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2 years ago

What is the y-intercept of the graph of the equation y = 2(x - 3)² + 7? -3 6 7 25

Mathematics

1 answer:

babunello [35]2 years ago

6 0

The y-intercept would be 25, if you want to find the y-intercept, plug in zero for x!

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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

2 years ago

16. A triangle has side lengths of 6, 8, and 10. Is it a right triangle? Explain. (2 points)

timurjin [86]

Answer:

Yes, because when the side lengths of a triangle are in the ratio 3: 4: 5, then it is a right triangle. These sides are 6: 8: 10, then the triangle is a right one.

Step-by-step explanation:

7 0

2 years ago

William has 8 1/4 cups of fruit juice. If he divides the juice into 3/4 cup servings, how many servings will he have?

nikdorinn [45]

Answer: 11 servings

Step-by-step explanation:

To get the number of servings, all we need to do is divide 8 1/4 by 3/4

converting 8 1/4 to improper fraction will yield 33/4

8 1/4 ÷ 3/4

=33/4 ÷ 3/4

= 33/4 ÷ 4/3

The 4 at the numerator will cancel the 4 at the denominator. we will be left with;

=33/3 =11

Therefore, there will be 11 servings.

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2 years ago

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Help please I have like 20 minutes to complete this

Nataliya [291]

Answer: b

Step-by-step explanation:

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1 year ago

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If I have 10 apples and I eat 5 how many do I have

givi [52]

Answer:

10-5=5 the answer is 5

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2 years ago

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