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Dmitry [639]
2 years ago
15

Without using your calculator, decide which of these is larger: log8 62 or log7 50. How confident are you of your answer? Explai

n your thinking.
Mathematics
1 answer:
nataly862011 [7]2 years ago
6 0

Answer:

Step-by-step explanation:

log8 62 = x1

8^x1= 62

8^2 =64 >62 so <u>x1<2</u>

log7 50=x2

7^x2=50

7^2=49<50 so <u>x2>2</u>

we have, x1<2  and 2<x2

x1<2<x2

x1<x2

log8 62<log7 50

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A boat sails on a bearing of 038°anf then 5km on a bearing of 067°.
I am Lyosha [343]

This question is not complete

Complete Question

A boat sails 4km on a bearing of 038 degree and then 5km on a bearing of 067 degree.(a)how far is the boat from its starting point.(b) calculate the bearing of the boat from its starting point

Answer:

a)8.717km

b) 54.146°

Step-by-step explanation:

(a)how far is the boat from its starting point.

We solve this question using resultant vectors

= (Rcos θ, Rsinθ + Rcos θ, Rsinθ)

Where

Rcos θ = x

Rsinθ = y

= (4cos38,4sin38) + (5cos67,5sin67)

= (3.152, 2.4626) + (1.9536, 4.6025)

= (5.1056, 7.065)

x = 5.1056

y = 7.065

Distance = √x² + y²

= √(5.1056²+ 7.065²)

= √75.98137636

= √8.7167296826

Approximately = 8.717 km

Therefore, the boat is 8.717km its starting point.

(b)calculate the bearing of the boat from its starting point.

The bearing of the boat is calculated using

tan θ = y/x

tan θ = 7.065/5.1056

θ = arc tan (7.065/5.1056)

= 54.145828196°

θ ≈ 54.146°

7 0
2 years ago
Find the velocity in meters per second of a baseball thrown 38m from third base in 1.7s
frosja888 [35]
1.7 s<span>, then the </span>velocity<span> of the </span>baseball<span> is 22.35 </span>m/s<span> toward first base. hope this helps.</span>
3 0
2 years ago
5% of adults participate in at least 30 minutes of exercise each day. How likely is it that a randomly chosen adult will exercis
MaRussiya [10]

Answer:

5 out of 100 adults so not very likely

6 0
2 years ago
Norma received 1 penny on the first day of the month, and each day after that, she received triple the number of pennies that sh
hjlf

note that this isn't a summation problem, it just wants to find on what day will she get 10,000,000 dollars in 1 day

convert that the pennies to make it easier (100 pennies=1 dollar so that's 1,000,000,000 or a billion pennies) (note that 1,000,000,000=10^9)

each day is 3 times of the other

first day is 1, 2nd is 1*3, 3rd day is 1*3*3, 4th day is 1*3*3*3, etc

hmm, so after n days, the number of pennies is 1*3^{n-1}

one long way is to keep dividing by 3 to find how many times we need to do that to find n

easier way is to do this:

1,000,000,000=3^{n-1}

take ln of both sides

ln(1,000,000,000)=ln(3^{n-1})

ln(10^9)=ln(3^{n-1})

use properties of logarithms

9ln(10)=(n-1)ln(3)

divide both sides by ln(3)

\frac{9ln(10)}{ln(3)}=n-1

add 1 to both sides

\frac{9ln(10)}{ln(3)}+1=n

using your calculator we get 19.863=n

so after 19.863 days

but we need a whole number of days so round up to 20

20 days

it will be on day 20 of the month

4 0
2 years ago
Read 2 more answers
Jose drove from newyork to Florida. Resting for 1 hour for every 5 hours he drove. if he drove for 35 hours. how many hours did
g100num [7]
7 hours because 35 / 5 is 7
7 0
1 year ago
Read 2 more answers
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