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3 years ago

Hi help me 20 points!

Mathematics

1 answer:

Andrei [34K]3 years ago

8 0

Answer:

I'm pretty sure its D

Step-by-step explanation:

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Please help !!!!!!!!

Annette [7]

The answer is D cuz it cross the x

5 0

2 years ago

Find an equation of the tangent plane to the given surface at the specified point. z = ln(x − 8y), (9, 1, 0)

Archy [21]

Answer:

x - 8y - z = 1

Step-by-step explanation:

Data provided according to the question is as follows

f(x,y) = z = ln(x - 8y)

Now the equation for the tangent plane to the surface

For z = f (x,y) at the point P $(x_0,y_0,z_0)$ is

$z - z_0 = f_x(x_0,y_0)(x-x_0) + f_y(x_0,y_0)(y-y_0)\\$

Now the partial derivatives of f are

$f_x(x,y) = \frac{1}{x-8y} \\\\f_y(x,y) = \frac{8}{x-8y} \\\\P(x_0,y_0,z_0) = (9,1,0)\\\\f_z(9,1,0) = (\frac{1}{x-8y})_^{(9,1,0)}$

$\\\\=\frac{1}{9-8}$

= 1

Now

$f_y(9,1,0)=(\frac{8}{x-8y})_{(9,1,0)}\\\\ = -\frac{8}{9 - 8}$

= -8

So, the tangent equation is

$z - 0 = 1\times (x - 9) -8\times (y - 1)$

Now after solving this, the following equation arise

z = x - 9 - 8y + 8

z = x - 8y - 1

Therefore

x - 8y - z = 1

4 0

3 years ago

A $500 television is on sale for 20% off. However, you must pay 6% in sales tax. What is the final price of the television after

GrogVix [38]

20% off means you are paying 80% of the original price ( 100% - 20% = 80%)

Multiply the price of the tv by 80% to find the sale price:

500 x 0.80 = 400

Now multiply the sales price by 1 plus the tax rate to find final cost:

400 x 1.06 = 424

Final price including tax is $424

5 0

3 years ago

Paul is saving for a down payment to buy a house. The account earns 13% interest compound quarterly, and he wants to have $15,00

Tatiana [17]

Answer:

The principal must be = $8991.88

Step-by-step explanation:

Formula for compound interest is:

$A = P(1 + \frac{r}{n})^{nt}$

Where A is the amount after 't' years.

P is the principal amount

n is the number of times interest is compounded each year.

r is the rate of interest.

Here, we are given that:

Amount, A = $15000

Rate of interest = 13 % compounded quarterly i.e. 4 times every year

Number of times, interest is compounded each year, n = 4

Time, t = 4 years.

To find, Principal P = ?

Putting all the given values in the formula to find P.

$15000 = P(1 + \frac{13}{400})^{4\times 4}\\\Rightarrow 15000 = P(1 + 0.0325)^{16}\\\Rightarrow 15000 = P(1.0325)^{16} \\\Rightarrow 15000 = P \times 1.66817253\\\Rightarrow P = \dfrac{15000}{1.66817253}\\\Rightarrow P \approx \$8991.88$

So, <em>the principal must be = $8991.88</em>

4 0

3 years ago

Find the value of tan theta if sin theta = 12/13 and theta is in quadrant 2

nadya68 [22]

In quadrant 2, $\sin\theta>0$ and $\cos\theta$ . Use the Pythagorean identity to establish that

$\sin^2\theta+\cos^2\theta=1\implies\cos\theta=-\sqrt{1-\sin^2\theta}=-\dfrac5{13}$

Then

$\tan\theta=\dfrac{\sin\theta}{\cos\theta}=\dfrac{\frac{12}{13}}{-\frac5{13}}=-\dfrac{12}5$

7 0

3 years ago