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3 years ago

Complete the proof in picture

Mathematics

1 answer:

BARSIC [14]3 years ago

5 0

it won't let me type the answer I may be missing something but it says I am using rude words so sorry if I am

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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

3 years ago

How do you get the range?

stira [4]

Answer:

[7, -8)

Step-by-step explanation:

qwerttiwisnxnsnandj ahjsxkkanas gwhdjxx

4 0

2 years ago

Read 2 more answers

For there are 48 apples and 60 bananas and 96 oranges each basket must contain the same number of each type of frut Search inste

vaieri [72.5K]

This question is incomplete

Complete Question

For there are 48 apples and 60 bananas and 96 oranges each basket must contain the same number of each type of fruit. Find the greatest number of baskets you can have

Answer:

The greatest number of baskets you can have is 12 baskets.

And each baskets would contain:

4 apples, 5 bananas and 8 oranges

Step-by-step explanation:

The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

The factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

Then the greatest common factor is 12.

Therefore, the greatest number of baskets you can have is 12 baskets.

Each baskets would have

For apples

48 apples

48 apples / 12 baskets = 4 apples per basket

For bananas

60 bananas

60 bananas/12 baskets = 5 bananas per basket

For Oranges

96 Oranges/ 12 baskets = 8 oranges per baskets

8 0

2 years ago

Variables are defined by what?

skad [1K]

Answer:

A variable is a quantity that may change within the context of a mathematical problem or experiment. ... The letters x, y, and z are common generic symbols used for variables. Sometimes, we will choose a letter that reminds us of the quantity it represents, such as t for time, v for voltage, or b for bacteria.

Step-by-step explanation:

thats true❤️

8 0

2 years ago

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What is the future value of $11,600 invested for 17 years at 7.25 percent compounded annually? $32,483.60 $27,890.87 $38,991.07

Black_prince [1.1K]

The main formula is A=P(1+r/n)^nt, where A=amount of $ in the account at the specified time, P=principal (amount originally invested), r=interest rate, expressed as a decimal number, t=time, in years, of the investment, and n=number of times the account is compounded annually.
In our equation:
P=$11,600
r=7.25%=.0725
t=17 years
n=1 (compounded annually)
A= 11600(1+.[0725/1])^(1*17)
=11600(1+.0725)^17
=11600(1.0725)^17
=11600(3.286654969)
A=$38125.20

7 0

3 years ago

Read 2 more answers