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3 years ago

The sum of all positive integers less than 300 which are not divisible by 3.

Mathematics

1 answer:

dimaraw [331]3 years ago

7 0

Answer:

30000

Step-by-step explanation:

all positive integers less than 300 (300 exclusive)

1,2,3,4,5..........149,150,151.......296,297,298,299

there are (1+299) (2+298) (3+297)...(149+151) 149 pairs of 300 + 150

300 x 149 + 150 = 44850

all positive integers less than 300 which are divisible by 3

3,6,9,12..........294,297 i.e. 3 x (1,2,3,4.......49,50,51.....97,98,99)

3 x ((100 x 49) + 50) = 3 x 4950 = 14850

Answer: 44850 - 14850 = 30000

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A boat sails on a bearing of 77 degrees for 135 miles and then turns and sails 207 miles on a bearing of 192 degrees. Find the d

Andrew [12]

Answer:

193.53 miles

Step-by-step explanation:

Please see the diagram for understanding of how the angles were derived,

Applying Alternate Angles, ABO =77 degrees

The bearing from B to C is 192=180+12 degrees

Subtracting 12 from 77, we obtain the angle at B as 65 degrees.

We want to determine the boat's distance from its starting point.

In the diagram, this is the line AC.

Applying Law of Cosines:

$b^2=a^2+c^2-2acCosB\\b^2=207^2+135^2-2(207)(135)Cos65^\circ\\b^2=37453.8654\\b=\sqrt{37453.8654} \\b=193.53\: miles$

The distance of the boat from its starting point is 193.53 miles (correct to 2 decimal places).

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3 years ago

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san4es73 [151]

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3 years ago

Read 2 more answers

A detective finds a victim of murder at 9 am. At that time, the temperature of the body is 90.3 degrees F. One hour later, the b

LekaFEV [45]

Answer:

Step-by-step explanation:

Given

at 9 am temperature of the body is $90.3^{\circ}F$

1 hr later temperature $89^{\circ}F$

Temperature of room $T=68^{\circ}F$

According to newtons law

$\frac{\mathrm{d} T}{\mathrm{d} t}=-k\left ( T-T_{room}\right )$

$\frac{\mathrm{d} T}{\mathrm{d} t}=-k\left ( T-68\right )$

$\frac{dT}{T-68}=-kdt$

Integrating

$=\int \frac{dT}{T-68}=-kdt$

$\ln |T-68|=-kt+c$

$T-68=Ae^{-kt}$

Now at 9 am i.e. t=0,

$90.3=A+68$

$A=22.3$

At 10 am i.e. t=1 hr T=89

$89-68=22.3e^{-k}$

$e^{-k}=21$

$k=0.06006$

Temperature of Normal human body is $T=98.6 ^{\circ}F$

$98.6-68=e^{-0.06006t}$

$30.6=e^{-0.06006t}$

Taking log both sides

$t=-5.27$

i.e. 5 hr and 16.2 min

i.e. victim murdered at 3 am and 43.8 min

7 0

3 years ago

Consider the quadratic function Y= -(x-3)^2+4

wlad13 [49]

Answer:

-(x^2-2*x*3+3^2)+4=-x^2+6x-9+4=x^2+6x-5

Step-by-step explanation:

4 0

3 years ago

20% of what number is 90?

ehidna [41]

90 = (20)(x)
so you have to solve for x
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answer is 450

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3 years ago