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2 years ago

Here's a graph of a linear function. Write the equation that describes that function.

Mathematics

1 answer:

Nataly [62]2 years ago

7 0

Y=1/4x+3 i think is the right answer because your y-intercept is 3 and you go up one and over 4

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Newton's law of cooling is:

Mnenie [13.5K]

Answer:

$t = \frac{ln(\frac{21}{59})}{-0.15}=6.887 hr$

So it would takes approximately 6.9 hours to reach 32 F.

Step-by-step explanation:

For this case we have the following differential equationÑ

$\frac{du}{dt}= -k (u-T)$

We can reorder the expression like this:

$\frac{du}{u-T} = -k dt$

We can use the substitution $w = u-T$ and $dw =du$ so then we have:

$\frac{dw}{w} =-k dt$

IF we integrate both sides we got:

$ln |w| = -kt +C$

If we apply exponential in both sides we got:

$w = e^{-kt} *e^c$

And if we replace w = u-T we got:

$u(t)= T + C_1 e^{-kt}$

We can also express the solution in the following terms:

$u(t) = (T_i -T_{amb}) e^{kt} +T_{amb}$

For this case we know that $k =-0.15 hr$ since w ehave a cooloing, $T_{i}= 70 F, T_{amb}=11F$ , we have this model:

$u(t) = (70-11) e^{-0.15t} +11$

And if we want that the temperature would be 32F we can solve for t like this:

$32 = 59 e^{-0.15 t} +11$

$21=59 e^{-0.15 t}$

$\frac{21}{59} = e^{-0.15 t}$

If we apply natural logs on both sides we got:

$ln (\frac{21}{59}) =-0.15 t$

$t = \frac{ln(\frac{21}{59})}{-0.15}=6.887 hr$

So it would takes approximately 6.9 hours to reach 32 F.

7 0

3 years ago

Two sides of a right triangle have the lengths 4 and 5. What is the product of the possible lengths of the third side? Express t

marishachu [46]

Answer:

19.2

Step-by-step explanation:

1st Case:

4 and 5 are legs of the right triangle.

Using the pythagorean therom: a^2+b^2=c^2

We can say that 4^2+5^2=x^2

16+25=x^2

41=x^2

x=√41

√41 is about 6.4

x=6.4

2nd Case

5 is the hypotenuse of the right triangle and 4 is the legs.

Using the pythagorean therom: a^2+b^2=c^2

We can say that 4^2+x^2=5^2

16+x^2=25

x^2=9

x=3

Final Step

We need to multiply the two possible lengths for x. So for case 1 the length of x was 6.4 and for case two the length was 3. 6.4*3=19.2

Anwser: 19.2

6 0

3 years ago

Calcular los perimetros de las siguientes figuras porfa ayúdenme ya

Basile [38]

Answer:

solo suma todos los valores x+4(3)+(x+x)

en el segundo x+5(2)+x+3(2)

en el tercero x-3+(2x+5)+(2x+5)

y en el cuarto x(3)+(x+4)

7 0

3 years ago

Solve equation 4(k-6)-(3k +2)=-5

Alja [10]

4 (k-6)-(3k+2)=-5
4k-24-3k-2=-5
k-26=-5
k=21

4 0

3 years ago

A _______, which operates by a belt that connects to the crankshaft, pressurizes the air entering the intake manifold to improve

balandron [24]

D supercharge is the answer

8 0

3 years ago

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