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3 years ago

What is the answer to 12(4x+2)

Mathematics

2 answers:

Umnica [9.8K]3 years ago

7 0

The answer to this problem is 1/2

AlexFokin [52]3 years ago

3 0

Probably 6
I may be wrong but try it

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At what point on the paraboloid y = x2 + z2 is the tangent plane parallel to the plane 3x + 2y + 7z = 2? (if an answer does not

Nikitich [7]

If $f(x, y, z) = c$ represent a family of surfaces for different values of the constant $c$ . The gradient of the function $f$ defined as $\nabla f$ is a vector normal to the surface $f(x, y, z) = c$ .

Given the paraboloid

$y = x^2 + z^2$ .

We can rewrite it as a scalar value function f as follows:

$f(x,y,z)=x^2-y+z^2=0$

The normal to the paraboloid at any point is given by:

$\nabla f= i\frac{\partial}{\partial x}(x^2-y+z^2) - j\frac{\partial}{\partial y}(x^2-y+z^2) + k\frac{\partial}{\partial z}(x^2-y+z^2) \\ \\ =2xi-j+2zk$

Also, the normal to the given plane $3x + 2y + 7z = 2$ is given by:

$3i+2j+7k$

Equating the two normal vectors, we have:

$2x=3\Rightarrow x= \frac{3}{2} \\ \\ -1=2 \\ \\ 2z=7\Rightarrow z= \frac{7}{2}$

Since, -1 = 2 is not possible, therefore there exist no such point on the paraboloid $y = x^2 + z^2$ such that the tangent plane is parallel to the plane 3x + 2y + 7z = 2.

4 0

4 years ago

Noelle and Micah went to the bank to open new checking accounts. The equation C=0.2n+1.20 represents the monthly cost, C, in dol

Kaylis [27]

Answer:

C = $2.40

n = 6

Step-by-step explanation:

For Noelle,

Equation that represents the monthly cost 'C',

C = 0.2n + 1.20

Here, n = number of checks written in a month

For Micah,

Monthly cost for writing checks 'C' = $1.20

Number of checks 'n' = 3

Since, Cost of writing checks ∝ Number of checks written

C' ∝ n

C' = kn

k = $\frac{C'}{n}$

Here, k = proportionality constant

For C' = 1.2 and n = 3

k = $\frac{1.2}{3}$

k = 0.4

Equation will be,

C' = 0.4n

For any month C = C'

Therefore, 0.2n + 1.20 = 0.4n

0.4n - 0.2n = 1.20

0.2n = 1.20

n = 6

Number of checks written by Noelle and Micah = 6

For n = 6,

C = 0.2(6) + 1.20

C = $2.40

Cost of writing checks = $2.40

7 0

3 years ago

Marla's mom bought a 36-pack of water bottles at the supermarket. Each bottle has 500 mL of water. How many liters of water is t

PolarNik [594]

Answer:

18 L

Step-by-step explanation:

36 packs * 500 mL = 18000 mL

18000 mL / 1000 = 18 L

4 0

3 years ago

After losing 22 lb in each of the first two

Pavel [41]

Answer:

Weight on 1 may = 104 lb

Step-by-step explanation:

Given:

Weight on last may = 110 lb

Weight gain for to week = 2 x 19 = 38 lb

Weight lose for to week = 2 x 22 = 44 lb

Find:

Weight on 1 may

Computation:

Weight on 1 may = Weight on last may - Weight gain for to week + Weight lose for to week

Weight on 1 may = 110 - 44 + 38

Weight on 1 may = 104 lb

4 0

3 years ago

Find all constants a such that the vectors (a, 4) and (2, 5) are parallel.

Nezavi [6.7K]

Answer:

$\displaystyle a = \frac{8}{5}$ .

Step-by-step explanation:

Two vectors $(x_1,\, y_1)$ and $(x_2,\, y_2)$ are parallel to one another if and only if the ratio between their corresponding components are equal:

$\displaystyle \frac{x_1}{x_2} = \frac{y_1}{y_2}$ .

Equivalently:

$\displaystyle \frac{x_1}{y_1} = \frac{x_2}{y_2}$ .

For the two vectors in this equation to be parallel to one another:

$\displaystyle \frac{a}{4} = \frac{2}{5}$ .

Solve for $a$ :

$\displaystyle a = \frac{8}{5}$ .

$\displaystyle \frac{8}{5}$ would be the only valid value of $a$ ; no other value would satisfy the $\displaystyle \frac{x_1}{y_1} = \frac{x_2}{y_2}$ equation.

4 0

3 years ago