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harkovskaia [24]
3 years ago
13

Please HELP ASAP!!!!!!!

Mathematics
1 answer:
Mars2501 [29]3 years ago
6 0

Question1. We want to find the equation of the circle with center at (-3, 1) and through the point (2, 13).

Use the distance formula to find the radius.

r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

r=\sqrt{(2- - 3)^2+(13-1)^2}

r=\sqrt{5^2+12^2}

r=\sqrt{25+144}

r=\sqrt{169}

r = 13

The equation of the circle is given by:

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

Where (a,b)=(-3,1) is the center and r=13 is the radius.

We substitute to get:

{(x + 3)}^{2}  + ( {y - 1)}^{2}  =  {13}^{2}

{(x + 3)}^{2}  + ( {y - 1)}^{2}  = 169

Question 2) The given circle has equation:

{x}^{2}  +  {(y - 6)}^{2}  = 50

We want to find the center and radius of this circle.

We need to compare to

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

Rewriting the given equation will make it easy for us;

{(x - 0)}^{2}  +  {(y - 6)}^{2}  = ( {5 \sqrt{2} )}^{2}

Therefore the center is (0,6) and the radius is

5 \sqrt{2}

Question 3. We want to find the diameter of the circle with equation:

{(x + 4)}^{2}  + ( {y - 9)}^{2}  = 18

By comparing to

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

We have

{r}^{2}  = 18

r =3  \sqrt{2}

By the diameter is twice the radius.

diameter = 2 \times 3 \sqrt{2}  = 6 \sqrt{2}

Question 4. We want to find the equation of the circle with center at (-3, 0) and diameter 20.

We use the formula:

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

where (a,b)=(-3,0) is the center and r=20 is the radius.

{(x -  - 3)}^{2}  +  {(y - 0)}^{2}  =  {20}^{2}

{(x  + 3)}^{2}  +  {y }^{2}  =400

Question 5) We want to find the center and radius of

{(x - 5)}^{2}  +  {(y  + 2)}^{2}  = 16

We compare this equation to

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

Then we can see that:

- a =  - 5 \\ a = 5

- b = 2 \\ b =  - 2

{r}^{2}  = 16

r = 4

Therefore the center is ((5,-2) and the radius is 4.

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Plot the vertex and the axis of symmetry of this function on the provided graph. f(x) = (x + 2)2 − 6
Nookie1986 [14]

Answer:

See attached image

Step-by-step explanation:

This equation for a parabola is given in vertex form, so it is very simple to extract the coordinates of its vertex, by using the opposite of the number that accompanies the variable "x" in the squared expression (opposite of 2) for the vertex's x-value, and the value of the constant (-6) for the vertex's y-value.

The vertex coordinates are therefore: (-2,-6)

The equation of the axis of symmetry of the parabola is a vertical line passing through the vertex. Since all vertical lines have the shape x = constant in our case, in  order to pass through (-2,-6) the vertical line is defined by the equation: x = -2.

See image attached to find the vertex drawn as a red point, and the axis of symmetry as an orange vertical line passing through it.

3 0
3 years ago
Which is equivalent to 80^1/4x ?
Anestetic [448]

Answer: This expression is equivalent to 3^x

Step-by-step explanation: In this question the important concept is to write 80 in exponential form and multiply the exponents.

=80^1/4x

=(3^4)^1/4x

=3^x

4 0
3 years ago
Time intervals measured with a stopwatch typically have an uncertainty of about 0.2 seconds, due to human reaction time at the s
Yakvenalex [24]

Answer:

a) 2,650%

b) 27,400%

c) 164,900%

Step-by-step explanation:

We want to measure the percentage we would have to increase the typical value to obtain the values given in a), b) and c).  

But 0.2 increased in x% equals  

0.2 + 0.2(x/100) =0.2(1+x/100)

So, if we want to increase 0.2 in x%, we must multiply it by (1+x/100)

a)

We need to find the value of x such that

0.2(1+x/100) = 5.5 ⇒ (1+x/100)=5.5/0.2 ⇒  1+x/100=27.5

⇒  x/100=26.5 ⇒ x=2,650%

b)

0.2(1+x/100) = 55 ⇒ (1+x/100)=55/0.2 ⇒  1+x/100=275

⇒  x/100=274 ⇒ x=27,400%

c)

5.5 min = 5.5*60 s = 330

0.2(1+x/100) = 330 ⇒ (1+x/100)=330/0.2 ⇒  1+x/100=1,650

⇒  x/100=1,649 ⇒ x=164,900%

4 0
3 years ago
Rank the following from most precise to least precise.1.4515100.0034
aalyn [17]

The level of precision is given by the number of decimal places.

1.45 has a precision of 2 ( two decimal digits)

.0034 has a precision of 4 ( 4 decimal digits)

Numbers that end in zeros have negative precision:

100: has a precision of -2 ( 2 zeros)

15 : Whole numbers has precision 0.

From most precise to least precise:

.0034 - 1.45- 15 - 100

8 0
1 year ago
A population of values has a normal distribution with μ = 157.7 and σ = 57 . You intend to draw a random sample of size n = 24 .
alexgriva [62]

Answer:

z=1.64

And if we solve for a we got

a=157.7 +1.64*57=251.18

So the value of height that separates the bottom 95% of data from the top 5% is 251.18.  

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

X \sim N(157.7,57)  

Where \mu=157.7 and \sigma=57

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.05   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.95 of the area on the left and 0.05 of the area on the right it's z=1.64. On this case P(Z<1.64)=0.95 and P(z>1.64)=0.05

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=1.64

And if we solve for a we got

a=157.7 +1.64*57=251.18

So the value of height that separates the bottom 95% of data from the top 5% is 251.18.  

5 0
3 years ago
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