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3 years ago

Which logarithmic equation is equivalent to the exponential equation below? e^a=47.38

2 answers:

8 0

$\bf \textit{exponential form of a logarithm}\\\\
log_{{ a}}{{ b}}=y \implies {{ a}}^y={{ b}}\qquad\qquad 
% exponential notation 2nd form
{{ a}}^y={{ b}}\implies log_{{ a}}{{ b}}=y \\\\
-------------------------------\\\\
e^a=47.38\implies log_e(47.38)=a\implies ln(47.38)=a$

Vesnalui [34]3 years ago

3 0

Answer:

In 47.38=a

Step-by-step explanation:

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What is the distance between (8, -3), (4,-7)?

Papessa [141]

Answer:

$4\sqrt{2}$ which is none of your choices....

Did you mean (8,-3) and (4,-7)?

Step-by-step explanation:

We need to first find the distance between the x's.

Then the distance between the y's.

The distance between the x's is 8-4=4.

The distance between the y's is -3-(-7)=4.

So the distance between two points $(x_1,y1)\text{ and }(x_2,y_2)$ is $\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$ .

So we already found x1-x2 and y1-y2 so now we have:

$\sqrt{(4)^2+(4)^2}$

$\sqrt{16+16}$

$\sqrt{2(16)$

$\sqrt{16}\sqrt{2}$

$4\sqrt{2}$

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3 years ago

If you are dealt 4 cards from a shuffled deck of 52 cards, find the probability of getting 2 queens and 2 kings.

aivan3 [116]

Answer:

1.083

Step-by-step explanation:

Exact form: 13/12

Decimal form: 1.083 (put a line above the 3)

Mixed number form: 1 1/12

4 0

3 years ago

STION 1

Lorico [155]

Answer:

1.1.1- Michael has 200 lovebirds in total

1.1.2- There are 40 birds in each cage

1.1.3- 120/80 = 3/2

Step-by-step explanation:

120+80=200

200÷5=40

120÷40=3, 80÷40=2

7 0

3 years ago

The scale on a map is 1: 75 000. (a) Calculate the ACTUAL distance, in km, between two places which are 16 cm apart on the map.

finlep [7]

Answer:

a. 1 200 000 km

b. 0.000 773 cm

c. 67 500 000 000 km²

d. 0.000 000 016 cm²

Step-by-step explanation:

a. Calculate the ACTUAL distance, in km, between two places which are 16 cm apart on the map.

Since the scale is 1 : 75000 that is 1 cm : 75000 km, we want to find the actual distance of 16 cm on the map. Let x be the actual distance in km.

So, 1 cm : 75000 km = 16 cm : x km

So, 1 cm/75000 km = 16 cm/x km

Thus x km = 16 cm × 75000 km/1 cm = 1 200 000 km

(b) Calculate length of a road on the map which is 0.58 km.

Let y be the length of road on the map. So, using our scale

1 cm : 75000 km = y cm : 0.58 km

So, 1 cm/75000 km = y cm/0.58 km

Thus y cm = 0.58 km × 1 cm/75000 km = 0.000 773 cm

(c) Calculate, in km², the ACTUAL area of a lake which is 12 cm2 on the map.

Since the scale is 1 : 75000 , the scale for the area would be the square of this. So, 1² : 75000² = 1 : 5 625 000 000 which is 1 cm² : 5 625 000 000 km²

Let z be the actual area of the lake.

So, 1 cm² : 5 625 000 000 km² = 12 cm² : z km²

So, 1 cm²/5 625 000 000 km² = 12 cm²/z km²

Thus z km² = 12 cm² × 5 625 000 000 km²/1 cm² = 67 500 000 000 km²

(d) Calculate the area of a play field on the map which has has an actual area of 90 km².

Let a represent the area of the play field on the map. Using our scale for the area,

1 cm² : 5 625 000 000 km² = a cm² : 90 km²

So, a cm² = 90 km² × 1/5 625 000 000 km² = 0.000 000 016 cm²

4 0

3 years ago

Given: ABCD is a trapezoid with AB || DC. If m∠A = 125 and m∠B = 99, find m∠C/

Pavlova-9 [17]