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irakobra [83]
3 years ago
6

Bella plans to put $200 into a savings account. She can place her money into an account represented by p(x) = 3x + 200, or into

another account represented by n(x) = 200(1.04)x. Which account has the highest value in 4 years? Which account has the highest in 15 years?
p(x) has the highest value in 4 years; p(x) has the highest value in 15 years
n(x) has the highest value in 4 years; p(x) has the highest value in 15 years
n(x) has the highest value in 4 years; n(x) has the highest value in 15 years
p(x) has the highest value in 4 years; n(x) has the highest value in 15 years
Mathematics
1 answer:
eimsori [14]3 years ago
4 0
P(x) has the highest value in n(x) has the highest value in 15 years

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Find an equation of the sphere containing all surface points P = (x, y, z) such that the distance from P to A(−3, 6, 3) is "twic
Marina86 [1]

Answer:

Equation of Sphere =  x^{2} + y^{2} + z^{2} - 18x - 4/3y +10z + 142/3 = 0

Step-by-step explanation:

Data Given:

P = (x,y,z)

Distance from P to A (-3,6,3) = Twice the distance from P to B(6,2,-3)

Solution:

Find the equation of the sphere:

It is given that:

PA = 2PB

Squaring both sides:

(PA)^{2} = (2PB)^{2}

(PA)^{2} = 4 (PB)^{2}

(x - (-3))^{2} + (y - 6)^{2} + (z-3)^{2} = 4 x (x-6)^{2} + (y-2)^{2} + (z-(-3))^{2}

Solving the above equation:

(x + 3))^{2} + (y - 6)^{2} + (z-3)^{2} = 4 x {(x-6)^{2} + (y-2)^{2} + (z + 3))^{2}}

x^{2} + 9 + 6x + y^{2} + 36 - 12y + z^{2} + 9 - 6z = 4 { x^{2} + 36 - 12x + y^{2} + 4 - 4y + z^{2} + 9 + 6z}

x^{2} + 9 + 6x + y^{2} + 36 - 12y + z^{2} + 9 - 6z = 4x^{2} + 144 - 48x +4y^{2} + 16 - 16y + 4z^{2} + 36 + 24z

Putting the right hand side = 0 and solving the equation:

x^{2} - 4x^{2} + y^{2} - 4y^{2} + z^{2} - 4z^{2} + 6x + 48x - 12y +16y -6z - 24z + 9 + 36 + 9 -144 - 16 - 36 = 0

-3x^{2} - 3y^{2}  -3z^{2}  + 54x + 4y -30z -142  = 0

Taking (-) common

- ( 3x^{2} + 3y^{2} + 3z^{2}  - 54x - 4y +30z + 142) = 0

3x^{2} + 3y^{2} + 3z^{2}  - 54x - 4y +30z + 142 = 0

dividing the whole equation by 3

x^{2} + y^{2} + z^{2} - 54/3x - 4/3y +30/3z + 142/3 = 0

x^{2} + y^{2} + z^{2} - 54/3x - 4/3y +30/3z + 142/3 = 0

x^{2} + y^{2} + z^{2} - 18x - 4/3y +10z + 142/3 = 0

7 0
3 years ago
It takes Mark 3 minutes to make 1 1/2 inches of a bracelet. If he works at the same speed, how many minutes will it take him to
RUDIKE [14]

Answer:

  24 minutes

Step-by-step explanation:

Working at the same speed, the ratio of time to length is the same:

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  t = 12(3/1.5) = 12(2) = 24

It will take Mark 24 minutes to make a 12-inch bracelet.

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3 years ago
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Does anyone have a coursehero account that I can borrow
vagabundo [1.1K]

Answer:

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Step-by-step explanation:

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5 0
3 years ago
Geometry help! Please prove the following is a square with full explanation, I'm really lost.
Hoochie [10]

We have to show that this is a square, meaning all the sides are perpendicular and the same distance.  

A(3,4), B(2,-2), C(-4,-1), D(-3,5)

For each side we calculate the squared distance and the slope.  We don't have to bother to take the square root.  We'll subtract the points first because that difference, called the direction vector, goes into both the calculation of the slope and of the distance.

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BC=C-B=(-6, 1).  slope=1/-6=-1/6.   BC²=(-6)²+1²

CD=D-C=(1, 6).   slope=6/1=6    CD²=1²+6²=37

DA=A-D=(6,-1)   slope=-1/6     DA²=37

We see the negative reciprocal slopes, alternating between 6 and -1/6, indicating perpendicular sides.  We see they all have squared distance 37.  Equal perpendicular sides proves its a square.

If we do these problems enough we learn:  There's no point taking the square root.  In fact, there's really no point computing the slopes and the squared distances; we can see it's a square from the pattern of the direction vectors of the sides:  (-1, -6) (-6, 1) (1, 6) (6,-1)

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3 years ago
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