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3 years ago

A can of soda is placed inside a cooler. As the soda cools, its temperature T(x)

Mathematics

1 answer:

solniwko [45]3 years ago

8 0

Answer:

The initial temperature of the soda is 16°C

The temperature of the soda after 18 minutes is -12°C

Step-by-step explanation:

T(x) = -12+28e^-0.38x

When x = 0

T(0) = -12+28e^-0.38(0) = -12+28e^0 = -12+28(1) = -12+28 = 16°C

Initial temperature of the soda is 16°C

When x = 18

T(18) = -12+28e^-0.38(18) = -12+28e^-6.84 = -12+28(0.0011) = -12+0.0308 = -11.9692°C = -12°C (to the nearest degree)

The temperature of the soda after 18 minutes is -12°C

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Help Please! Find The Missing Sides Using Special Right Triangles.

matrenka [14]

Answer:

Choice 1

Step-by-step explanation:

m^2 +n^2=13^2

m^2=13^2-n^2

n^2=13^2-m^2

Both m & n =(13 x sq rt 2)/2

To put it another way:

m=(sq rt 2)/2 x 13

n=(sq rt 2)/2 x 13

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3 years ago

When Nabhitha goes bowling, her scores are normally distributed with a mean of 115

frutty [35]

Answer:

By the Empirical Rule, in 99.7% of the games that Aubree bowls she scores between 148 and 232Step-by-step explanation:The Empirical Rule states that, for a normally distributed random variable:68% of the measures are within 1 standard deviation of the mean.95% of the measures are within 2 standard deviation of the mean.99.7% of the measures are within 3 standard deviations of the mean.In this problem, we have that:Mean = 190Standard deviation = 14Using the empirical rule, what percentage of the games that Aubree bowls does she score between 148 and 232?148 = 190 - 3*14So 148 is 3 standard deviations below the mean.232 = 190 + 3*14So 232 is 3 standard deviations above the meanBy the Empirical Rule, in 99.7% of the games that Aubree bowls she scores between 148 and 232

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2 years ago

Help with this proof

mixer [17]

Essentially, what we need to do here is prove that BE=EC, BE=CB, and.or CE=BC therefore making it isosceles. With ∠AEC=∠DEB, we know AE=DE, so EC=EB (the points go in order). Therefore, as EC=EB, BEC is isosceles (it has at least 2 equal sides).

Feel free to ask further questions!

7 0

3 years ago

Find the work required to move an object in the force field F = e^x + y (1, 1, z) along the straight line from A(0, 0, 0) to B(-

DENIUS [597]

$\vec F(x,y,z)=(e^x+y)(1,1,z)$

is conservative if we can find a scalar function $f$ such that $\nabla f=\vec F$ . This would require

$f_x=e^x+y$

$f_y=e^x+y$

$f_z=(e^x+y)z$

Integrating both sides of the first equation wrt $x$ gives

$f(x,y,z)=e^x+xy+g(y,z)$

Differentiating both sides of this wrt $y$ gives

$f_y=x+g_y=1\implies g_y=1-x\implies g(y,z)=y-xy+h(z)$

but we assumed $g$ was a function of $y$ and $z$ , independent of $x$ . So there is no such $f$ and $\vec F$ is not conservative.

To find the work, first parameterize the path (call it $C$ ) by

$\vec r(t)=(1-t)(0,0,0)+t(-4,5,-5)=(-4t,5t,-5t)$

for $0\le t\le1$ . Then

$\vec r'(t)=(-4,5,-5)$

and the work is given by the line integral,

$W=\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\int_0^1(e^{-4t}+5t,e^{-4t}+5t,-(e^{-4t}+5t)5t)\cdot(-4,5,-5)\,\mathrm dt$

$W=\displaystyle\int_0^1(125t^2+5t+(25t+1)e^{-4t})\,\mathrm dt=\boxed{\frac{2207}{48}-\frac{129}{16e^4}}$

8 0

3 years ago

I have a circular piece of fabric I am going to make a tablecloth. The radius of the fabric is 2 meters. What is the area of the

Bond [772]

Answer:

$4\pi$

12.57

Step-by-step explanation:

I have a circular piece of fabric I am going to make a tablecloth. The radius of the fabric is 2 meters. What is the area of the tablecloth I can make

Essentially, you are attempting to find the area of a circle with a radius of 2 meters.

The formula for an area of a circle is $\pi r^2$ , or pi times radius squared.

Plugging in 2 meters as your radius, that gets your answer to be $4\pi$ , or 12.57 in decimal.

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3 years ago