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astraxan [27]
3 years ago
15

The expression y2 – 10y + 24 has a factor of y – 4. What is another factor of y2 – 10y + 24?

Mathematics
1 answer:
charle [14.2K]3 years ago
4 0
We may answer the question above by dividing the expression y² - 10x + 24 with the given factor, y - 4. The division would give an answer of y - 6. Thus,

                                <span>y² - 10x + 24 = (y - 4)(y - 6)

The answer is the fourth choice, y - 6.</span>
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2 years ago
A hiker is hiking in a valley. The height of the valley is h(x,y)=4x2+y2 where x and y are the east-west and north-south distanc
Ainat [17]

Answer:

A. \frac{\partial{h}}{\partial{t}}=0

Step-by-step explanation:

A. The problems asked for 2 ways to solve it, expanding the equation with the substitution  x(t)=2 cos(t) and y(t)=4 sin(t) to differentiate it . The other way is by chain rule.

Expanding and differentiating:

We start by substituting x(t)=2 cos(t) and y(t)=4 sin(t) in h(x,y)=4x2+y2:

h(x,y)=4x^{2}+y^{2}= 4(2cos(t))^{2}+(4sin(t))^{2}\\h(x,y)=4(4cos^{2}(t))+(16sen^{2}(t))\\h(x,y)=16cos^{2}(t)+16sen^{2}(t)=16(sen^{2}(t)+cos^{2}(t))\\h(x,y)=16

So, in the path that the hiker chose:

\frac{\partial{h}}{\partial{t}}=0

Chain rule:

We start differentiating h(x,y) using chain rule as follows:

\frac{\partial{h}}{\partial{t}}= \frac{\partial{h}}{\partial{x}}\frac{\partial{x}}{\partial{t}}+\frac{\partial{h}}{\partial{y}}\frac{\partial{y}}{\partial{t}}

Now, it´s easy to find all these derivatives:

\frac{\partial{h}}{\partial{x}}=8x\\\frac{\partial{x}}{\partial{t}}=-2sin(t)\\\frac{\partial{h}}{\partial{y}}=2y\\\frac{\partial{y}}{\partial{t}}=4cos(t)

Now we replace them in the chain rule, with the replacement x=2cos(t) and y=4sin(t) in the x,y that are left and we operate everything:

\frac{\partial{h}}{\partial{t}}= 8x(-2sin(t))+2y(4cos(t)

\frac{\partial{h}}{\partial{t}}= 8(2cos(t))(-2sin(t))+2(4sin(t))(4cos(t)

\frac{\partial{h}}{\partial{t}}= -32cos(t)sin(t)+32sin(t)cos(t)

\frac{\partial{h}}{\partial{t}}= 0

This will be our answer

6 0
3 years ago
2<br> -2y - 7+ 5y = 13 - 2y<br> Is there one solution no solution or infinite solutions?
Oksanka [162]

Answer:

one solution;y=-4

Step-by-step explanation:

-2y-7+-5y=13-2y

-7y-7=13-2y

-5y-7=13

-5y=20

y=-4

3 0
3 years ago
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