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3 years ago

At what point of the curve y = cosh(x does the tangent have slope 2?

1 answer:

5 0

The hyperbolic cos (cosh) is given by
cosh (x) = (e^x + e^-x) / 2
The slope of a tangent line to a function at a point is given by the derivative of that function at that point.
d/dx [cosh(x)] = d/dx[(e^x + e^-x) / 2] = (e^x - e^-x) / 2 = sinh(x)
Given that the slope is 2, thus
sinh(x) = 2
x = sinh^-1 (2) = 1.444

Therefore, the curve of y = cosh(x) has a slope of 2 at point x = 1.44

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Help Me Now!!!<br> need help with b c and d

algol [13]

Answer:

b) Take the current height, and add up 15.

c) y = 80x + 15

where y is the height of the water in the pool, in centimeters

where x is the time since the hose is in the pool, in hours

d) 180 = 80x + 15

165 = 80x

x = 165/80 = 2.0625 hours, which is also 2 hours and 3 minutes.

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3 years ago

The point (17,−9) is translated to the point (6,2). Select the description of the translation.

zubka84 [21]

Answer:

11 up , 11 left

Step-by-step explanation:

Given

$(17, -9)$ to $(6,2)$

Required

Determine the translation rule

Considering the x coordinates.

From 17 to 6

6 is to the left of 17.

Using the translation rule:

$x = x' + b$

$17 = 6 + b$

$17 - 6 = b$

$11 = b$

$b = 11$

<em>Hence: From 17 to 6 is 11 units left translation</em>

Considering the y coordinates.

From -9 to 2

2 is at the top -9.

Using the translation rule:

$y = y' + b$

$-9 = 2 + b$

$-9 - 2 = b$

$-11= b$

$b = -11$

The negative value impies a upward translation.

Hence: From -9 to 2 is 11 units up translation

4 0

2 years ago

PLZZZZZZZZZZZZ PLZZZZZZZZZZZZ PLZZZZZZZZZZZZ HELP ASAP PLZZZZZZZZZZZZ NO LINKS PLEASE!!!

alex41 [277]

Answer:

(.085 x 65) + 65 = $70.525 or $70.53 (if we rounding)

(5.525) + 65 =

3 0

3 years ago

Will mark BRAINLIEST! PLEASE HELP!

yulyashka [42]

Answer:

3 bob's burger= 23.67

2 starry night= 17.98

4 clear= 42

Step-by-step explanation:

3 x 7.89= 23.67

2 x 8.99= 17.98

4 x 10.50= 42

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3 years ago

In a recent study of 42 eighth graders, the mean number of hours per week that they watched television was 19.6. Assume the popu

olya-2409 [2.1K]

Answer:

$19.6-2.42\frac{5.8}{\sqrt{42}}=17.43$

$19.6+2.42\frac{5.8}{\sqrt{42}}=21.77$

And the best option for this case would be:

a. (17.5, 21.7)

Step-by-step explanation:

Information given

$\bar X= 19.6$ represent the sample mean

$\mu$ population mean

$\sigma= 5.8$ represent the population deviation

n=42 represent the sample size

Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The degrees of freedom, given by:

$df=n-1=42-1=41$

Since the Confidence is 0.98 or 98%, the significance would be $\alpha=0.02$ and $\alpha/2 =0.1$ , and the critical value would be $t_{\alpha/2}=2.42$

Replacing we got:

$19.6-2.42\frac{5.8}{\sqrt{42}}=17.43$

$19.6+2.42\frac{5.8}{\sqrt{42}}=21.77$

And the best option for this case would be:

a. (17.5, 21.7)

8 0

3 years ago