Grandmother decides to give a monthly allowance to her granddaughter from the trust fund. The allowance is to start at $ at the birth of her granddaughter, and then increase by $ each month afterwards. Describe the grandmother's gifts, approximately, in terms of a continuous rate (in dollars per year). (Use a linearly increasing function with no constant term for .)

Given:

x-intercepts of the hyperbola are ±4.

The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].

Center of the hyperbola is at origin.

To find:

The equation of the hyperbola.

Solution:

The general equation of a hyperbola:

[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex]            ...(i)

Where, (h,k) is the center of the hyperbola, ±a are x-intercepts, [tex](\pm c,0)[/tex] are foci.

Center of the hyperbola is at origin. So, h=0 and k=0.

x-intercepts of the hyperbola are ±4. So,

[tex]\pm a=\pm 4[/tex]

[tex]a=4[/tex]

The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].

[tex]\pm c=\pm 2\sqrt{5}[/tex]

[tex]c=2\sqrt{5}[/tex]

We know that,

[tex]a^2+b^2=c^2[/tex]

[tex](4)^2+b^2=(2\sqrt{5})^2[/tex]

[tex]16+b^2=20[/tex]

[tex]b^2=20-16[/tex]

[tex]b^2=4[/tex]

Taking square root on both sides, we get

[tex]b=\sqrt{4}[/tex]                    [b>0]

[tex]b=2[/tex]

Substituting [tex]h=0,k=0,a=4,b=2[/tex] in (i), we get

[tex]\dfrac{(x-0)^2}{4^2}-\dfrac{(y-0)^2}{2^2}=1[/tex]

[tex]\dfrac{x^2}{4^2}-\dfrac{y^2}{2^2}=1[/tex]

Therefore, the correct option is (d).

Answer:

x=6.25 and y=1.5

Step-by-step explanation:

Given equation

2x+5y=20

y=0.4x-1

Putting the value of y in above equation

2x+5(0.4x-1)=20

2x+2x-5=20

4x-5=20

4x=20+5

4x=25

x=6.25

Now,

y=0.4x-1( Given)

Putting the value of x=6.25 in above equation y

y=0.4(6.25)-1

y=2.5-1

y=1.5

Given:

Consider the dimensions of the rectangular prism are 3.4 ft by 0.8 ft by 0.6 ft.

To find:

The volume of rectangular prism.

Solution:

The volume of a cuboid or rectangular prism is:

[tex]V=l\times b\times h[/tex]

Where, l is length, b is breadth and h is height of the prism.

The dimensions of the rectangular prism are 3.4 ft by 0.8 ft by 0.6 ft. So, the volume of the prism is:

[tex]V=3.4\times 0.8\times 0.6[/tex]

[tex]V=1.632[/tex]

Therefore, the volume of the rectangular prism is 1.632 cubic feet ​.

9514 1404 393

Explanation:

This is a self-answering question: you solve it by graphing the equations.

The solution is where the lines intersect. The point of intersection of the lines is the point that satisfies all the equations for the lines, hence is a solution to the system. If they do not intersect, there are no solutions. If the lines are coincident, there are an infinite number of solutions.

__

The equations can be graphed by any of a number of methods. (My favorite is to let a graphing calculator do it.) The method of choice depends on the coefficients and the form the equations are given in. Methods of graphing are a topic for a more lengthy discussion.

Answer:

There are more females dropping than males each year and that there are more females than males

Answer:

Step-by-step explanation:

The element decay percentage rate of change 2.22% per minute.

Radioisotope, radionuclide, or radioactive nuclide, any of several species of the same chemical element with different masses whose nuclei are unstable and dissipate excess energy by spontaneously emitting radiation in the form of alpha, beta, and gamma rays.

Here, mass decreases by 73% every hour.

Weight of element X is 680 grams.

According to question,

f(t) = 680 (1 - 73%)ⁿ

f(t) = 680 (1 - 0.73)ⁿ

f(t) = 680 X 0.27ⁿ

f(t) = 680 X 0.9778ⁿ

f(t) = 680 X (1 - 0.02322)ⁿ

Thus, the element decay percentage rate of change 2.22% per minute.

Learn more about radioactive isotope from:

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Answer:

A) 3 ways

B) sorry don't know.

Step-by-step explanation:

2 P and 2 N

3P and 1 N

4P

So 3 ways.

