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3 years ago

Solve and type in a different form by using the given theorems of logarithms. log10 (M/N) =

Mathematics

1 answer:

dedylja [7]3 years ago

4 0

Answer:

log₁₀ M - log₁₀ N

Step-by-step explanation:

I want to believe that 10 is the base of the logarithm.

So, we shall have

Log₁₀ M/N =

Using the law of logarithm that says:

Log (AB) = Log A + Log B and

log (A/B) = Log A - log B.

∴Log₁₀ M/N = Log₁₀ M - Log₁₀ N

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The captain of a boat knows that a lighthouse on the coast is 100 ft

Tatiana [17]

Answer:

Height of the light house $=7.5\ feet$

Step-by-step explanation:

Distance of light house from boat = 100 ft

Angle of elevation from boat to the top of light house = 2°

Height above water while taking measurement = 4 ft

The figure of the situation is shown below.

For Δ ABC

$\tan2\°=\frac {AB}{BC}$

$\tan2\°=\frac {AB}{100}$

$0.035=\frac {AB}{100}$

Multiplying both sides by 100.

$100\times 0.035=100\times\frac {AB}{100}$

$3.5=AB$

∴ $AB=3.5$

Height of the light house $=3.5+4=7.5\ feet$

3 0

3 years ago

Please help me find the area of shaded region and step by step

Bumek [7]

Answer:

Part 1) $A=60\ ft^2$

Part 2) $A=80\ cm^2$

Part 3) $A=96\ m^2$

Part 4) $A=144\ cm^2$

Part 5) $A=9\ m^2$

Part 6) $A=(49\pi -33)\ in^2$

Step-by-step explanation:

Part 1) we know that

The shaded region is equal to the area of the complete rectangle minus the area of the interior rectangle

The area of rectangle is equal to

$A=bh$

where

b is the base of rectangle

h is the height of rectangle

$A=(12)(7)-(8)(3)$

$A=84-24$

$A=60\ ft^2$

Part 2) we know that

The shaded region is equal to the area of the complete rectangle minus the area of the interior square

The area of square is equal to

$A=b^2$

where

b is the length side of the square

$A=(12)(8)-(4^2)$

$A=96-16$

$A=80\ cm^2$

Part 3) we know that

The area of the shaded region is equal to the area of four rectangles plus the area of one square

$A=4(4)(5)+(4^2)$

$A=80+16$

$A=96\ m^2$

Part 4) we know that

The shaded region is equal to the area of the complete square minus the area of the interior square

$A=(15^2)-(9^2)$

$A=225-81$

$A=144\ cm^2$

Part 5) we know that

The area of the shaded region is equal to the area of triangle minus the area of rectangle

The area of triangle is equal to

$A=\frac{1}{2}(b)(h)$

where

b is the base of triangle

h is the height of triangle

$A=\frac{1}{2}(6)(7)-(6)(2)$

$A=21-12$

$A=9\ m^2$

Part 6) we know that

The area of the shaded region is equal to the area of the circle minus the area of rectangle

The area of the circle is equal to

$A=\pi r^{2}$

where

r is the radius of the circle

$A=\pi (7^2)-(3)(11)$

$A=(49\pi -33)\ in^2$

7 0

3 years ago

Point r is at 2,1.2 and point t is at 2,2.5 on a coordinate grid. The distance between the two points is. .

Diano4ka-milaya [45]

Answer:

1.3

Step-by-step explanation:

The two points lie on the same vertical line (x=2), so the distance between them is the difference of their y-coordinates:

2.5 - 1.2 = 1.3 . . . distance between the points

5 0

3 years ago

traveling at 65 mph, how many minutes, rounded to the nearest whole number, does it take to drive 125 miles from San Diego to ma

kkurt [141]

You have to make proportions
65mi/1h=125mi/xhours
you end up with 65x=125
125/65=1.92hours--> round it to 2 hours
it takes 2 hours

5 0

3 years ago

A Farmer Leans a 12 ft Ladder Against A Barn. The Base of the Ladder Is 6ft From The Barn.l To The Nearest Foot, How High on the

vlada-n [284]

Answer:

10 ft to nearest foot.

Step-by-step explanation:

We use the Pythagoras theorem:

12^2 = 6^2 + h^2 where h is the height on the barn

h^2 = 12^2 - 6^2

h^2 = 144 - 36 = 102

h= √108 = 10.39

5 0

2 years ago