Can anyone help me with this please?

The Equation of parabola with focus (3,1) and directrix y = 3 is [tex]10x^2 + 9y^2-60x -14y+91 =0[/tex]

A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.

Here, focus (3,1) and directrix y=3

Let the locus of parabola be (x, y)

We know that, in Parabola

Distance between locus to focus = Distance between locus to directrix line

[tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex] = [tex]\frac{Ax_{1}+By_{1}+C }{\sqrt{A^2 + B^2 + C^2} }[/tex]

[tex]\sqrt{(x-3)^2+(y-1)^2} = \frac{0.x+1.y-3}{\sqrt{0^2+1^2+(-3)^2} }[/tex]

On squaring both sides, we get

[tex](x-3)^2 + (y-1)^2 = (\frac{y-3}{\sqrt{10} } )^2[/tex]

[tex]x^2 -6x + 9 + y^2 -2y + 1 = \frac{y^2 -6y +9}{10}[/tex]

[tex]10x^2 + 9y^2-60x -14y+91 =0[/tex]

Thus, The Equation of parabola with focus (3,1) and directrix y = 3 is [tex]10x^2 + 9y^2-60x -14y+91 =0[/tex]

Learn more about Parabola from :

https://brainly.com/question/4074088

#SPJ1

By using the reciprocal identity the value   [tex]Sin \theta[/tex] will be  [tex]\dfrac{5}{27}{[/tex]

In trigonometry, quotient identities refer to trig identities that are divided by each other.

So here we have

[tex]Cosec\theta = \dfrac{27}{5}[/tex]

Now we have to find the reciprocal identity,

[tex]Sin\theta=\dfrac{1}{Cosec\theta}[/tex]

[tex]Sin\theta}=\dfrac{1}{\dfrac{27} { 5} }[/tex]

[tex]Sin\theta=\dfrac{5}{27}[/tex]

hence by using the reciprocal identity the value   [tex]Sin \theta[/tex] will be  [tex]\dfrac{5}{27}{[/tex]

To know more about Reciprocating identity follow

https://brainly.com/question/15769816

#SPJ1

Answer:

Below.

Step-by-step explanation:

The value of r + x is always irrational.

The value of r. s is sometimes irrational:

- for example √2 * √3 = √6 which is irrational,

but √3 * √3 = √9 = 3 which is rational.

Answer:

its the first one you listed

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

total cost =$ 16 +$ 4.56=$ 20.56

change received = $25 - $ 20.56 = $4.44 .

Step-by-step explanation:

therefore your answer is 4,44 hope this helps

The theorem is used to find the side and angles of a triangle. The value of y from the given diagram is 0.64

The given diagram are right angled triangle

From the lower triangle

sin45 = a/2√2
1/√2 = a/2√2

1 = a/2
a = 2

Determine the value of y

tan 60 = opp/adj

tan 60 =y/2

y = 2 tan60

y = 0.64

Hence the value of y from the given diagram is 0.64

Learn more on SOH CAH TOA here: https://brainly.com/question/20734777

#SPJ1

Answer:

42

Step-by-step explanation:

well , here we can find the unknown variable which is X

127 = 3X+2 ( vertically opposite angles are equal)

127 = 3X+2

3x+2= 127

collecting like terms

3x = 127-2

3x = 125

dividing bothsides by 3

3x/3 = 125/3

x = 41.66

x = 42 (approximately)

function g that represents the height above the ground (in feet) in terms of the time since the Ferris wheel began rotating if the Ferris wheel rotates at a speed of 2 radians per second is g(t) = 25cos(2t) feet+30

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

The height g(t) above the center after t minutes is given by

g(t) = 25cos(r(t))

g(t) = 25cos(2t) feet+30

Learn more about this concept here:

https://brainly.com/question/14052747

#SPJ1

Answer: 375 bolts

Step-by-step explanation:

Just do 225*(40/24)

Answer:

volume= lxbxh= 10*8*2= 160 cm3

Answer:

d

Step-by-step explanation:

that's the answer to the question

Answer:

D 36.6

Step-by-step explanation:

Here, there is a triangle inscribed inside of a semicircle where the triangle is unshaded and the remained of the semicircle is shaded and we want to find the area of that shaded untouched area of the semicircle.
To do so we must find the area of the two shapes individually and then subtract the area of the triangle from the area of the semi circle as the triangle is what is uncovering the semicircle.

Finding the area of the semicircle

Area of a semicircle = (πr²)/2 where r = radius

Here we are given the diameter of the semicircle which is 13cm. We can easily convert the diameter to radius by dividing it by 2 as the radius is equal to half the diameter

Radius = 1/2 diameter , so radius = 13 / 2 = 6.5cm

We have A = πr²/2

==> plug in radius or r = 6.5

A = π(6.5)²/2

==> simplify exponent

A = π(42.25)/2

==> multiply π and 42.25 ( note that π = 3.14 approximately

A = 132.665/2

==> divide 132.665 by 2

A = 66.366

So the area of the semicircle is 66.366cm²

Finding the area of the triangle

The area of a triangle can be calculated by dividing the product of the base length and height ( formula = bh / 2 where b = base length and h = height )

Here the base length appears to be 5cm and the height appears to be 12cm so b = 5 and h = 12

So we have A = bh/2

==> plug in b = 5 and h = 12

A = (12)(5)/2

==> multiply 12 and 5

A = 60 / 2

==> divide 60 by 2

A = 30

So the area of the triangle is 30cm²

Subtracting the area of the triangle from the area of the semicircle

Finally to find the area of the shaded region we subtract the area of the triangle from the area of the semicircle

We have area of triangle = 30cm² and area of semicircle = 66.366

So area of shaded region = 66.366 - 30 = 36.366

D , 36.6 is closest to our answer therefore the answer is D

Answer:

53.5

Step-by-step explanation:

First, set the numbers out as a data set:

{51 , 51 , 52 , 53 , 54 , 54 , 54 , 55}

The median is the number that is found in the middle of the set. In this case, there are 8 numbers, and the middle numbers are 53 & 54. Find the mean of the numbers:

(53 + 54)/2 = (107)/2 = 53.5

53.5 is your answer.

