Find the equation of the tangent plane to (a) z = 4x 2 − y 2 + 2y at (−1, 2, 4)

HELPPPPPPPPP 55 POINTS Isabel graphed the following system of equations.

Arturiano [62]

Answer:

1. Substitute y = -3x +4 for y in the first equation

2. Combine like terms and isolate x

3. Substitute in x into the 2nd equation to get y

Step-by-step explanation:

1. Substitute y = -3x +4 for y in the first equation

2x- (-3x+4) = 6

2. Combine like terms

5x -4 = 6

5x -4 +4 = 6+4

5x=10 Divide by 5 to isolate x

5x/5 =10/5

x=2

3. Substitute in x into the 2nd equation to get y

y = -3x +4

y = -3(2) +4

y = -6+4

y=-2

(2,-2)

5 0

4 years ago

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21m. what is the volume of the sphere.

Goshia [24]

Answer:

The volume of the sphere is 14m³

Step-by-step explanation:

Given

Volume of the cylinder = $21m^3$

Required

Volume of the sphere

Given that the volume of the cylinder is 21, the first step is to solve for the radius of the cylinder;

<em>Using the volume formula of a cylinder</em>

The formula goes thus

$V = \pi r^2h$

Substitute 21 for V; this gives

$21 = \pi r^2h$

Divide both sides by h

$\frac{21}{h} = \frac{\pi r^2h}{h}$

$\frac{21}{h} = \pi r^2$

The next step is to solve for the volume of the sphere using the following formula;

$V = \frac{4}{3}\pi r^3$

Divide both sides by r

$\frac{V}{r} = \frac{4}{3r}\pi r^3$

Expand Expression

$\frac{V}{r} = \frac{4}{3}\pi r^2$

Substitute $\frac{21}{h} = \pi r^2$

$\frac{V}{r} = \frac{4}{3} * \frac{21}{h}$

$\frac{V}{r} = \frac{84}{3h}$

$\frac{V}{r} = \frac{28}{h}$

Multiply both sided by r

$r * \frac{V}{r} = \frac{28}{h} * r$

$V = \frac{28r}{h}$ ------ equation 1

From the question, we were given that the height of the cylinder and the sphere have equal value;

This implies that the height of the cylinder equals the diameter of the sphere. In other words

$h = D$ , where D represents diameter of the sphere

Recall that $D = 2r$

So, $h = D = 2r$

$h = 2r$

Substitute 2r for h in equation 1

$V = \frac{28r}{2r}$

$V = \frac{28}{2}$

$V = 14$

Hence, the volume of the sphere is 14m³

4 0

3 years ago

Read 2 more answers

A total of $37185 is invested at an annual interest rate of 2% compounded quarterly. Find the balance after 11 years.

vazorg [7]

A=37,185×(1+0.02÷4)^(4×11)
A=46,309.97

8 0

3 years ago

Find the following measure for this figure.

miv72 [106K]

l=11
r=5

Now

LSA:-

πrl
π(11)(5)
55πunits ²

4 0

2 years ago

If you mix the butter and the honey together, how many tablespoons will there be in all? Write your answer as a reduced fraction

konstantin123 [22]

Answer:

battery is the answer

Step-by-step explanation:

7 0

3 years ago