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kolbaska11 [484]
3 years ago
15

if the vertex of a parabola is (-4,6) and another point on the curve is (-3,14), what is the coefficient of the squared expressi

on in the parabola's equation?
Mathematics
1 answer:
Softa [21]3 years ago
3 0

Answer:

8

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (- 4, 6 ), thus

y = a(x + 4)² + 6

To find a substitute (- 3, 14) into the equation

14 = a(- 3 + 4)² + 6 ( subtract 6 from both sides )

8 = a

Thus the coefficient of the x² term is a = 8

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6 0
3 years ago
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2 years ago
The dye dilution method is used to measure cardiac output with 3 mg of dye. The dye concentrations, in mg/L, are modeled by c(t)
Lemur [1.5K]

Answer:

Cardiac output:F=0.055 L\s

Step-by-step explanation:

Given : The dye dilution method is used to measure cardiac output with 3 mg of dye.

To Find : Find the cardiac output.

Solution:

Formula of cardiac output:F=\frac{A}{\int\limits^T_0 {c(t)} \, dt} ---1

A = 3 mg

\int\limits^T_0 {c(t)} \, dt =\int\limits^{10}_0 {20te^{-0.06t}} \, dt

Do, integration by parts

[\int{20te^{-0.6t}} \, dt]^{10}_0=[20t\int{e^{-0.6t} \,dt}-\int[\frac{d[20t]}{dt}\int {e^{-0.6t} \, dt]dt]^{10}_0

[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20}{0.6}\int {e^{-0.6t} \,dt]^{10}_0

[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20e^{-0.6t}}{(0.6)^2}]^{10}_{0}

[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-200e^{-6}}{0.6}+\frac{20e^{-6}}{(0.6)^2}]+\frac{20}{(0.60^2}

[\int{20te^{-0.6t}} \, dt]^{10}_0=\frac{20(1-e^{-6}}{(0.6)^2}-\frac{200e^{-6}}{0.6}

[\int{20te^{-0.6t}} \, dt]^{10}_0\sim {54.49}

Substitute the value in 1

Cardiac output:F=\frac{3}{54.49}

Cardiac output:F=0.055 L\s

Hence Cardiac output:F=0.055 L\s

4 0
2 years ago
Three hikers equally shared One-half gallon of water. Explain how you would use an area model to find the amount of water each h
givi [52]

Answer:

1/6 gallon of water

Step-by-step explanation:

Number of hikers = 3

Quantity of water shared = 1/2 gallon of water

If the water was shared equally among the hikers, then,

Amount of water each hiker drank = Quantity of water shared ÷ Number of hikers

= 1/2 ÷ 3

Multiply 1/6 by the reciprocal of 3

The reciprocal of 3 = 1/3

1/2 ÷ 3

= 1/2 × 1/3

= (1 * 1) / (2 * 3)

= 1/6

Amount of water each hiker drank = 1/6 gallon of water

7 0
2 years ago
Please help me :(((((
notsponge [240]

question 3: -2

question 4: 0

Ordered pairs in a graph go in the sequence of (x, y)

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