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3 years ago

Please help me with these questions

Mathematics

1 answer:

Scrat [10]3 years ago

3 0

3. Answer: y = 4

<u>Step-by-step explanation:</u>

Need to find the slope (m):

$\dfrac{y_2-y_1}{x_2-x_1}$

$\dfrac{4 - 4}{-3-1}$

= $\dfrac{0}{-4}$

= 0

Now input ONE of the points (1, 4) and the slope (m = 0) into the Point-Slope formula:

y - y₁ = m(x - x₁)

y - 4 = 0(x - 1)

y - 4 = 0

y = 4

********************************************************************

4. Answer: $\bold{y = \dfrac{2}{3}x + 3}$

<u>Step-by-step explanation:</u>

$y - y_1 = m(x - x_1)$

$y - 1 = \dfrac{2}{3}(x - (-3))$

$y - 1 = \dfrac{2}{3}(x + 3)$

$y - 1 = \dfrac{2}{3}x + 2$

$y = \dfrac{2}{3}x + 3$

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Complete the square and write in standard form. Show all work.What would be the conic section:CircleEllipseHyperbolaParabola

mote1985 [20]

ANSWER

This is an ellipse. The equation is:

$\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1$

EXPLANATION

We have to complete the square for each variable. To do so, we have to take the first two terms and compare them with the perfect binomial squared formula,

$(a+b)^2=a^2+2ab+b^2$

For x we have to take 16x² and -32x. Since the coefficient of x is not 1, first, we have to factor out the coefficient 16,

$16x^2-32x=16(x^2-2x)$

Now, the first term of the expanded binomial would be x and the second term -2x. Thus, the binomial is,

$(x-1)^2=x^2-2x+1$

To maintain the equation, we have to subtract 1,

$16(x^2-2x+1-1)=16((x-1)^2-1)=16(x-1)^2-16$

Now, we replace (16x² - 32x) from the given equation by this equivalent expression,

$16(x-1)^2-16+9y^2+72y+16=0$

The next step is to do the same for y. We have the terms 9y² + 72y. Again, since the coefficient of y² is not 1, we factor out the coefficient 9,

$9y^2+72y=9(y^2+8y)$

Following the same reasoning as before, we have that the perfect binomial squared is,

$(y+4)^2=y^2+8y+16$

Remember to subtract the independent term to maintain the equation,

$9(y^2+8y)=9(y^2+8y+16-16)=9((y+4)^2-16)=9(y+4)^2-144$

And now, as we did for x, replace the two terms (9y² + 72y) with this equivalent expression in the equation,

$16(x-1)^2-16+9(y+4)^2-144+16=0$

Add like terms,

$\begin{gathered} 16(x-1)^2+9(y+4)^2+(-16-144+16)=0 \\ 16(x-1)^2+9(y+4)^2-144=0 \end{gathered}$

Add 144 to both sides,

$\begin{gathered} 16(x-1)^2+9(y+4)^2-144+144=0+144 \\ 16(x-1)^2+9(y+4)^2=144 \end{gathered}$

As we can see, this is the equation of an ellipse. Its standard form is,

$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$

So the next step is to divide both sides by 144 and also write the coefficients as fractions in the denominator,

$\begin{gathered} \frac{16(x-1)^2}{144}+\frac{9(y+4)^2}{144}=\frac{144}{144} \\ \\ \frac{(x-1)^2}{\frac{144}{16}}+\frac{(y+4)^2}{\frac{144}{9}}=1 \end{gathered}$

Finally, we have to write the denominators as perfect squares, so we identify the values of a and b. 144 is 12², 16 is 4² and 9 is 3²,

$\frac{(x-1)^2}{(\frac{12}{4})^2}+\frac{(y+4)^2}{(\frac{12}{3})^2}=1$

Note that we can simplify a and b,

$\frac{12}{4}=3\text{ and }\frac{12}{3}=4$

Hence, the equation of the ellipse is,

$\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1$

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1 year ago

Can the formula F=ma be a direct variation equation? If so, which variable would have to be held constant?

ANEK [815]

Yes it can be a direct variation. it follows the form y = kx
The only variable that cannot be held constant is F, but we can hold the mass constant and vary the acceleration OR we can hold the acceleration constant and vary the mass. Either one would work, but the easiest would be to vary the mass and hold the acceleration constant since we are all pulled by the same action gravity

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3 years ago

2. Tina uSUally brings her children every Sunday afternoon at the children's park in their barangay. The park is 350m Iong and 2

Verdich [7]

Answer: kindly check explanation

Step-by-step explanation:

Given the following :

Total area of parknand path way = 74,464 m2.

Dimension of park = 350m by 200m

Using the area of rectangle formula:

Area = Length * width

Area of park = 350m * 200m

Area of park = 70,000

Area of path = (74,464 - 70,000) = 4,464m2

Since path has uniform width, then width of the the path is sqrt(4464) = 66.8m

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Answer:

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What angle do the minute and hour hands of a clock make at 8:00

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