~

Answer:

equate the two euations

y = 2x - 1 multiply by 4

4y = 8x - 4 equate with the second equation

5x - 4y = 1

5x = 8x - 4 + 1

8x - 5x = 3

3x = 3

x = 1

substitute for x in any of the two equations

y = 2x - 1

y = 2(1) - 1

y = 2 - 1

y = 1

Therefore, according the solution we have got.

Yes, (1,1) is a solution to the system.

Answer:

0.43%

Step-by-step explanation:

In order to change a decimal to a percentage, you multiply it by 100. You can also move the decimal point to the right two times. By doing so, you get 0.43%. Someone tell me if I did it wrong please.

Answer:

1122

If you do 18 (the first number in the sequence) plus 69 because you have to do 70 minus 1 equals 69. So 18 plus 69 then you times 16 (how many you have to get to the next number).

18+69×16=1122

Step-by-step explanation:

Answer:

Ricky had 1201 hits and

Pedro hade 1481 hits

Step-by-step explanation:

Let Ricky be 'y'.

Since, Pedro hit 280 mroe than Ricky.

Pedro is 'y+ 280'

Thus,

y + y+ 280 = 2682

2y = 2402

y = 1201

Ricky had 1201 hits and

Pedro hade 1201 + 280 = 1481 hits

Answer:

See below ~

Step-by-step explanation:

Let :

Solving :

Solution :

We know 4² = 16 , 4¹= 4

In this case we have :-

[tex] {4}^{x} = 14[/tex]

and we have to find the value of x

14 is less than 16 so x will be less than 2

14 is greater than 4 so x will be greater than 1

we can find the value of

[tex] {4}^{1.5} = {4}^{ \frac{3}{2} } \\ { (\sqrt{4}) }^{3} = {2}^{3} = 8[/tex]

so we can say 14 is much larger than 8 which means x will be much larger than 1.5

so according to above ideas we can say our answer is 2nd option which is 1.9037 is our answer

[tex]x \approx1.9037[/tex]

[tex]~~~~~~~4^x = 14 \\\\\implies \ln 4^x = \ln 14\\\\\implies x \ln 4 = \ln 14\\ \\\implies x = \dfrac{\ln 14}{ \ln 4}\\\\\implies x \approx 1.9037[/tex]

Answer:

Hope this helps. Credit to the other user.

Step-by-step explanation:

[tex]\textit{Sum and Difference Identities} \\\\ sin(\alpha - \beta)=sin(\alpha)cos(\beta)- cos(\alpha)sin(\beta) \\\\ cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(A-B+C)\implies sin[~(\stackrel{Z}{A-B})~+C]\implies sin(Z+C) \\\\\\ sin(Z)cos(C)+cos(Z)sin(C)\implies sin(A-B)cos(C)+cos(A-B)sin(C) \\\\[-0.35em] ~\dotfill\\\\ \textit{and since we know that}\\\\ sin(A-B)\implies sin(A)cos(B)-cos(A)sin(B)[/tex]

[tex]cos(A-B)\implies cos(A)cos(B)+sin(A)sin(B)\\\\ then \\\\[-0.35em] ~\dotfill\\\\\ [sin(A)cos(B)-cos(A)sin(B)]cos(C)+[cos(A)cos(B)+sin(A)sin(B)]sin(C) \\\\\\ ~\hfill \begin{array}{cllll} sin(A)cos(B)cos(C)-cos(A)sin(B)cos(C)\\\\ +\\\\ cos(A)cos(B)sin(C)+sin(A)sin(B)sin(C) \end{array}~\hfill[/tex]

Step-by-step explanation:

6x+1≤4x−9

6x-4x≤-9-1

2x≤-10

inequality changes when divided or multiplied with negative

Answer:

[tex]y=\frac{4}{3} x-9[/tex]

Step-by-step explanation:

Here this is in standard form. Hope this helps!

Answer:

y=4/3x-9

Step-by-step explanation:

equasion for linear function is y=mx+b where y is m is slope and b is y intercept. just plug in your variables

Answer:

I think it is 15. if I am wrong sorry, but if I am right mark brainliest!!

Answer:

the length of the line is 7

Step-by-step explanation:

it is b. 7

Answer:

C.

Step-by-step explanation:

-5.3 rounds up to -5

7.9 rounds up to 8

sum is 3

2.4 rounds to 2, not 3

It's not reasonable

so, the answer is C.

Answer:

C. Since -5.3 rounds to -6 and 7.9 rounds to 8, the sum rounds to 2. Her answer of 2.4 is not equal to 3. So, it is not reasonable.

Step-by-step explanation:

https://brainly.com/question/27663230

Answer: ya were right its 135

Step-by-step explanation:

we kno that QRS is 180 degrees.

so to get QRT we subtract 45 from 180.

180 - 45

135

ya were right

Answer:

135

Step-by-step explanation:

QRT and TRS add to 180

180-45=135