All categories

3 years ago

Show that the equation 2x + 3 cos x + e ^ x = 0 has a root on the interval [- 1, 0]

Mathematics

1 answer:

ExtremeBDS [4]3 years ago

5 0

If x = -1, you have

2(-1) + 3 cos(-1) + e ⁻¹ ≈ -0.0112136 < 0

and if x = 0, you have

2(0) + 3 cos(0) + e ⁰ = 4 > 0

The function f(x) = 2x + 3 cos(x) + eˣ is continuous over the real numbers, so the intermediate value theorem applies, and it says that there is some -1 < c < 0 such that f(c) = 0.

You might be interested in

Which statement is true?

diamong [38]

3 is correct , base is never equal to 1 cause all of solves of logarithm will be 0

7 0

3 years ago

Read 2 more answers

Identify the underlined place in 83.5851. Then, round the number to that place.

djyliett [7]

So assuming the underlined decimal is the second 8, let's answer the question.

Hundreds: 0 | Tens: 8 | ones: 3 | . | tenths: 5 | hundredths: 8 | thousandths: 5 | 10 thousandths: 1

So since the second 8 is in the hundredths place, we know it's either B or C.

When we round for 5, we always round up, so the answer would be 83.59

So the answer is B.

Hope this helped! If you have any more questions or don't understand please comment or DM me. :)

6 0

3 years ago

Suppose f(x)=x^2+3 and g(x)=x-2 find (f-g)(x

SSSSS [86.1K]

Answer:

x^2-x+5

Step-by-step explanation:

(f-g)(x)=f(x)-g(x)

= (x^2 + 3) - (x - 2) (Don’t forget the -1 multiplies to the x AND -2

= x^2 + 3 - x + 2

=x^2-x+5

6 0

3 years ago

You invest $500.00 in a savings account that gives 4.9% annual interest, compounded quarterly. How much money will you have at t

QveST [7]

I like it is letter d

6 0

3 years ago

A crossover trial is a type of experiment used to compare two drugs. Subjects take one drug for a period of time and then switch

zysi [14]

Answer:

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{-0.714 -0}{\frac{1.38}{\sqrt{7}}}=-1.369$

$df=n-1=7-1=6$

$p_v =2*P(t_{(6)}$

We see that the p value is higher than the ususal significance levels commonly used of 1% or 5% so then we can conclude that we FAIL to reject the null hypothesis, and there is not enough evidence to conclude that we have a different response between the two drugs

Step-by-step explanation:

We have the following info given by the problem

Subject 1 2 3 4 5 6 7

Drug A 6 3 4 5 7 1 4

Drug B 5 1 5 5 5 2 2

x=value for drug A , y = value for drug B

x: 6 3 4 5 7 1 4

y: 5 1 5 5 5 2 2

We want to verify if the mean response differs between the two drugs then the system of hypothesis for this case are:

Null hypothesis: $\mu_y- \mu_x = 0$

Alternative hypothesis: $\mu_y -\mu_x \neq 0$

We can begin calculating the difference $d_i=y_i-x_i$ and we obtain this:

d: -1, -2, 1, 0, -2, 1, -2

Now we can calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}=-0.714$

Now we can find the the standard deviation for the differences, and we got:

$s_d =\sqrt{\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1}}=1.38$

And now we can calculate the statistic given by :

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{-0.714 -0}{\frac{1.38}{\sqrt{7}}}=-1.369$

Now we can find the degrees of freedom given by:

$df=n-1=7-1=6$

We can calculate the p value, since we have a two tailed test the p value is given by:

$p_v =2*P(t_{(6)}$

7 0

3 years ago