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3 years ago

7

Pam says that the temperature of liquid drops more in the first three minutes of cooling then it does between time nine minutes

and time 12 minutes. Is pam correct give a reason for your answer

1 answer:

liberstina [14]3 years ago

5 0

Answer:

Pam is correct!

Step-by-step explanation:

Pam is correct it would be between nine minutes and 12!

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In-s [12.5K]

For a function to begin to qualify as differentiable, it would need to be continuous, and to that end you would require that $a$ is such that

$\displaystyle\lim_{x\to0^-}g(x)=\lim_{x\to0^+}g(x)\iff\lim_{x\to0}ax=\lim_{x\to0}x^2-3x$

Obviously, both limits are 0, so $g$ is indeed continuous at $x=0$ .

Now, for $g$ to be differentiable everywhere, its derivative $g'$ must be continuous over its domain. So take the derivative, noting that we can't really say anything about the endpoints of the given intervals:

$g'(x)=\begin{cases}a&\text{for }x0\end{cases}$

and at this time, we don't know what's going on at $x=0$ , so we omit that case. We want $g'$ to be continuous, so we require that

$\displaystyle\lim_{x\to0^-}g'(x)=\lim_{x\to0^+}g'(x)\iff\lim_{x\to0}a=\lim_{x\to0}2x-3$

from which it follows that $a=-3$ .

3 0

3 years ago

Help help math math math

marysya [2.9K]

507 i think. you just square 13 then multiply that by pi which is 3

6 0

3 years ago

Read 2 more answers

Find area of the shaded region.

Monica [59]

Answer:

The area of the shaded region is about 38.1 square centimeters.

Step-by-step explanation:

We want to find the area of the shaded region.

To do so, we can first find the area of the sector and then subtract the area of the triangle from the sector.

The given circle has a radius of 6 cm.

And the given sector has a central angle of 150°.

The area for a sector is given by the formula:

$\displaystyle A=\pi r^2\cdot \frac{\theta}{360^\circ}$

In this case, r = 6 and θ = 150°. Hence, the area of the sector is:

$\displaystyle \begin{aligned}A&=\pi(6)^2\cdot \frac{150}{360}\\ &=36\pi\cdot \frac{5}{12}\\&=3\pi \cdot 5\\&=15\pi \text{ cm}^2\end{aligned}$

Now, we can find the area of the triangle. We can use an alternative formula:

$\displaystyle A=\frac{1}{2}ab\sin(C)$

Where a and b are the side lengths, and C is the angle between them.

Both side lengths of the triangle are the radii of the circle. So, both side lengths are 6.

And the angle C is 150°. Hence, the area of the triangle is:

$\displaystyle A=\frac{1}{2}(6)(6)\sin(150)=18\sin(150)$

The area of the shaded region is equivalent to the sector minus the triangle:

$A_{\text{shaded}}=A_{\text{sector}}-A_{\text{triangle}}$

Therefore:

$A_{\text{shaded}}=15\pi -18\sin(150)$

Use a calculator:

$A_{\text{shaded}}=38.1238...\approx 38.1\text{ cm}^2$

The area of the shaded region is about 38.1 square centimeters.

6 0

3 years ago

Please help explain how to solve problem 16?

Anarel [89]

Here is the problem.....√(15x + 10) = 2x+3

to remove the square root, we do the opposite which is to square everything.

(√(15x + 10))² = (2x + 3)² (the square negates the square root)
15x + 10 = (2x +3)(2x + 3) (use the distributive property to continue)
15x + 10 = 4x² + 6x + 6x + 9 (combine like terms)
15x + 10 = 4x² + 12x + 9 (subtract 15x and 10 from each side)
-15x - 10 -15x - 10
0 = 4x² - 3x - 1 (factor completely)
(x - 1) (4x + 1) (set each to equal 0)

x - 1 = 0 4x + 1 = 0
x = 1 4x = -1
x = -1/4

place both into the equation to check for reasonableness...we see the negative number is not reasonable, but the x value of 1 is a solution.

answer is 1

4 0

3 years ago

Ryan counts 505,515, 525, 535, 545, 555. By which number does Ryan skip count?

raketka [301]

The Anwser would se 7,363

5 0

2 years ago