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2 years ago

If you stand facing east and turn through 3/4 of a revolution, in which direction will you be facing?

Mathematics

1 answer:

KatRina [158]2 years ago

7 0

You will be facing north

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Write the equation of the sphere in standard form. x2 + y2 + z2 + 8x − 6y + 4z + 20 = 0

Nuetrik [128]

Answer:

$(x+4)^2 + (y-3)^2 + (z+2)^2 - 3^2 = 0$

Step-by-step explanation:

You have to find a, b, c, r so that the polynomial expands to match the given equation.

$(x-a)^2 + (y-b)^2 + (z-c)^2 - r^2 =\\x^2-2ax+a^2+\\y^2-2by+b^2+\\z^2-2cz+c^2-r^2 =\\ x^2 + y^2 + z^2 + 8x - 6y + 4z + 20$

$(a^2+b^2+c^2-r^2-20)+\\x(-8-2a)+y(6-2b)+z(-4-2c)=0$

$-8-2a=0, 6-2b=0, -4-2c=0\\a=-4, b=3, c=-2$

$(-4)^2+3^2+(-2)^2-r^2-20 = 0$

$16+9+4-20=r^2$

$r^2=9$

$r=3$

$(x+4)^2 + (y-3)^2 + (z+2)^2 - 3^2 = 0$

5 0

3 years ago

Mr. Hon purchases a new car every 4 years. Ms. Jasper purchases a new car every 6 years. They both purchased new cars this year.

Kipish [7]

Answer:

12 years

Step-by-step explanation:

Given that Mr. Hon purchases a new car every 4 years. Ms. Jasper purchases a new car every 6 years.

Assuming that they purchase new cars together after n years.

So, n must a multiple of 4 as well as multiple 6, i.e the number n is the lowest multiple (LCM) of 4 and 6.

As LCM od 4 and 6 is 12, so n=12.

Hence, after 12 years they will purchase news cars together.

5 0

3 years ago

If F(x)=3x^2-2 find (-3) x f (x)

Ivan

Answer:

-9x²+6

Step-by-step explanation:

f(x)=3x^2-2

g(x)=(-3) x f (x)

g(x)= -3*3x²-3*(-2)= -9x²+6
g(x)= -9x²+6

4 0

3 years ago

Read 2 more answers

Lea and Marie are washing all the windows in their house. It would take Lea 80 minutes to wash the windows by herself, and it wo

kvv77 [185]

The rate of the windows washed would be the amount of windows per minute. so the missing value is the amount of windows that she has washed

5 0

3 years ago

Read 2 more answers

Find the equation of the line with a slope of 3/4 and passes through (4-2)

Ira Lisetskai [31]

Answer:

y = 3/4x - 5

Step-by-step explanation:

An equation of a line can be written in slope-intercept form:

y = mx + b

where m is the slope and b is the y-intercept.

Let's plug in what we know.

The slope is 3/4.

y = 3/4x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the point (4, -2). Plug in the x and y values into the x and y of the standard equation.

-2 = 3/4(4) + b

To find b, multiply the slope and the input of x(4)

-2 = 3 + b

Now, subtract 3 from both sides to isolate b.

-5 = b

Plug this into your standard equation.

y = 3/4x - 5

This is your equation. It has a slope of 3/4, and passes through (4, -2)

Hope this helps!

5 0

2 years ago

If you stand facing east and turn through 3/4 of a revolution, in which direction will you be facing?​

If you stand facing east and turn through 3/4 of a revolution, in which direction will you be facing?