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

remember that:

a*i + b*j + c*k can be written as a vector: (a, b, c)

We know the acceleration of the particle, and we want to find the velocity of the particle, so we just need to integrate two times.

a(t) = (8*t, sin(t), cos(2*t))

integrating that, we get:

V(t) = ( (1/2)*8*t^2, -cos(t), sin(2*t)/2) + v0

where v0 is the vector that defines the velocity at t = 0

in the question you wrote:

V(0) = i

so i suppose that this is:

V(0) = (1, 0, 0)

Then the velocity equation gives:

V(t) = ( (1/2)*8*t^2, -cos(t), sin(2*t)/2) + (1, 0, 0)

V(t) = (4*t^2 + 1, -cos(t), sin(2*t)/2)

Now to get the position equation, we integrate it again

r(t) = ((4/3)*t^3 + t, -sin(t), -cos(2*t)/4) + r0

where r0 is the initial position, in the question you wrote:

r(0) = j

so we get:

r(0) = (0, 1, 0)

replacing that we get:

r(t) = ((4/3)*t^3 + t, -sin(t), -cos(2*t)/4) + (0, 1, 0)

r(t) = ((4/3)*t^3 + t, -sin(t) + 1, -cos(2*t)/4)

Writing this in the same notation than in the question, we get:

r(t) = [(4/3)*t^3 + t}*i + [-sin(t) + 1]*j + [-cos(2*t)/4]*k

b) Now we want to graph this:

The image isn't really good but can be used to understand the motion of the particle.

Answer:

14w

Step-by-step explanation:

Hope this helps

Answer:

2+4+6+...+2k+2(k+1) = k(k+1) + (k+1)(k+1)

Step-by-step explanation:

Proved case for n

2+4+6+...+2n = n(n+1) ................(1)

for n = k + 1, we replace n by k and add n = k+1 on both sides (

2+4+6+...+2k+2(k+1) = k(k+1) + 2(k+1))

rearrange by factoring the right-hand-side

2+4+6+...+2k+2(k+1) = (k+1)(k+2)

which if we substitute n=k+1, we get back

2+4+6+...+2(n-1) + 2(n) = n(n+1)  ...............(2)

This means that equation (1) is applicable to case n+1, and the proof by induction is completed.

Answer:

3.141

Step-by-step explanation:

3 decimals is .xxx, and you round the last digit up, so it becomes 3.141

Answer:

3.141

Step-by-step explanation:

since the forth number behind the decimal place is bigger than 5 we round up the third number.

I hope this helps in anyway.

Answer:

dvide 54 by 6 then the answer you get  subrtact it by 3 then the answer you get multiply iy by 2 then thats will be your answer

Step-by-step explanation:

remember always use PEMDAS always add or subract wich ever comes first and if theres none of that then do Multiply or devide wich ever comes first  ( btw your answer is   ( 3 )

Answer:

Cannot be factored

Step-by-step explanation:

Given

[tex]\frac{x^2}{9} + 1 + \frac{9}{x^2}[/tex]

Required

Factorize

Take LCM

[tex]\frac{x^2}{9} + 1 + \frac{9}{x^2} = \frac{x^4+9x^2+81}{9x^2}[/tex]

The expression cannot be factored

The solution is : x = 19 is the extraneous solution Li Juan obtained.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Here, we have,

The given equation is 13 - 2w = w + 6.

We need to solve the equation by squaring both sides of the equation.

Now,  13 - 2w = w + 6 squaring both sides of the equation.

That is, (13-2w)²= 169 - 52w + 4w²

(w+6)²= w²+ 12w + 36

Setting them equal, we get

169 - 52w + 4w² = w² + 12w + 36

⇒3w²- 64w + 133 = 0

Now, using the quadratic formula, we get

x = (64±√(64² - 4×3×133))/6

⇒x = (64±√2500)/6.

⇒x = (64±√50)/6.

⇒x = 19 or 14/6 = 7/3.

Solving the original equation, we get

7 = 3w⇒w = 7/3

Therefore, x = 19 is the extraneous solution Li Juan obtained.

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complete question:

Li Juan solves the equation below by first squaring both sides of the equation.

13 - 2w = w + 6

What extraneous solution does Li Juan obtain?

Answer:

28/16=14/8 true

3/5=9/15 true

4/32=10/78 false

3/4=12/16 true

Step-by-step explanation:

DID IT ON BRIDGE

Answer:

73

Step-by-step explanation:

-9+84+(-2) =

-9+82 =

= 73

Hope this helps

Answer:

1205.76 m^3

Step-by-step explanation:

given:

radius = 8m

height = 18 m

volume of a cone = πr2h/3

=3.14 * (8)^2 * 18/3

=3.14 *64 *18/3

=3617.28/3

=1205.76 m^3

Answer:

Step-by-step explanation:

make it 1 triangle and trapezium

1) 1/2 x 7 x 8 = 28 in2

Answer:

56 in^2

Step-by-step explanation:

A = b* h

A = (8) * (7)

A = 56

A = 56 in ^2

Hope this helps!

