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Sergio [31]
2 years ago
13

Zachary purchased a computer for $1,500 on a payment plan. Four months after he purchased the computer, his balance was $960. Si

x months after he purchased
the computer, his balance was $690. What is an equation that models the balance y after x months?
The equation hh models the balance y after x months
(Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation. Do not include the $ symbol in your answer.)
Mathematics
1 answer:
ruslelena [56]2 years ago
4 0

Answer:

y=-135x+1500

Step-by-step explanation:

first you see that the starting point of the equation in $1500( y-axis) which would be the b part of the equation

Next you would take (4,960) which is at 4 months he had $960 left and (6,690) where at 6 months he had $690 left.

You would do change of y over change of x to get -135 as your slope

then you would plug in the finial equation y= -135x(slope)+ 1500( your starting point)

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The liquid base of an ice cream has an initial temperature of 86°C before it is placed in a freezer with a constant temperature
Karolina [17]

The temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C

From Newton's law of cooling, we have that

T_{(t)}= T_{s}+(T_{0} - T_{s})e^{kt}

Where

(t) = \ time

T_{(t)} = \ the \ temperature \ of \ the \ body \ at \ time \ (t)

T_{s} = Surrounding \ temperature

T_{0} = Initial \ temperature \ of \ the \ body

k = constant

From the question,

T_{0} = 86 ^{o}C

T_{s} = -20 ^{o}C

∴ T_{0} - T_{s} = 86^{o}C - -20^{o}C = 86^{o}C +20^{o}C

T_{0} - T_{s} = 106^{o} C

Therefore, the equation T_{(t)}= T_{s}+(T_{0} - T_{s})e^{kt} becomes

T_{(t)}=-20+106 e^{kt}

Also, from the question

After 1 hour, the temperature of the ice-cream base has decreased to 58°C.

That is,

At time t = 1 \ hour, T_{(t)} = 58^{o}C

Then, we can write that

T_{(1)}=58 = -20+106 e^{k(1)}

Then, we get

58 = -20+106 e^{k(1)}

Now, solve for k

First collect like terms

58 +20 = 106 e^{k}

78 =106 e^{k}

Then,

e^{k} = \frac{78}{106}

e^{k} = 0.735849

Now, take the natural log of both sides

ln(e^{k}) =ln( 0.735849)

k = -0.30673

This is the value of the constant k

Now, for the temperature of the ice cream 2 hours after it was placed in the freezer, that is, at t = 2 \ hours

From

T_{(t)}=-20+106 e^{kt}

Then

T_{(2)}=-20+106 e^{(-0.30673 \times 2)}

T_{(2)}=-20+106 e^{-0.61346}

T_{(2)}=-20+106\times 0.5414741237

T_{(2)}=-20+57.396257

T_{(2)}=37.396257 \ ^{o}C

T_{(2)} \approxeq  37.40 \ ^{o}C

Hence, the temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C

Learn more here: brainly.com/question/11689670

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F(x) = kx
12 = 8k
k = 12/8 = 3/2

Required equation is f(x) = 3/2 x
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A bond quoted at 93 (1/8) is equal to ___ per 1,000.00 of the face amount.
Ksju [112]
The number a bond is the percentage of the value of the bond that the bond is worth. Because the bond is quoted at 93, the bond is worth $930 per $1,000.
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2 years ago
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Evaluate the given integral by changing to polar coordinates. 8xy dA D , where D is the disk with center the origin and radius 9
BabaBlast [244]

Answer:

0

Step-by-step explanation:

∫∫8xydA

converting to polar coordinates, x = rcosθ and y = rsinθ and dA = rdrdθ.

So,

∫∫8xydA = ∫∫8(rcosθ)(rsinθ)rdrdθ = ∫∫8r²(cosθsinθ)rdrdθ = ∫∫8r³(cosθsinθ)drdθ

So we integrate r from 0 to 9 and θ from 0 to 2π.

∫∫8r³(cosθsinθ)drdθ = 8∫[∫r³dr](cosθsinθ)dθ

= 8∫[r⁴/4]₀⁹(cosθsinθ)dθ

= 8∫[9⁴/4 - 0⁴/4](cosθsinθ)dθ

= 8[6561/4]∫(cosθsinθ)dθ

= 13122∫(cosθsinθ)dθ

Since sin2θ = 2sinθcosθ, sinθcosθ = (sin2θ)/2

Substituting this we have

13122∫(cosθsinθ)dθ = 13122∫(1/2)(sin2θ)dθ

= 13122/2[-cos2θ]/2 from 0 to 2π

13122/2[-cos2θ]/2 = 13122/4[-cos2(2π) - cos2(0)]

= -13122/4[cos4π - cos(0)]

= -13122/4[1 - 1]

= -13122/4 × 0

= 0

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3 years ago
The spinner is divided into 4 equal parts: yellow (Y), green, (G), blue (B) and red (R). Dorian says that if you spin the spinne
inessss [21]

Answer:

The spinner can land on the same color twice in a row, so there should be 16 possible outcomes

Step-by-step explanation:

4 possible outcomes with the same color

RR, OO, GG and BB.

Total Ways = 12+4=16

8 0
2 years ago
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