HELP ME PLEASE I RELOADED IT AND IT GAVE ME ANOTHER QUESTION IM GONNA CRY

A line tangent to the curve f(x)=1/(2^2x) at the point (a, f(a)) has a slope of -1. What is the x-intercept of this tangent?

kirza4 [7]

Answer:

x-intercept = 0.956

Step-by-step explanation:

You have the function f(x) given by:

$f(x)=\frac{1}{2^{2x}}$ (1)

Furthermore you have that at the point (a,f(a)) the tangent line to that point has a slope of -1.

You first derivative the function f(x):

$\frac{df}{dx}=\frac{d}{dx}[\frac{1}{2^{2x}}]$ (2)

To solve this derivative you use the following derivative formula:

$\frac{d}{dx}b^u=b^ulnb\frac{du}{dx}$

For the derivative in (2) you have that b=2 and u=2x. You use the last expression in (2) and you obtain:

$\frac{d}{dx}[2^{-2x}]=2^{-2x}(ln2)(-2)$

You equal the last result to the value of the slope of the tangent line, because the derivative of a function is also its slope.

$-2(ln2)2^{-2x}=-1$

Next, from the last equation you can calculate the value of "a", by doing x=a. Furhtermore, by applying properties of logarithms you obtain:

$-2(ln2)2^{-2a}=-1 \\\\2^{2a}=2(ln2)=1.386\\\\log_22^{2a}=log_2(1.386)\\\\2a=\frac{log(1.386)}{log(2)}\\\\a=0.235$

With this value you calculate f(a):

$f(a)=\frac{1}{2^{2(0.235)}}=0.721$

Next, you use the general equation of line:

$y-y_o=m(x-x_o)$

for xo = a = 0.235 and yo = f(a) = 0.721:

$y-0.721=(-1)(x-0.235)\\\\y=-x+0.956$

The last is the equation of the tangent line at the point (a,f(a)).

Finally, to find the x-intercept you equal the function y to zero and calculate x:

$0=-x+0.956\\\\x=0.956$

hence, the x-intercept of the tangent line is 0.956

5 0

2 years ago

Please answer the following

natulia [17]

Answer:

cot∅ = (-2√30)/7.

Step-by-step explanation:

Given the value of csc∅ = -13/7 and ∅ is in quad III.

We know y = r sin∅ and r > 0. So csc∅ = r/y = -13/7 = 13/(-7).

It means y = -7, r = 13.

We know x² + y² = r².

x² = r² - y²

x² = (13)² - (-7)² = 169 - 49 = 120.

x = √120 = 2√30.

we know cot∅ = x/y = (2√30)/(-7) = (-2√30)/7.

Hence, cot∅ = (-2√30)/7.

4 0

3 years ago

Researchers studying the acquisition of pronunciation often compare measurements made on the recorded speech of adults and child

dolphi86 [110]

Answer:

(A) The additional information that is needed to confirm about the conditions for this test have been met is ‘Population is approximately normal.

(B) The test statistic = 1.9965

(C1) P-value = 0.0556

(C2) There is no significant difference between mean VOT for children and adults.

D1) It is possible to make type II error.

(D2) There should be a difference in the VOT of adults and children.

Step-by-step explanation:

Let na be the number of adults = 20

xa mean VOT for adults = 88.17

sa standard deviatiation of VOT for adults = 24.74

Let nc be the number of children = 10

xc mean VOT for children =60.67

sc standard deviatiation of VOT for children = 39.89

(A) From the information the population variances are unknown and the two sample are assumed to be independent and the sample the sample size are smaller that is (n<30).

This indicates that the additional information that is required for the conditions of the test to be satisfied is 'distribution of the population'. the addition assumption to be made is, that the population distribution is normal.

(b) Calculating the test statistics using the formula;

t = (xa -xc)/SE - d

where SE = standard deviation , d= hypothesized difference = 0

But SE = √sa²/na +sc²/nc

= √24.74 ²/20 + 39.89²/10

= √189.72559

= 13.774

Substituting into test statistics equation, we have

t = (xa -xc)/SE - d

= (88.17 - 60.67/13.774

= 1.9965

Therefore the test statistic is 1.9965

(c) Calculating the p-value, we have;

Degree of freedom = na + nc -2

= 10+ 20 -2

= 28

The p-value for t=1.9965 at 28 degrees of freedom and 0.05 level of significance is 0.0556.

The p-value 0.0556 is greater than given level of significance 0.05 hence we fail to reject the null hypothesis and conclude that there is no significant difference between mean VOT for children and adults.

(D1) From the information in part (C) the null hypothesis is not rejected.

Since the null hypothesis is not rejected, there might be a chance that not rejecting null hypothesis would be wrong. In this type of situation the error that can occur would be type II error.

(D2) The type of error describe in the context of this study is obtained by the concept of the type II error which tells that the null hypothesis is not rejected when it is actually false.

7 0

3 years ago

Find the common difference of the arithmetic sequence -4, 1, 6,...

Serggg [28]

4 I think is the right answer but I’m not sure so sorry if u get this wrong

6 0

1 year ago

Min has a shelf filled with books. The books have different thicknesses. This line plot shows the thickness of each book. He pil

Vladimir [108]

Answer:

$2\frac{1}{4} \ inch$