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1 year ago

The temperature outside changed from 82°F to 46°F over a period of six days. If the temperature changed by the same amount

Mathematics

2 answers:

ehidna [41]1 year ago

8 0

Answer:

B. -6

Step-by-step explanation:

You know immediately that it will be negative, because the temp is going down.

To find the exact answer, start by finding the difference between the two temps

82-46 = 36

since its a six day period, divide 36 by 6

36/6 = 6

so, the answer is -6

ehidna [41]1 year ago

6 0

To find the daily change, let’s first find the total change
46 – 82 = -36 °F

we have 6 days, so divide
-36 / 6 = -36 °F per day

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An evergreen nursery usually sells a certain shrub after 5 years of growth and shaping. The growth rate during those 5 years is

ivanzaharov [21]

Answer:

$h(t) = 0.75t^2 + 4t + 12$

Step-by-step explanation:

The equation given calculates the derivative of the height in relation to the time, that is, the rate of change of the height. To find the equation for the height, we need to integrate this equation:

$dh/dt = 1.5t + 4$

Multiplying both sides by 'dt', we have:

$dh = (1.5t + 4)dt$

Using the integral in both sides:

$\int dh = \int (1.5t + 4) dt$

$h = 0.75t^2 + 4t + h(0)$

$h = 0.75t^2 + 4t + 12$

So the height after t years is represented by this equation:

$h(t) = 0.75t^2 + 4t + 12$

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melomori [17]

Step-by-step explanation:

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2 years ago

The formula for the area A of a triangle is A=(1/2)bh, where b is the length of the base and h is the height. Rearrange the form

zalisa [80]

Answer:

$b=\dfrac{2A}{h}$

Step-by-step explanation:

The formula for the area of a triangle is given by :

$A=\dfrac{1}{2}bh$ ...(1)

Where b is the length of the base and h is the height.

We need to find the value of b from the above formula.

Cross multiplying equation (1) we get :

$2A=bh$

Now dividing both sides by h. So,

$\dfrac{2A}{h}=\dfrac{bh}{h}\\\\b=\dfrac{2A}{h}$

So, the correct option is (D) i.e. $\dfrac{2A}{h}$ .

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2 years ago

A spinning giant star of initial radius R1 and angular speed ω1 suddenly collapses radially inward reaching a new radius R2 = 0.

tiny-mole [99]

Answer:

K1/K2=4

Step-by-step explanation:

The kinetic energy of a rotating sphere is given by:

$K=\frac{I*\omega^{2} }{2}$

The moment of inertia of a solid sphere is given by

$I=\frac{2MR^{2} }{5}$

The initial kinetic energy is therefore

$K_1=\frac{2MR^{2}*\omega^{2} }{10}$

$K_1=\frac{MR_1^{2}*\omega^{2} }{5}$

The final kinetic energy is given by

$K_2=\frac{MR_2^{2}*\omega^{2} }{5}$

Therefore the relation K1/K2 if R2 = 0.5R1

$\frac{K_1}{K_2} =\frac{5M(R_1)^{2}*\omega^{2} }{5*M(0.5R_1)^{2} \omega^{2}}$

The text says nothing about the final angular velocity just the collapse of the collapse of the radius

$\frac{K_1}{K_2} =\frac{1 }{(0.5)^{2} }=4$

3 0

2 years ago

In Problems 23–30, use the given zero to find the remaining zeros of each function

Talja [164]

Answer:

x = 2i, x = -2i and x = 4 are the roots of given polynomial.

Step-by-step explanation:

We are given the following expression in the question:

$f(x) = x^3 - 4x^2+ 4x - 16$

One of the zeroes of the above polynomial is 2i, that is :

$f(x) = x^3 - 4x^2+ 4x - 16\\f(2i) = (2i)^3 - 4(2i)^2+ 4(2i) - 16\\= -8i+ 16+8i-16 = 0$

Thus, we can write

$(x-2i)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16$

Now, we check if -2i is a root of the given polynomial:

$f(x) = x^3 - 4x^2+ 4x - 16\\f(-2i) = (-2i)^3 - 4(-2i)^2+ 4(-2i) - 16\\= 8i+ 16-8i-16 = 0$

Thus, we can write

$(x+2i)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16$

Therefore,

$(x-2i)(x+2i)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16\\(x^2 + 4)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16$

Dividing the given polynomial:

$\displaystyle\frac{x^3 - 4x^2 + 4x - 16}{x^2+4} = x -4$

Thus,

$(x-4)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16$

X = 4 is a root of the given polynomial.

$f(x) = x^3 - 4x^2+ 4x - 16\\f(4) = (4)^3 - 4(4)^2+ 4(4) - 16\\= 64-64+16-16 = 0$

Thus, 2i, -2i and 4 are the roots of given polynomial.

4 0

2 years ago