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3 years ago

Find all of the critical points of p (t). p (t) = t 2 + 5t + 6.

Mathematics

1 answer:

svp [43]3 years ago

8 0

Please, use " ^ " to denote exponentiation: p(t) = t^2 + 5t + 6.

To find the critical points, differentiate p(t) with respect to t, set the result = to 0, and then solve the resulting equation for t:

p '(t) = 2t + 5 = 0

Solving for t: 2t = -5, and so t = -5/2. (-5/2, p(-5/2)) is the critical point. That evaluates to (-5/2, -0.25). This happens to be the vertex of a parabola that opens up.

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A piece of cardboard measures 10 ft by 10 ft. Four equal squares of size x are removed from the corners. After removing the squa

Gnesinka [82]

Answer:

The value of x would be $\frac{5}{3}$

Step-by-step explanation:

Given,

The dimension of the cardboard = 10 ft by 10 ft,

∵ After removing four equal squares of size x ( in ft ) from the corners,

The dimension of the resultant box would be,

Length = ( 10 - 2x ) ft,

Width = ( 10 - 2x ) ft,

Height = x ft,

The volume of box,

$V=(10-2x)\times (10 - 2x)\times x=x(10-2x)^2 = x(100 - 40x + 4x^2)=100x - 40x^2 + 4x^3$

Differentiating with respect to x,

$V'=100 - 80x + 12x^2$

Again differentiating with respect to x,

$V''=-80 + 24x$

For maxima or minima,

$V'=0$

$\implies 100 - 80x + 12x^2 = 0$

$\implies 3x^2 - 20x + 25=0$

By quadratic formula,

$x=\frac{20\pm \sqrt{20^2-4\times 3\times 25}}{6}$

$x=\frac{20\pm \sqrt{400 - 300}}{6}$

$x=\frac{20\pm \sqrt{100}}{6}$

$x=\frac{20\pm 10}{6}$

$\implies x = \frac{10}{6}=\frac{5}{3}\text{ or } x = 5$

For x = 5/3, V'' = negative,

While for x = 5, V'' = Positive,

Hence, the value of x would be 5/3 ft for maximising the volume.

8 0

3 years ago

What is the answer in simplest term?

Burka [1]

Answer:

3*sqrt(3x)

--------------

Step-by-step explanation:

To rationalize the denominator, we need to get rid of the square root. We need to multiply by sqrt(12x)/sqrt(12x)

9 sqrt(12x)

---------- * -----------

sqrt(12x) sqrt(12x)

9sqrt(12x)

-----------------

12x

We can cancel 3 in the top and bottom

3sqrt(12x)

---------------

We also notice that 12 is made up of 4 and 3

3sqrt(4) sqrt(3x)

---------------

3sqrt(4) sqrt(3x)

----------------------

3*2sqrt(3x)

--------------

We can cancel a 2 in the top and bottom

3*sqrt(3x)

--------------

8 0

3 years ago

Read 2 more answers

Lexi picked 2 7/10 pounds of strawberries. That afternoon, Lexi’s sister ate 7/8 of the strawberries. How many pounds of strawbe

gavmur [86]

3 $\frac{3}{35}$ pound of strawberry

Step-by-step explanation:

Given parameters:

Pounds of strawberry picked by Lexi =2 $\frac{7}{10}$

Pounds of strawberry eaten by Lexi sister = $\frac{7}{8}$

Unknown:

Pound of strawberry Lexi's sister ate = ?

Solution:

This is a fraction word problem.

Let pound of strawberry eaten by Lexi's sister = K

We can establish that:

Pound of strawberry eaten by Lexi sister x K = Pound of strawberry picked by Lexi

Mathematically we have:

$\frac{7}{8}$ x K = 2 $\frac{7}{10}$

Learn more:

fractions brainly.com/question/1757979

#learnwithBrainly

K = $\frac{27 x 8}{10 x 7}$ = $\frac{216}{70}$

K = 3 $\frac{3}{35}$ pound of strawberry

8 0

2 years ago

A large western state consists of 2049 million acres of land. Approximately 40% of this land is federally owned. Find the number

creativ13 [48]

Rjrdjgveujsjosjsksnsjajbsjsjsnskansn

5 0

3 years ago

The average sunflower has 34 petals. What is the best estimate of the total number of petals on 9 sunflowers?

Rainbow [258]

Answer:

~306

Step-by-step explanation:

34 * 9 = 306

4 0

3 years ago