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3 years ago

Find an equation of the largest sphere with center (4, 3, 6) that is contained in the first octant.

1 answer:

8 0

See, pls, the offered explanation:
1. equation for sphere has a form: (x-x₀)²+(y-y₀)²+(z-z₀)²=r², where x₀, y₀ and z₀ are points of center (4;3;6), and r - radius of sphere.
2. according to the task the sphere must be in the 1-t octant and must be the largest, it means that among all the possible radius (4-0=4; 3-0=3; 6-0=6) need to choose the shortest one. r=3.
3. summary: (x-4)²+(y-3)²+(z-6)²=3.

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Building a is 190 feet shorter than building

MaRussiya [10]

We will solve this using a system of equations. The first part tells us that building a is 190 feet shorter than building b. Our first equation, then, is b=190+a. The second part tells us that the addition of the two buildings' heights is 1480. So our second equation is a + b = 1480. The first equation is already solved for b, so let's sub that value into the second equation for b: a+(190+a)=1480. 2a + 190 = 1480 and 2a = 1290. That means that building a is 645 feet tall. Building b is 190 feet taller, so b = 190 + 645, which is 835.

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3 years ago

What are the factors of58

liubo4ka [24]

1,2, 29,and 58 are the factors of 58.

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3 years ago

Ms. Larson was driving home from a vacation. At noon, she was 120 miles from home. Half an hour later, she was 98 miles from hom

melomori [17]

Answer: her speed was “44 miles per hour”

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3 years ago

Indicate in standard form the equation of the line passing through the given points.

lorasvet [3.4K]

Answer:

y = 6

Step-by-step explanation:

Let the y-intercept form of the equation of the line is,

y = mx + b

Here, m = Slope of the line

b = y-intercept

Slope of the line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by,

m = $\frac{y_2-y_1}{x_2-x_1}$

Slope of the passing through (0, 6) and (5, 6) will be,

m = $\frac{6-6}{0-5}$

m = 0

Equation of the line with m = 0 will be,

y = 0 + b

y = b

Since, line passes through (0, 6),

By substituting the values in the equation,

b = 6

Therefore, standard equation of the line passing through (0, 6) and (5, 6) will be,

y = 6

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3 years ago

Jayden has been reading a 275275275-page book for english class. on average, he has read about 101010 pages in 151515 minutes (\

Vitek1552 [10]

75 pages.
OK. Lots of copying errors here. I'll be using 275 page book, reading 10 pages per 15 minutes, skimming 15 pages per 10 minutes, 5 hours and 50 minutes to complete the book.
To make things easier, first convert the time to just minutes. So 5 * 60 + 50 = 300 + 50 = 350 minutes.

Now let's use the variable X for the number of minutes spent skimming and (350-X) for the number of minutes spent reading.
X * 15/10 + (350 - X)*10/15 = 275

Solve for X.
X * 15/10 + (350 - X)*10/15 = 275
X * 15/10 + 350*10/15 - X*10/15 = 275
X * 15/10 - X*10/15 = 275 - 350*10/15
X(15/10 - 10/15) = 275 - 3500/15
X(45/30 - 20/30) = 825/3 - 700/3
X(25/30) = 125/3
X = 125/3 * 30/25 = 125/1 * 10/25 = 5/1 * 10/1 = 50/1 = 50
So Jayden spent 50 minutes skimming. And at the rate of 15 pages every 10 minutes, he skimmed 50*15/10 = 750/10 = 75 pages.

7 0

3 years ago