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2 years ago

,...,.............................

Mathematics

2 answers:

frez [133]2 years ago

6 0

The answer is the letter D

Crazy boy [7]2 years ago

5 0

3/4 * 16/9

= (3*16)/(4*9)

= 48/36

= 4/3

I hope that's help:)

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Ap calc multiple choice question; attached below please explain how, please!

anygoal [31]

Answer:

C. $\frac{f(b)-f(1)}{b-1}=20$

General Formulas and Concepts:

Calculus

Mean Value Theorem (MVT) - If f is continuous on interval [a, b], then there is a c∈[a, b] such that $f'(c)=\frac{f(b)-f(a)}{b-a}$

MVT is also Average Value

Step-by-step explanation:

Step 1: Define

$f(x)=e^{2x}$

f'(c) = 20

Interval [1, b]

Step 2: Check/Identify

Function [1, b] is continuous.

Derivative [1, b] is continuous.

∴ There exists a c∈[1, b] such that $f'(c)=\frac{f(b)-f(a)}{b-a}$

Step 3: Mean Value Theorem

Substitute: $20=\frac{ f(b)-f(1)}{b-1}$
Rewrite: $\frac{ f(b)-f(1)}{b-1}=20$

And we have our final answer!

5 0

1 year ago

Tania wanted to watch the movie Earwig and the witch. On HBO you have to subscribe for $14.99 to be able to watch it. She has a

IrinaK [193]

Answer:

aprox 33%

Step-by-step explanation:

6 0

2 years ago

(1) Let {v1,v2,v3} be a set of vectors in Rn . If u is Span {v1,v2,v3}, show that 3u is in Span {v1,v2,v3}.

Evgesh-ka [11]

Answer:

(1)

Multiplying by 3 both sides of the equality you get that

$3u = 3c_1v_1+3c_2v_2+3c_3v_3$

3u is in the Span of the vectors $\{v_1,v_2,v_3\}$ .

(2)

That's not true, consider the following counter example.

$v_1 = (0,0,0,1)\\v_2 = (0,0,1,0)\\v_3 = (0,1,0,0)\\v_4 = (1,0,0,0)\\u = (0,1,1,1)$

$u$ is a linear combination of $v_1,v_2,v_3$ but is NOT a linear combination of $v_1,v_2,v_3,v_4.$

Step-by-step explanation:

(1)

As the hint indicates, you know that

$u = c_1 v_1 + c_2v_2+c_3v_3$

Then, if you multiply both sides of the equality by 3, you get that

$3u = 3c_1v_1+3c_2v_2+3c_3v_3$

And that's it. 3u is in the Span of the vectors $\{v_1,v_2,v_3\}$

(2)

That's not true, consider the following counter example.

$v_1 = (0,0,0,1)\\v_2 = (0,0,1,0)\\v_3 = (0,1,0,0)\\v_4 = (1,0,0,0)\\u = (0,1,1,1)$

$u$ is a linear combination of $v_1,v_2,v_3$ but is NOT a linear combination of $v_1,v_2,v_3,v_4.$

4 0

2 years ago

For which value of theta is cot theta equal to cos theta?

Oksi-84 [34.3K]

Answer:

$\frac{cos \theta}{sin \theta}= cos \theta$

If we multiply by cross we got:

$cos \theta = sin \theta cos \theta$

We can divide both sides of the last equation by $cos \theta$ and we got:

$sin \theta = 1$

And if we apply arcsin in both sides we got:

$\theta = arcsin (1) = \frac{\pi}{2}$

And the best solution would be:

C) pi/2

Step-by-step explanation:

For this case we want to solve the following equation:

$cot \theta = cos \theta$

And we know that by definition $cot \theta = \frac{cos \theta}{\sin \theta}$

And replacing we got:

$\frac{cos \theta}{sin \theta}= cos \theta$

If we multiply by cross we got:

$cos \theta = sin \theta cos \theta$

We can divide both sides of the last equation by $cos \theta$ and we got:

$sin \theta = 1$

And if we apply arcsin in both sides we got:

$\theta = arcsin (1) = \frac{\pi}{2}$

And the best solution would be:

C) pi/2

8 0

2 years ago

A boat takes 4 hours to go 12 miles upstream. It can go 32 miles downstream in the same time. Find the rate of the current and t

galina1969 [7]

The speed upstream is the difference between the boat speed and the current speed. It is (12 mi)/(4 h) = 3 mph.

The speed downstream is the sum of the boat speed and the current speed. It is (32 mph)/(4 h) = 8 mph.

The speed of the boat is the average of these: (3 + 8)/2 = 5.5 mph.

The speed of the current is that less the difference: 5.5 - 3 = 2.5 mph.

_____

Check

Boat + Current = 5.5 + 2.5 = 8 mph

Boat - Current = 5.5 - 2.5 = 3 mph

8 0

2 years ago