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3 years ago

Please help! posted picture of question

Mathematics

2 answers:

schepotkina [342]3 years ago

8 0

The graph is decreasing at 1 through 6

snow_tiger [21]3 years ago

6 0

In the given interval 1 < x < 6, the function is decreasing.

As seen from the graph, the value of function is lower at every next value of x than its previous value. For example value function is lower at x = 2 as compared to x = 1. Likewise the value is lower at x = 3 than x = 1 and x = 2 and this continues till x= 6. Therefore, the function is decreasing.

Another way to look at the problem is see the slope of the function. The line is constantly falling down, which means it is a decreasing function.

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Hi, help with question 18 please. thanks

Vadim26 [7]

Answer:

See Below.

Step-by-step explanation:

We are given the equation:

$\displaystyle y^2 = 1 + \sin x$

And we want to prove that:

$\displaystyle 2y\frac{d^2y}{dx^2} + 2\left(\frac{dy}{dx}\right) ^2 + y^2 = 1$

Find the first derivative by taking the derivative of both sides with respect to <em>x: </em>

<em /> $\displaystyle 2y \frac{dy}{dx} = \cos x$ <em />

Divide both sides by 2<em>y: </em>

<h3><em /> $\displaystyle \frac{dy}{dx} = \frac{\cos x}{2y}$ <em /></h3>

<em />

Find the second derivative using the quotient rule:

$\displaystyle \begin{aligned} \frac{d^2y}{dx^2} &= \frac{(\cos x)'(2y) - (\cos x)(2y)'}{(2y)^2}\\ \\ &= \frac{-2y\sin x-2\cos x \dfrac{dy}{dx}}{4y^2} \\ \\ &= -\frac{y\sin x + \cos x\left(\dfrac{\cos x}{2y}\right)}{2y^2} \\ \\ &= -\frac{2y^2\sin x+\cos ^2 x}{4y^3}\end{aligned}$

Substitute:

$\displaystyle 2y\left(-\frac{2y^2\sin x+\cos ^2 x}{4y^3}\right) + 2\left(\frac{\cos x}{2y}\right)^2 +y^2 = 1$

Simplify:

$\displaystyle \frac{-2y^2\sin x-\cos ^2x}{2y^2} + \frac{\cos ^2 x}{2y^2} + y^2 = 1$

Combine fractions:

$\displaystyle \frac{\left(-2y^2\sin x -\cos^2 x\right)+\left(\cos ^2 x\right)}{2y^2} + y^2 = 1$

Simplify:

$\displaystyle \frac{-2y^2\sin x }{2y^2} + y^2 = 1$

Cancel:

$\displaystyle -\sin x + y^2 = 1$

Substitute:

$-\sin x + \left( 1 + \sin x\right) =1$

Simplify. Hence:

$1\stackrel{\checkmark}{=}1$

Q.E.D.

8 0

3 years ago

Please help me. -1/2x+3=-x+7

Ber [7]

Answer:

x=8

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

-1/2*x+3-(-x+7)=0

simplify 1/2

((0 - (1/2• x)) + 3) - (7 - x) = 0

Adding a whole to a fraction

Rewrite the whole as a fraction using 2 as the denominator :

3 3 • 2

3 = — = —————

1 2

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

-x + 3 • 2 6 - x

—————————— = —————

2 2

(6 - x)

——————— - (7 - x) = 0

ubtracting a whole from a fraction

Rewrite the whole as a fraction using 2 as the denominator :

7 - x (7 - x) • 2

7 - x = ————— = ———————————

1 2

Adding up the two equivalent fractions

(6-x) - ((7-x) • 2) x - 8

——————————————————— = —————

2 2

x - 8

————— = 0

When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

x-8

——— • 2 = 0 • 2

Now, on the left hand side, the 2 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

x-8 = 0

Solve : x-8 = 0

Add 8 to both sides of the equation :

x = 8

Hope this helps :)

5 0

3 years ago

Read 2 more answers

You have 6,368 grams of a radioactive kind of cobalt. If its half-life is 271 days, how much

Brums [2.3K]

$\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &6368\\ t=\textit{elapsed time}\dotfill &542\\ h=\textit{half-life}\dotfill &271 \end{cases} \\\\\\ A=6368\left( \frac{1}{2} \right)^{\frac{542}{271}}\implies A=6368\left( \frac{1}{2} \right)^2\implies A=1592$

3 0

3 years ago

In hypothesis testing, does choosing between the critical value method or the P-value method affect your conclusion? Explain.

slamgirl [31]

Answer:

Step-by-step explanation:

Yes, because the critical value method uses critical value(s) to identify the rejection region(s). The P-value method compares the P-value with the level of significance alpha.

Explanation: When you reduce your significance value, the critical value either gets smaller, or larger depending on the tails. This means that your test statistic would also have to get smaller or larger depending on the tail in order to reject the null hypothesis.

At test that rejected the null hypothesis at 5% may not reject it at 1%

8 0

4 years ago

An art class is planning to paint a rectangular mural with an area of 60 square feet. It has to be at least 4 feet high but no m

Stells [14]

The painting could be 5ft high and 12ft long, or it could be 4ft high and 15ft long, or it could also be 6ft high and 10 ft long

8 0

3 years ago

Read 2 more answers