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PilotLPTM [1.2K]
3 years ago
15

Rewrite log(17a•2b) as a sum

Mathematics
1 answer:
fgiga [73]3 years ago
4 0

log( 17a . 2b ) =

log( 17 × a × 2 × b ) =

log( 17 ) + log( a ) + log( 2 ) + log ( b )

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Find the shortest distance, d, from the point (5, 0, −6) to the plane x + y + z = 6.
DENIUS [597]

Answer:

\frac{7}{\sqrt{3}}

Step-by-step explanation:

The shortest distance d, of a point (a, b, c) from a plane mx + ny + tz = r is given by:

d = |\frac{(ma + nb + tc - r)}{\sqrt{m^2 + n^2 + t^2}} |                   --------------------(i)

From the question,

the point is (5, 0, -6)

the plane is x + y + z = 6

Therefore,

a = 5

b = 0

c = -6

m = 1

n = 1

t = 1

r = 6

Substitute these values into equation (i) as follows;

d = |\frac{((1*5) + (1*0) + (1 * (-6)) - 6)}{\sqrt{1^2 + 1^2 + 1^2}} |

d = |\frac{((5) + (0) + (-6) - 6)}{\sqrt{1 + 1 + 1}} |

d = |\frac{(-7)}{\sqrt{3}} |

d = \frac{7}{\sqrt{3}}

Therefore, the shortest distance from the point to the plane is  d = \frac{7}{\sqrt{3}}

5 0
3 years ago
A the zoo, the zookeeper make 4,000 pounds of ice. The zookeeper can make 400 pounds per day. How many days will it take to make
Nataliya [291]

Answer:

10 days.

Step-by-step explanation:

to find what you multiply from 400 to get to 4000, you divide 4000 by 400, which is 10, plug that in, 400 pounds x 10 days = 4000 pounds.

6 0
2 years ago
Read 2 more answers
Which inequality is shown in the graph?
sergij07 [2.7K]

Answer:

The answer to your question is: letter C

Step-by-step explanation:

Data

Find the Parabola's equation and express the equation as an inequality.

Vertex = (0, -5)

Equation

                               (x- h) ² = 4p(y - k)

                               x² = y + 5

                              y = x² - 5

But, we need the area upper the parabola, then

                              y ≥ x² - 5

5 0
3 years ago
What is the midpoint of the line segment with endpoints ( 3.5,2.2) and (1.5,-4.8)?
Fantom [35]

Answer:

Option A) (2.5,-1.3) is correct

The midpoint of the given line segment is M=(2.5,-1.3)

Step-by-step explanation:

Given that the line segment with end points (3.5, 2.2) and (1.5, -4.8)

To find the mid point of these endpoints midpoint formula is M=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)

Let (x_1,y_1) be the point (3.5, 2.2) and (x_2, y_2) be the point (1.5, -4.8)

substituting the points in the formula

M=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)

M=\left(\frac{3.5+1.5}{2}, \frac{2.2-4.8}{2}\right)

=\left(\frac{5}{2}, \frac{-2.6}{2}\right)

=\left(2.5,-1.3\right)

Therefore M=(2.5,-1.3)

The midpoint of the given line segment is M=(2.5,-1.3)

8 0
3 years ago
Garden A has 9 more currant bushes than Garden B. If 3 currant bushes are transplanted from Garden B to Garden A, then Garden A
marusya05 [52]

Answer:

42

Step-by-step explanation:

Let x = the original number of bushes in garden A

Let x-9 = the original number of bushes in garden B

x-9-3=x-12 = bushes in garden B after transplanting 3

x+3 = bushes in garden A after transplanting 3

x+3=1.5(x-12)

x+3=1.5x-18

0.5x=21

x=42

There were 42 current bushes in garden A

3 0
3 years ago
Read 2 more answers
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