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3 years ago

Verify the property a x (b+c) =(a x b)+(a x c) by taking: a = -7, b = (2/5), c = (-3/7)

Mathematics

1 answer:

Margaret [11]3 years ago

5 0

(-7)*(2/5 + (-3/7))
= -14/5 + 3
=1/5

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Question 5 (1 point)

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A: Add up to 180 degrees

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3 years ago

HELP LOTS OF POINTS

Ray Of Light [21]

Answer:

16 units

Step-by-step explanation:

4+6+8=18

18-2=16

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3 years ago

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We take a milk carton from the refrigerator and put it on the table at room temperature. We assume that the temperature of the c

Kisachek [45]

We can solve this problem using separation of variables.

Then apply the initial conditions

EXPLANATION

We were given the first order differential equation

$\frac{dT}{dt}=k(T-a)$

We now separate the time and the temperature variables as follows,

$\frac{dT}{T-a}=kdt$

Integrating both sides of the differential equation, we obtain;

$ln(T-a)=kt +c$

This natural logarithmic equation can be rewritten as;

$T-a=e^{kt +c}$

Applying the laws of exponents, we obtain,

$T-a=e^{kt}\times e^{c}$

$T-a=e^{c}e^{kt}$

We were given the initial conditions,

$T(0)=4$

Let us apply this condition to obtain;

$4-20=e^{c}e^{k(0)}$

$-16=e^{c}$

Now our equation, becomes

$T-a=-16e^{kt}$

or

$T=a-16e^{kt}$

When we substitute a=20,
we obtain,

$T=20-16e^{kt}$

b) We were also given that,

$T(5)=8$

Let us apply this condition again to find k.

$8=20-16e^{5k}$

This implied

$-12=-16e^{5k}$

$\frac{-12}{-16}=e^{5k}$

$\frac{3}{4}=e^{5k}$

We take logarithm to base e of both sides,

$ln(\frac{3}{4})=5k$

This implies that,

$\frac{ln(\frac{3}{4})}{5}=k$

$k=-0.2877$

After 15 minutes, the temperature will be,

$T=20-16e^{-0.2877\times 15}$

$T=20-0.21376$

$T=19.786$

After 15 minutes, the temperature is approximately 20°C

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3 years ago

Jane bought an item for $40 that, after seeing it had a 20% discount. janes friend said the original price was $48. is she right

ale4655 [162]

Jane's friend is wrong, the original price would be $200

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3 years ago

Evaluate 3 to the power of 3 + 6 (2 + 3/6)

melamori03 [73]

If 3 + 6(2 + 3/6) is actually the power, then simplify 3 + 6(2 + 3/6) as a first step. Must follow Order of Operations rules (PEMDAS): mult and div BEFORE addition and subtraction.

Thus, 3 + 6(2 + 3/6) = 3 + 6 (15/6)
= 3 + 15 = 18.

Then: 3^18 is the answer. You could expand this if you wanted, but what would be the point of that?

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3 years ago