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3 years ago

Task 1:

Mathematics

1 answer:

laiz [17]3 years ago

4 0

Answer:

The toy's maximum height is $10.12\ \text{feet}$ .

Step-by-step explanation:

The equation that models the toy's height in feet from the ground at t seconds after he threw it is given by :

$h = -2t^2 + 7t + 4$ .....(1)

It is required to find the toy's maximum height. For maxima or minima, put

$\dfrac{dh}{dt}=0$

Plugging the value of t in above equation,

$\dfrac{d(-2t^2 + 7t + 4)}{dt}=0\\\\-4t+7=0\\\\t=\dfrac{7}{4}\\\\t=1.75\ s$

Now put t = 1.75 s in equation (1) such that,

$h = -2(1.75)^2 + 7(1.75) + 4\\\\h=10.12\ \text{feet}$

So, the toy's maximum height is $10.12\ \text{feet}$ .

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12 grapes cost 90 $how many can bought in 40$

likoan [24]

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Note: By 90 I assume you mean 90 cents. The same for 40.

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2 years ago

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Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were millio

JulijaS [17]

Answer:

The amount of oil was decreasing at 69300 barrels, yearly

Step-by-step explanation:

Given

$Initial =1\ million$

$6\ years\ later = 500,000$

Required

At what rate did oil decrease when 600000 barrels remain

To do this, we make use of the following notations

t = Time

A = Amount left in the well

So:

$\frac{dA}{dt} = kA$

Where k represents the constant of proportionality

$\frac{dA}{dt} = kA$

Multiply both sides by dt/A

$\frac{dA}{dt} * \frac{dt}{A} = kA * \frac{dt}{A}$

$\frac{dA}{A} = k\ dt$

Integrate both sides

$\int\ {\frac{dA}{A} = \int\ {k\ dt}$

$ln\ A = kt + lnC$

Make A, the subject

$A = Ce^{kt}$

$t = 0\ when\ A =1\ million$ i.e. At initial

So, we have:

$A = Ce^{kt}$

$1000000 = Ce^{k*0}$

$1000000 = Ce^{0}$

$1000000 = C*1$

$1000000 = C$

$C =1000000$

Substitute $C =1000000$ in $A = Ce^{kt}$

$A = 1000000e^{kt}$

To solve for k;

$6\ years\ later = 500,000$

i.e.

$t = 6\ A = 500000$

So:

$500000= 1000000e^{k*6}$

Divide both sides by 1000000

$0.5= e^{k*6}$

Take natural logarithm (ln) of both sides

$ln(0.5) = ln(e^{k*6})$

$ln(0.5) = k*6$

Solve for k

$k = \frac{ln(0.5)}{6}$

$k = \frac{-0.693}{6}$

$k = -0.1155$

Recall that:

$\frac{dA}{dt} = kA$

Where

$\frac{dA}{dt}$ = Rate

So, when

$A = 600000$

The rate is:

$\frac{dA}{dt} = -0.1155 * 600000$

$\frac{dA}{dt} = -69300$

<em>Hence, the amount of oil was decreasing at 69300 barrels, yearly</em>

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2 years ago

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GalinKa [24]

Answer:

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Step-by-step explanation:

let the two numbers = x and y

Their sum: x + y = 60 ------ (1)

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Let the larger number = y

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Substitute the value of y into equation (1)

x + (2x + 6) = 60

x + 2x + 6 = 60

3x + 6 = 60

3x = 60 - 6

3x = 54

x = 54 / 3

x = 18

y = 2x + 6

y = 2(18) + 6

y = 36 + 6

y = 42

The two numbers are 18 and 42

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2 years ago