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2 years ago

What are the values of x and y?

Mathematics

1 answer:

tresset_1 [31]2 years ago

6 0

Step-by-step explanation:

y is easy.

it is the Hypotenuse (baseline) of the small right-angled triangle created by the height (8) of the main triangle, the segment 6 of the main Hypotenuse and y.

so, Pythagoras :

y² = 8² + 6² = 64 + 36 = 100

y = 10

x is a bit more complex.

I think the easiest way to get it is to know that the height of a right-angled triangle to the Hypotenuse is the square root of the product of both segments of the Hypotenuse.

so, if we call the segments of the Hypotenuse a and b with a = 6, we have

x = a + b = 6 + b

height (8) = sqrt(a×b) = sqrt(6b)

therefore,

6b = height² = 8² = 64

b = 64/6 = 32/3 = 10 2/3 = 10.66666666...

so,

x = 6 + 10.66666... = 16.666666666...

round it to what is needed. e.g. 2 positions after the decimal point (hundredths) ? then it would be 10.67

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Answer:

See the explanation for the answer

Step-by-step explanation:

We shall analyse this in the open source statisitcal packageR , the complete R snippet is as follows

# read the data into R dataframe

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str(data.df)

# perform anova analysis

a<- aov(lm(time~type*vis,data=data.df))

#summarise the results

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# plots

boxplot(time~type*vis, data=data.df,ylab="Values",

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interaction.plot(type,vis,time, type="b", col=c(2:6),

leg.bty="o", leg.bg="beige", lwd=2, pch=c(18,24,22),

xlab="Type",

ylab="Value",

main="Interaction Plot")

The results are

> summary(a)

Df Sum Sq Mean Sq F value Pr(>F)

type 1 121278 121278 478.18 2.59e-05 *** ### signficant as the p value is less than 0.05

vis 1 9730 9730 38.36 0.00345 ** ### signficant as the p value is less than 0.05

type:vis 1 9316 9316 36.73 0.00374 ** ### signficant as the p value is less than 0.05 , hence the interaction effect is significant . The p values are highlighted

Residuals 4 1015 254

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

7 0

3 years ago

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Answer:

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2 years ago

Find the area of the shaded portion in the circle.

Anastasy [175]

See the attached picture to better understand the problem

we know that
<span>the area of the shaded portion in the circle=area 1+area 2

step 1
find area 1
area 1=area of semi circle
area 1=pi*r</span>²/2
diameter=12 units
radius r=12/2----> 6 units

r=6 units
area 1=pi*6²/2----> 56.52 units²

step 2
find the area 2

area 2=area sector CADC-area triangle ACD

in the right triangle ABC
BC=3
AC=r-----> AC=6
AB=?
applying Pythagoras Theorem
AC²=AB²+BC²------> AB²=6²-3²-----> AB²=27----> AB=3√3 units
area triangle ACD=b*h/2
b=2*3√3---> 6√3 units
h=3 units
area triangle ACD=6√3*3/2----> 9√3 units²-----> 15.59 units²

find the angle ACB
tan ∠ACB=AB/BC-----> 3√3/3---> √3
∠ACB=arc tan (√3)-----> 60°

the central angle ACD=60*2-----> 120°

area of sector CADC=(120/360)*pi*r²----> (120/360)*pi*6²---> 37.68 units²
area 2=area sector CADC-area triangle ACD
area 2=37.68-15.59----> 22.09 units²

step 3
the area of the shaded portion in the circle=area 1+area 2
the area of the shaded portion in the circle= 56.52 +22.09----> 78.61 units²

the answer is
the area of the shaded portion is 78.61 units²