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4 years ago

Question 10

Mathematics

1 answer:

Bond [772]4 years ago

3 0

Answer:

( x - 2)^2 + ( y - 3)^2 = 34

Step-by-step explanation:

The equation of the circle with a center and a point

( x - a) ^2 + ( y - b) ^2 = r^2

( a, b) - the center of the circle

( x, y) - any point on the circle

r^2 - radius of the circle

( -3 , 6) - point - ( x, y)

x = -3

y = 6

( 2 , 3) - center-( a, b)

a = 2

b = 3

Step 1: substitute the center into the equation

( x - 2)^2 + ( y - 3)^2 = r^2

Step 2: sub the point into the equation

( x - 2)^2 + ( y - 3)^2 = r^2

( -3 - 2)^2 + ( 6 - 3)^2 = r^2

( -5)^2 + 3^2 = r^2

25 + 9 = r^2

34 = r^2

Step 3: sub the radius into the equation

( x - 2)^2 + ( y - 3)^2 = r^2

( x - 2)^2 + ( y - 3)^2 = 34

Therefore, the equation of the circle is

( x - 2)^2 + ( y - 3)^2 = 34

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Agata [3.3K]

This equation is written in slope-intercept form y = mx + b

m = slope

b = y-intercept

In this equation the slope is -4/5

Hope This Helped! Good Luck!

7 0

3 years ago

The mean number of children among a sample of 15 low-income households is 2.8. The mean number of children among a sample of 19

gtnhenbr [62]

Answer:

Step-by-step explanation:

Let's put the data as below:

n1=15 x1=2.8 s1=1.6 and s1²=2.56

n2=19 x2=2.4 s2=1.7 and s2²=2.89

alpha= 0.05

To test the hypothesis:

H0= There is no sufficient evidence that low income household have fewer children

H1=There is sufficient evidence that low income household have fewer children

Assume that population variances are equal.

the t-static for two samples,

$t=\frac{x1-x2}{Sp\sqrt{\frac{1}{n1}-\frac{1}{n2} \\} } }$ ~t with min (n1-1,n2-1)df

The pooled variance estimate Sp equals:

$Sp^{2}=\frac{(n1-1)s1^{2}+(n2-1)s2^{2} }{n1+n2-2}$

Sp²=2.7456

Sp=1.65699

Degrees of freedom=n1+n2-2=32

Under null hypothesis:

$tcal=\frac{|2.8 - 2.4|}{1.6599\sqrt{\frac{1}{15}+\frac{1}{19} } }$

$tcal=0.6989$

The critical value ttab=2.0369 for alpha=0.05

So we reject our null hypothesis H0

So there is sufficient evidence that low income households have fewer children than high income households

6 0

4 years ago

Please help ASAP!!!

slavikrds [6]

Answer:

a) the platform is 110 feet above the ground.

b) It takes 8.69 sec for the rock to hit the ground

Step-by-step explanation:

This situation is modelled by the following function: $f(x) = -5x^2 + 40x + 30\\$

We need to answer the following questions.

a) How high above the ground is the platform?

First we find x using the formula: $x=-\frac{b}{2a}$

we have b = 40 and a = -5

Putting values and finding x

$x=-\frac{b}{2a}\\x=-\frac{40}{2(-5)}\\x=-\frac{40}{-10}\\x=4$

Now putting x=4 in the function to find how high above the ground is the platform

$f(x) = -5x^2 + 40x + 30\\Put\:x=4\\f(4)=-5(4)^2+40(4)+30\\f(4)=-5(16)+160+30\\f(4)=-80+160+30\\f(4)=110$

So, the platform is 110 feet above the ground.

b) How long does it take for the rock to hit the ground? Show all work to receive full credit!

We will factorise the given function $f(x) = -5x^2 + 40x + 30$ to find the time taken to hit the ground.

We can solve the equation using quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

We have a =-5, b=40, c=30

Putting values and finding x

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-40\pm\sqrt{(40)^2-4(-5)(30)}}{2(-5)}\\x=\frac{-40\pm\sqrt{1600+600}}{-10}\\x=\frac{-40\pm\sqrt{2200}}{-10}\\x=\frac{-40\pm46.9}{-10}\\x=\frac{-40+46.9}{-10},x=\frac{-40-46.9}{-10} \\x=-0.69,x=8.69$

So, we get values of x: x = -0.69 and x=8.69

As time cannot be negative, so we take x=8.69

So, It takes 8.69 sec for the rock to hit the ground

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NemiM [27]

Answer:

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Step-by-step explanation:

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