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3 years ago

What is the measure of angle RST? Options A) 15° B) 75° C) 105° D) 165°

Mathematics

2 answers:

svet-max [94.6K]3 years ago

7 0

The measurement of angle RST is 105

creativ13 [48]3 years ago

7 0

Answer:

Option C). 105°

Step-by-step explanation:

From the figure we can see a cyclic quadrilateral QRST

To find the measure of <RST

From the figure we can see that, angle RST is an obtuse angle.

The measure of angle RST is nearer to a right angle that is nearer to 90°

From the options we get the measure of angle RST = 105°

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Simplify the radical expression. √45 + √20 - √5

viva [34]

√45 = √9√5 = 3√5
√20 = √4√5 = 2√5

3√5+2√5-√5=4√5

answer = 4√5
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3 years ago

The population, P(t), of China, in billions, can be approximated by1 P(t)=1.394(1.006)t, where t is the number of years since th

vitfil [10]

Answer:

At the start of 2014, the population was growing at 8.34 million people per year.

At the start of 2015, the population was growing at 8.39 million people per year.

Step-by-step explanation:

To find how fast was the population growing at the start of 2014 and at the start of 2015 we need to take the derivative of the function with respect to t.

The derivative shows by how much the function (the population, in this case) is changing when the variable you're deriving with respect to (time) increases one unit (one year).

We know that the population, P(t), of China, in billions, can be approximated by $P(t)=1.394(1.006)^t$

To find the derivative you need to:

$\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=\\\\\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'\\\\1.394\frac{d}{dt}\left(1.006^t\right)\\\\\mathrm{Apply\:the\:derivative\:exponent\:rule}:\quad \frac{d}{dx}\left(a^x\right)=a^x\ln \left(a\right)\\\\1.394\cdot \:1.006^t\ln \left(1.006\right)\\\\\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=(1.394\cdot \ln \left(1.006\right))\cdot 1.006^t$

To find the population growing at the start of 2014 we say t = 0

$P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(0)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^0\\P(0)' = 0.00833901 \:Billion/year$

To find the population growing at the start of 2015 we say t = 1

$P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(1)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^1\\P(1)' = 0.00838904 \:Billion/year$

To convert billion to million you multiple by 1000

$P(0)' = 0.00833901 \:Billion/year \cdot 1000 = 8.34 \:Million/year \\P(1)' = 0.00838904 \:Billion/year \cdot 1000 = 8.39 \:Million/year$

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3 years ago

Solve the system of equations: y = 3x y=x2-4

Lubov Fominskaja [6]

Answer:

x = -4

y = -12

Step-by-step explanation:

Since y is 3x,

3x = 2x - 4

On solving we get x as -4

Substitute x and we get y as -12

3 0

3 years ago

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An airplane flies into the wind for 5 hours, traveling 900 miles. The airplane then

Musya8 [376]

Answer:

22.5 miles per hour

Step-by-step explanation:

Given system of equations

5(s-w)=900

4(s+w)=900

Set equations equal to each other

5(s-w)=4(s+w)

5s-5w=4s+4w

s-5w=4w

s=9w

Solve for w using the substitution s=9w

4(s+w)=900

4(9w+w)=900

4(10w)=900

40w=900

w=22.5

Therefore, the speed of the wind is 22.5 miles per hour

7 0

2 years ago

Find the area of the striped sector if ∠ A = 45° and the circle has a radius of 10 inches.

Pie

A diagram must be provided along with the question above. Based on my research, here is what I got.

100 pi is the area of the entire circle
That makes :
∠ A = 45°/360 = 1/8
 100pi/8 = 25 pi / 2

The answer is option D)25π over 2. I hope this answer helps.

4 0

3 years ago

Read 2 more answers