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3 years ago

5

Yesterday it was -14°F in Nome, Alaska. At the same time it was 43°F in Austin, Texas. What was the DIFFERENCE in the temperatur

es of these two cities?

1 answer:

Allisa [31]3 years ago

3 0

Answer:

57°F differences

Step-by-step explanation:

-14+57= 43

43-57= -14

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Help with 30 please. thanks.

Svet_ta [14]

Answer:

See Below.

Step-by-step explanation:

We have the equation:

$\displaystyle y = \left(3e^{2x}-4x+1\right)^{{}^1\! / \! {}_2}$

And we want to show that:

$\displaystyle y \frac{d^2y }{dx^2} + \left(\frac{dy}{dx}\right) ^2 = 6e^{2x}$

Instead of differentiating directly, we can first square both sides:

$\displaystyle y^2 = 3e^{2x} -4x + 1$

We can find the first derivative through implicit differentiation:

$\displaystyle 2y \frac{dy}{dx} = 6e^{2x} -4$

Hence:

$\displaystyle \frac{dy}{dx} = \frac{3e^{2x} -2}{y}$

And we can find the second derivative by using the quotient rule:

$\displaystyle \begin{aligned}\frac{d^2y}{dx^2} & = \frac{(3e^{2x}-2)'(y)-(3e^{2x}-2)(y)'}{(y)^2}\\ \\ &= \frac{6ye^{2x}-\left(3e^{2x}-2\right)\left(\dfrac{dy}{dx}\right)}{y^2} \\ \\ &=\frac{6ye^{2x} -\left(3e^{2x} -2\right)\left(\dfrac{3e^{2x}-2}{y}\right)}{y^2}\\ \\ &=\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\end{aligned}$

Substitute:

$\displaystyle y\left(\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\right) + \left(\frac{3e^{2x}-2}{y}\right)^2 =6e^{2x}$

Simplify:

$\displaystyle \frac{6y^2e^{2x}- \left(3e^{2x} -2\right)^2}{y^2} + \frac{\left(3e^{2x}-2\right)^2}{y^2}= 6e^{2x}$

Combine fractions:

$\displaystyle \frac{\left(6y^2e^{2x}-\left(3e^{2x} - 2\right)^2\right) +\left(\left(3e^{2x}-2\right)^2\right)}{y^2} = 6e^{2x}$

Simplify:

$\displaystyle \frac{6y^2e^{2x}}{y^2} = 6e^{2x}$

Simplify:

$6e^{2x} \stackrel{\checkmark}{=} 6e^{2x}$

Q.E.D.

6 0

2 years ago

Clarissa uses 8.6 pints of blue paint and white paint to paint her bedroom walls. 3/5 of this amount is blue paint, and the rest

xenn [34]

Answer:

3.44 pints of white paint

Step-by-step explanation:

3/5 x 8.6 = 5.16 pints

Clarissa uses 5.16 pints of blue paints

Subtract 5.16 from 8.6 to find out how many pints of white paint did Clarissa use.

8.6 - 5.16 = 3.44 pints of white paint

3 0

2 years ago

Is this right? I’m confused for answering either B or C.

boyakko [2]

your profile says you're 22 but I find that painfully challenging to believe. She knits 5 scarves in 2 hours. Divide 10 by 2, you get 5. 5x5 is 25. It's C. You shouldn't need help. This is sad.

3 0

3 years ago

Read 2 more answers

Given: Isosceles TriangleDEF. The measure of vertex Angle D is four times the measure of each base angle E and F.

777dan777 [17]

Answer:

D = 120° , E = 30° , F = 30°

Step-by-step explanation:

Let D = 4x

Let E&F = x

4x + x + × = 180°[angles in triangle is 180°]

6x = 180°

x = 180/6

x = 30°

E = 30°

F =30°

D =4(30°)

=120°

(Correct me if i am wrong)

4 0

3 years ago

Should the quotient of an integer divided by a nonzero integer always be a rational number? Why or Why not?

lubasha [3.4K]

Yes, it will always be a rational number. I'll expound on this by defining what a rational number is. It is any number that can be expressed as a fraction. Otherwise, it is called an irrational number with a non-terminating decimal expansion. So, although 1/3 has a non-terminating decimal expansion because it is equal to 0.33333333...., it is still a rational number because it can be expressed into a fraction.

8 0

3 years ago