3 0

Answer:

28

Step-by-step explanation:

We need to find the value of \Sigma_{x=0}^3\ 2x^2

We know that,

\Sigma n^2=\dfrac{n(n+1)(2n+1)}{6}

Here, n = 3

So,

\Sigma n^2=\dfrac{3(3+1)(2(3)+1)}{6}\\\\\Sigma n^2=14

So,

\Sigma_{x=0}^3\ 2x^2=2\times 14\\\\=28

So, the value of \Sigma_{x=0}^3\ 2x^2 is 28. Hence, the correct option is (d).

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Ethan earns $10 every hour for walking Ms. Barn's two dogs, plus an additional $7
MatroZZZ [7]
H=hour
10h+7=32 would be the best equation. Hope this helps!
3 0
2 years ago
In this problem we consider an equation in differential form Mdx+Ndy=0. (4x+2y)dx+(2x+8y)dy=0 Find My= 2 Nx= 2 If the problem is
zheka24 [161]

Answer:

f(x,y)=2x^2+4y^2+2xy=C_1\\\\Where\\\\y(x)=\frac{1}{4} (-x\pm \sqrt{-7x^2+C_1} )

Step-by-step explanation:

Let:

M(x,y)=4x+2y\\\\and\\\\N(x,y)=2x+8y

This is and exact equation, because:

\frac{\partial M(x,y)}{\partial y} =2=\frac{\partial N}{\partial x}

So, define f(x,y) such that:

\frac{\partial f(x,y)}{\partial x} =M(x,y)\\\\and\\\\\frac{\partial f(x,y)}{\partial y} =N(x,y)

The solution will be given by:

f(x,y)=C_1

Where C1 is an arbitrary constant

Integrate \frac{\partial f(x,y)}{\partial x} with respect to x in order to find f(x,y):

f(x,y)=\int\ {4x+2y} \, dx =2x^2+2xy+g(y)

Where g(y) is an arbitrary function of y.

Differentiate f(x,y) with respect to y in order to find g(y):

\frac{\partial f(x,y)}{\partial y} =2x+\frac{d g(y)}{dy}

Substitute into \frac{\partial f(x,y)}{\partial y} =N(x,y)

2x+\frac{dg(y)}{dy} =2x+8y\\\\Solve\hspace{3}for\hspace{3}\frac{dg(y)}{dy}\\\\\frac{dg(y)}{dy}=8y

Integrate \frac{dg(y)}{dy} with respect to y:

g(y)=\int\ {8y} \, dy =4y^2

Substitute g(y) into f(x,y):

f(x,y)=2x^2+4y^2+2xy

The solution is f(x,y)=C1

f(x,y)=2x^2+4y^2+2xy=C_1

Solving y using quadratic formula:

y(x)=\frac{1}{4} (-x\pm \sqrt{-7x^2+C_1} )

4 0
3 years ago
How to show the tens fact you used. write the difference. <br> 12-7=____<br> 10-___=____
prisoha [69]
The first answer is 5,but i don't know about the second one. (sorry)
3 0
2 years ago
The function f(x) varies directly with x, and f(x) = 45 when x = 9.
Paladinen [302]

Answer:

Option C = 15

Step-by-step explanation:

In principle when a function <em>f(x) </em>varies directly with <em>x</em> it suggests that any changes in x results in the equivalent changes in<em> f(x)</em>. If we have two variables, i.e. <em>y</em> representing<em> f(x)</em> and <em>x</em> representing itself, any increment/decrement in <em>x</em> will result to the same increment/decrement in <em>y</em> by a factor <em>a, thus we can say that y = ax, implying y and x have the same ratio. </em>

In the given question we know that <em>f(x) = 45</em> when x=9<em>, </em>which translates as

f(x=9) = 45

This tells us that f(x) varies by a factor (lets call it) a for a given value of x.

To find this factor we can just divide 45 with 9 which gives: \frac{45}{9} = 5

Thus the factor a here is a=5 which finally tells us that

f(x) = 5x    Eqn (1) our original function.

Since we now know our function we can plug in the value for x=3 and solve for f(x=3) as follow:

f(x=3)= 5*3

f(x=3) = 15

f(3) = 15

Looking at the given options in the question we can conclude that the correct answer is Option C = 15

3 0
3 years ago
Find the rate of change for the situation. A chef cooks 9 lbs of chicken for 36 people and 17 lbs of chicken for 68 people. 36 p
Alenkasestr [34]

Answer:

C. 1/4 lb of chicken per person

Step-by-step explanation:

Find the rate of change for the situation.

A chef cooks 9 lbs of chicken for 36 people and 17 lbs of chicken for 68 people.

A. 9/17lb per person

B. 4 lb per person

C. 1/4 lb per person

D. 36 people

Solution

9 lbs of chicken for 36 people

Chicken per person = Total lbs of chicken / Total number of people

= 9 lbs / 36 people

Chicken per person = 1/4 lb of chicken per person

17 lbs of chicken for 68 people

Chicken per person = Total lbs of chicken / Total number of people

= 17 lbs / 68 people

= 1/4 lb of chicken

Chicken per person = 1/4 lb of chicken per person

Therefore, the rate of change of the situation = 1/4 lb of chicken per person

6 0
3 years ago
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