Answer:

Height A = [tex]12\frac{3}{4}[/tex] inches

Step-by-step explanation:

Height A = Sum of widths of all sections of the cabinet + thickness of the wood

Height A = [tex]1\frac{1}{4}+\frac{1}{4}+4\frac{1}{2}+\frac{1}{4}+4\frac{1}{2}+2[/tex]

               = [tex](1+4+4+2)+(\frac{1}{4}+\frac{1}{4}+\frac{1}{2}+\frac{1}{4}+\frac{1}{2})[/tex]

               = [tex]11+(\frac{1+1+2+1+2}{4} )[/tex]

               = [tex]11+\frac{7}{4}[/tex]

               = [tex]11+1\frac{3}{4}[/tex]

               = [tex]11+1+\frac{3}{4}[/tex]

               = [tex]12\frac{3}{4}[/tex] inches

Answer:

A

Step-by-step explanation:

f has zero means that f(x)=0

if f(x)=0 we have to look intersection point or points in the graph on the x-axis.

for A

y=0

x=-3, x=4

for B

y=0

x=-4, x=3

for C

y=0

x=-4, x=-3

for D

y=0

x=3, x=4

Answer:

[tex]\frac{dh}{dt}=1.45cmsec^{-1}[/tex]

Step-by-step explanation:

Rate of Water Fill [tex]R=\frac{dv}{dt}=70cm^3[/tex]

Length [tex]l=8cm[/tex]

Height [tex]H=15cm[/tex]

Water level [tex]L_w= 4cm[/tex]

Generally the equation for relationship b/w h and a is mathematically given by

Since by the properties of similar triangles

 [tex]k=\frac{h}{1/2}[/tex]

Let

 [tex]h=15cm \\\\a=8cm[/tex]

 [tex]k=\frac{h}{1/2a}[/tex]

 [tex]k=\frac{15}{4}[/tex]

Therefore

 [tex]\frac{h}{1/2a}=\frac{15}{4}[/tex]

 [tex]a=\frac{8h}{15}[/tex]

Generally the equation for volume of Pyramid is mathematically given by

 [tex]V=\frac{1}{3}ah^2h[/tex]

Subsitute a

 [tex]V=\frac{1}{3}(\frac{8h}{15})h^2h[/tex]

Therefore

 [tex]\frac{dv}{dt}=\frac{(\frac{1}{3}(\frac{8h}{15})h^2h)}{dt}[/tex]

 [tex]\frac{dv}{dt}=\frac{64}{255}(h^2\frac{dh}{dt})[/tex]

Since

 [tex]\frac{dv}{dt}=70cm^3s^{-1}[/tex]

Therefore

 [tex]70cm^3s^{-1}=\frac{64}{255}(h^2\frac{dh}{dt})[/tex]

 [tex]\frac{dh}{dt}=\frac{70}{169}*\frac{225}{64}[/tex]

 [tex]\frac{dh}{dt}=1.45cmsec^{-1}[/tex]

Answer:

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Answer: You didnt mention how much Dan mows in 1 hour, but just do that divided by 60

Step-by-step explanation:

Answer:

[tex]\% = 11.96\%[/tex]

Step-by-step explanation:

Given

See attachment for box plot

Required

Percentage greater than or equal to 233

From the box plot, the maximum is:

[tex]Max = 244[/tex]

The minimum is:

[tex]Min = 152[/tex]

Percentage greater than 233 is calculated as:

[tex]\% = \frac{Max - 233}{Max - Min}[/tex]

[tex]\% = \frac{244 - 233}{244-152}[/tex]

[tex]\% = \frac{11}{92}[/tex]

Express as percentage

[tex]\% = \frac{11}{92}*100\%[/tex]

[tex]\% = \frac{1100}{92}\%[/tex]

[tex]\% = 11.96\%[/tex]

See the graph in the attached image.

Answer:

Step-by-step explanation:

The problem told you what all the variables represent, so all we have to do it fill them in accordingly and solve:

[tex]V=6440e^{(.068)(8)}[/tex] and

[tex]V=6440e^{.544}[/tex] and

V = 6440(1.7228846) so

V = $11,095.38

Answer:

Is 32,13

Step-by-step explanation:

Because one is not bigger than five so it disappears.