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3 years ago

1.your aswer:

Mathematics

2 answers:

Alexxandr [17]3 years ago

8 0

Answer:

Tess is correct

lutik1710 [3]3 years ago

3 0

Answer:

Tess is correct

Step-by-step explanation:

First off, to find out the new discounted price without the sales tax, you multiply $24.50 by 15% (0.15). This gives you $3.68. You then subtract the $3.68 from $24.50. You get $20.82. To find the total with sales tax you then multiply the $20.82 by 10% (0.1). You add the discounted price with the sales tax and get the conclusion that they have enough money for the book.

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Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 2 cos(t) + sin(2t),[0, π/2].

castortr0y [4]

Answer:

The absolute maximum is $\frac{3\sqrt 3}2$ and the absolute minimum value is $0.$

Step-by-step explanation:

Differentiate of $f$ both sides w.r.t. $t$ ,

$f(t)=2 \cos t+\sin 2t$

$\Rightarrow f'(t)=-2\sin t+2\cos 2t$

Now take $f'(t)=0$

$\Rightarrow -2\sin t+2\cos 2t=0$

$\Rightarrow 2\cos 2t=2\sin t$

$\Rightarrow \cos 2t=\sin t$

$\Rightarrow 1-2\sin ^2t =\sin t \quad \quad [\because \cos 2t = 1-2\sin ^2t]$

$\Rightarrow 2\sin ^2t+\sin t-1=0$

$\Rightarrow 2\sin ^2t+2\sin t-\sin t-1=0$

$\Rightarrow 2\sin t(\sin t+1)-1(\sin t+1)=0$

$\Rightarrow (\sin t+1)(2\sin t-1)=0$

$\Rightarrow \sin t+1=0 \;\text{and}\; 2\sin t-1=0$

$\Rightarrow \sin t =-1 \;\text{and}\; \sin t =\frac 12$

In the interval $0\leq t\leq \frac {\pi}2$ , the answer to this problem is $\frac {\pi}6$

Now find the second derivative of $f(t)$ w.r.t. $t$ ,

$f''(t)=-2\cos t-4\sin 2t$

$\Rightarrow \left[f''(t)\right]_{t=\frac {\pi}6}=-2\times \frac {\sqrt 3}2-4\times \frac{\sqrt 3}2=-3\sqrt 3$

Thus, $f(t)$ is maximum at $t=\frac {\pi}6$ and minimum at $t=0$

$\left[f(t)\right]_{t=\frac {\pi}6}=2\times \frac {\sqrt 3}2+\frac{\sqrt 3}2=\frac{3\sqrt 3}2\;\text{and}\;\left[f(t)\right]_{t=\frac{\pi}2}= 2\times 0+0=0$

Hence, the absolute maximum is $\frac{3\sqrt 3}2$ and the absolute minimum value is $0$ .

7 0

3 years ago

When a system of equations has no solution, the system is called

Dahasolnce [82]

No solution is what it is called

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3 years ago

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If Ahmad’s balance is $85, what will the minimum payment be?

Kruka [31]

his balance will be 20 dollars

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3 years ago

Brianna has to complete 5 pages of writing. She has written 1 1/3 pages. How much more does Brianna need to write? A 4/5 B 3 2/3

enot [183]

Answer:

b, 3 2/3

Step-by-step explanation:

if you add 1 1/3 and 3 2/3 you get 5

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3 years ago

Write a function rule for the table.

Pavlova-9 [17]

The correct answer is: [C]: " p = 6.25 h " .
______________________________________________________
Explanation:
______________________________________________________

It is clear that "pay" is a function of "hours worked" ;

So, we can eliminate: "Choice [B]: " h = 6.25p" .
______________________________________________________
Try, Choice [A]: " p = h + 12.5 " ; and 14.50 ≠ 12.50 ; (12.50 is the amount shown in the table. So, we can already eliminate "Choice [A]".
_____________________________________________
Now that we have eliminated choices [A] and [B];

we are left with choices: [C] and [D]:
_____________________________________________
Consider choice [C]: " p = 6.25h " ;
 when "h = 2" ; does: "p = 12.5" (as shown on table)?? ;

i.e. " 12.5 =? 6.25 * (2) ?? Yes! This choice is a POSSIBILITY.
_____________________________________________
Consider choice [D]: " p = 12.5h" .

When "h = 2, does "p = 12.5" (as shown on table)? No!
→ We can see from this very answer choice
(the equation itself) that when "h = 2" ;
the value of "p" is DOUBLE [that of "12.5"].
________________________________________________
The correct answer is: Answer choice: [C]: " p = 6.25 h " .
_________________________________________________

6 0

3 years ago

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