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2 years ago

What is the closest point on the line y = 2x - 5 to (4, 8)?

Mathematics

1 answer:

Gekata [30.6K]2 years ago

7 0

Answer: I think it is (6.5, 8).

Step-by-step explanation:

I don't know if you had any choices, but I graphed it on Desmos and that was the closest point. I hope this helps!! :)

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Find the rate of change of f(x, y, z) = xyz in the direction normal to the surface yx2 + xy2 + yz2 = 3 at (1, 1, 2).

Paladinen [302]

Answer:

Rate of change = 18/√74

Step-by-step explanation:

The rate of change of f at x_o in the direction of the unit vector v is given by: ∇f(x_o) × v

Now, for us to get the direction of the unit vector, since we are told that f(x, y, z) = xyz in the direction normal to the surface yx² + xy² + yz² = 3, we will use; g(x, y, z) = yx² + xy² + yz² = 3 and k =3 to give;

∇g(x,y,z) = (2xy + y², (x² + 2xy + z²), 2yz)

So;

∇g(1, 1, 2) = (2(1 × 1) + 1²) , (1² + 2(1 × 1) + 2²), 2(1 × 2))

This gives;

∇g(1, 1, 2) = (3, 7, 4)

Now,

||∇g(1, 1, 2)|| = √(3² + 7² + 4²)

||∇g(1, 1, 2)|| = √74

Normal vector would be given by the formula;

v = [∇g(1, 1, 2)]/[||∇g(1, 1, 2)||]

Thus;

v = (3, 7, 4)/√74

Let's not forget that our ∇f(1, 1, 2) = (1, 1, 2)

Thus, rate of change is given by;

∇f(1, 1, 2) × v = (1, 1, 2) × (3, 7, 4)/√74

This gives;

Rate of change = [(1 × 3) + (1 × 7) + (2 × 4)]/√74 = 18/√74

7 0

3 years ago

In a taste test, 50 participants are randomly given a beverage to sample.

SOVA2 [1]

Answer:

20 out of the 50 participants are assigned to consume Drink A.

However, it is asking us the probability that a participant did NOT consume Drink A, so there are 30 participants that consumed another drink.

The probability is 30/50, or 60%, that a participant did not sample Drink A.

5 0

3 years ago

Read 2 more answers

Answer question (picture below) and show work please

antiseptic1488 [7]

Answer:

$A(x)=7x^2-2x+10$

Step-by-step explanation:

Long Division

The polynomial long division implies the sequential division of each term of the dividend polynomial by the terms of the divisor polynomial. The procedure is a well-know sequence of steps from which there are two outputs: the quotient and the remainder.

We have two mathematical models, one for the total number of visitors who went to a theme park:

$F(x)=126x^3+279x^2+90x+450$

The other for the number of shows played at the theme park in the same period

$G(x)=18x+45$

Where x is the number of days since October 1. We are required to find the expression for the average number of visitors per show. It comes by dividing F(x) by G(x). We must perform a long division as shown below.

The average number of visitors per show is

$A(x)=7x^2-2x+10$

For example, day 5

$A(5)=7\ 5^2-2(5)+10=175$

There were 175 visitors per show (on average)

7 0

3 years ago

Will give brainliest!Please find the area!

sveticcg [70]

Answer:

70,000 brainliest meee

Step-by-step explanation:

6 0

3 years ago

In a cookie jar containing 6 chocolate chip cookies, 8 sugar cookies, and 10 peanut butter cookies, what is the probability that

Stells [14]

Hello there.

Question: I<span>n a cookie jar containing 6 chocolate chip cookies, 8 sugar cookies, and 10 peanut butter cookies, what is the probability that a person who isn’t looking as they pull out one cookie, will get a chocolate chip cookie?

Answer: First you need to calculate the total of cookies in the jar.
6 + 10 + 8 = 24.
There are 6 chocolate chip cookies.
Therefore the fraction is </span> $\frac{6}{24}$
You can simplify it after that if you wish to.

In short, Your answer is $\frac{6}{24}$ .
In simplified form it would be $\frac{1}{4}$ .

Hope This Helps You!
Good Luck Studying ^-^

8 0

3 years ago