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3 years ago

6

Find the perimeter of this semi-circle with radius, r = 22cm. Give your answer rounded to 1 DP.

1 answer:

shepuryov [24]3 years ago

3 0

Answer:

69.1 cm

Step-by-step explanation:

Circumference of a circle

c = 2πr

Half of that would be a semi-circle

c = πr

c = π * 22

c = 69.115038379

Rounded

69.1 cm

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Find the value of x from this adjoining figure

Fiesta28 [93]

Answer:

$x=15^\circ$

Step-by-step explanation:

Please refer to the attached figure for labeling of given diagram:

We are given the following angles:

$\angle AOC = 3x^\circ\\\angle BOD = 2x^\circ\\\angle EOF = 7x^\circ$

Angles opposite to each other when they are formed by crossing of two lines are known as vertically opposite angles. And vertically opposite angles are always equal to each other.

Using property of vertically opposite angles:

$\angle EOF = \angle AOB = 7x^\circ$

Line CD is a straight line, so $\angle COD = 180^\circ$

Also,

$\angle COD = \angle COA+\angle AOB+\angle BOD = 180^\circ\\\Rightarrow 3x + 7x + 2x=180^\circ\\\Rightarrow 12x =180^\circ\\\Rightarrow x = \dfrac{180}{12}\\\Rightarrow x = 15^\circ$

Hence, <em>answer</em> is $x = 15^\circ$ .

5 0

3 years ago

When rabbits were introduced to the continent of Australia they quickly multiplied and spread across the continent since there w

Lady bird [3.3K]

Answer:

a. $y=6(1.7472)^x$

b. $y=6e^{0.558t}$

c.13.3 months

Step-by-step explanation:

a.-Given the first term at $t_0$ is 6 and the second term at $t_3$ is 32.

-Let's take rabbit population as a function of time to be

$y=ab^x$

where y is the population at time x and a the initial population at $t_0\\$

#We substitute our values to calculate the value of the constant b:

$y_x=ab^x\\\\y_3=ab^3\\\\32=6b^3\\\\b=1.472$

#Replace b in the population function:

$y=ab^x, b=1.7472,a=6\\\\\therefore y=6(1.7472)^x$

Hence, the regression for the rabbit population as a function of time x is $y=6(1.7472)^x$

b. The exponential function in terms of base $e$ is usually expressed as:

$A=A_0e^{kt}$

Where:

$A_0$ -is the initial population at $t_o$

$A$ -is the population at time t.

$k-$ is the exponential growth constant.

$e-$ the exponent

Our function in terms of base exponent is rewritten as:

$y=A_0e^{kt}$

#Substitute with actual figures to solve for t:

$y=A_0e^{kt}, y=32, xt=3, A_0=6\\\\32=6e^{3k}\\\\3k=In (32/6)\\\\k=0.5580$

Hence, the regression equation in terms of base e is $y=6e^{0.558t}$

c. We substitute y with any number higher than 10,000 to estimate the time for the rabbits to exceed 10,000.

-We know that $y=6e^{0.558t}.$

Therefore we calculate t as(take y=10001):

$y=6e^{0.558t}, y=10001\\\\10001=6e^{0.558t}\\\\1666.8333=e^{0.558t}\\\\0.558t= In 1666.8333\\\\t=13.2951$

Hence, it takes approximately 13.3 months for the population to exceed 10000

3 0

4 years ago

You purchase a new shirt that cost $15.00. Sales tax is added at the register at a rate of 8%. How much sales tax will be added

zhannawk [14.2K]

Answer:

16.2 U.S. Dollars - I hope this helps! :D

Step-by-step explanation:

8 0

3 years ago

Alice walks 6 over 10 mile ever day. How far does alice in 5 days?

leva [86]

Answer:

3 miles

Step-by-step explanation:

6/10x5=30/10

30/10=3

5 0

3 years ago

Solve for x in the triangle. Round your answer to the nearest tenth.

joja [24]

Answer:

Step-by-step explanation:

label sides adjacent h and o

sin(30) times 12 = 6 = 10

8 0

3 years ago