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faltersainse [42]
3 years ago
11

Hello there help me please i will reward you

Mathematics
1 answer:
natima [27]3 years ago
4 0
Multiply anything by zero gives zero.
0 × (x + 2) = 0
(x - 6) × 0 = 0
One must equal zero

set them equal to zero and solve for x.

x - 6 = 0
x = 6

x + 2 = 0
x = -2





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Find the points on the cone z2 = x2 + y2 that are closest to the point (6, 2, 0).
aliya0001 [1]

Answer:

The closest points on the cone are;

(6, 2, -√10) and (6, 2, √10)

Step-by-step explanation:

Let B(x, y, z) denote a point on the cone.

Therefore, the distance between the points (6, 2, 0) and B(x, y, z) is;

d = √[(x - 6)² + (y - 2)² + (z - 0)²]

d = √[(x - 6)² + (y - 2)² + z²]

Since we are given that z² = x² + y², we now have;

d = √[(x - 6)² + (y - 2)² + x² + y²]

Taking the square of both sides gives;

d² = [(x - 6)² + (y - 2)² + x² + y²]

x² is an increasing function. Thus, minimizing d is also the same as to minimize f (x, y) = d²

Thus, f' = 0. So;

df/dx = 2(x - 6) + 2x = 0

2x - 12 + 2x = 0

4x = 12

x = 12/4

x = 3

Similarly,

df/dy = 2(y - 2) + 2y = 0

2y - 4 + 2y = 0

4y - 4 = 0

4y = 4

y = 4/4

y = 1

Now,from earlier;

z² = x² + y²

Thus;

z = ±√(3² + 1²)

z = ±√10

Thus, the closest points on the cone are;

(6, 2, -√10) and (6, 2, √10)

7 0
3 years ago
In Europe, gasoline efficiency is measured in km/L. If your car's gas mileage is 31.0mi/gal , how many liters of gasoline would
maw [93]
We need to convert the mileage from mi/gal units into to km/L units using the conversion factors.

(31.0 mi/gal) x (1 km / 0.6214 mi) x (1 gal / 3.78 L) = 13.20 km/L

Next, we divide the distance by the mileage. 
(142 km) / (13.20 km/L) = 10.79 L

<span>Therefore, you need 10.79 liters of gasoline.</span>
7 0
3 years ago
Read 2 more answers
Mahra saw an ad for three t-shirts for $33 and four t-shirts costing $42. Is the relationship of price and number of t-shirts a
slamgirl [31]

Answer

no  because as per the first ad the rate of a shirt is 11 dollars wherelse if u take second one its 2 dollars lesser

Step-by-step explanation:

1 shirt=33/3

=11

11*4=44

*=multiplication

4 0
3 years ago
Volume of a cylinder with a 3 inch diameter is two times the volume of a cylinder with the same height in a 1/2 inch radius what
Alex73 [517]

Answer:

yes

Step-by-step explanation:

yes yes yes

5 0
3 years ago
​34% of working mothers do not have enough money to cover their health insurance deductibles. You randomly select six working mo
tamaranim1 [39]

Answer:

solution below

Step-by-step explanation:

The question says 6 working mother's were selected so <u>n = 6</u><u> </u><u>not</u><u> </u><u>0</u><u>.</u><u>6</u>

We are expected to find

P(X = 0,1,2,3,4,4,6)

1. <u>When x = 0</u>

6C0*(0.34)⁰*(0.66)⁶

= 1 *1* 0.827

= 0.0827

<u>2. When X = 1</u>

6C1*(0.34)¹*(0.66)⁵

= 6 x 0.34 x 0.252

= 0.2555

<u>3. When X = 2</u>

6C2*(0.34)²*(0.66)⁴

= 15 x 0.1156 x 0.1897

= 0.3289

<u>4. When x = 3</u>

6C3*(0.34)³*(0.66)³

20 x 0.039304 x 0.2875

= 0.2599

<u>5. When X = 4</u>

6C4*(0.34)⁴*(0.66)²

= 15 x 0.01336 x 0.4356

= 0.8729

<u>6. When x = 5</u>

6C5*(0.34)⁵*(0.66)¹

= 6 x 0.0045 x 0.66

= 0.01782

<u>7. When x = 6</u>

6C6*(0.34)⁶*(0.66)⁰

1 x 0.0015 x 1

= 0.0015

5 0
3 years ago
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