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2 years ago

Find the area. Simplify your answer.

Mathematics

1 answer:

bija089 [108]2 years ago

6 0

Step-by-step explanation:

area of rectangle=length×breadth=(2x+3)(3x+7)

=6x²+9x+14x+21=6x²+23x+21

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Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x) = 6x(1/3) + 3x(4/3). You must justi

stealth61 [152]

Applying our power rule gets us our first derivative,

$\rm f'(x)=6\frac13x^{-2/3}+3\cdot\frac43x^{1/3}$

simplifying a little bit,

$\rm f'(x)=2x^{-2/3}+4x^{1/3}$

looking for critical points,

$\rm 0=2x^{-2/3}+4x^{1/3}$

We can apply more factoring.
I hope this next step isn't too confusing.
We want to factor out the smallest power of x from both terms,
and also the 2 from each.

$0=2x^{-2/3}\left(1+2x\right)$

When you divide x^(-2/3) out of x^(1/3),
it leaves you with x^(3/3) or simply x.

Then apply your Zero-Factor Property,

$\rm 0=2x^{-2/3}\qquad\qquad\qquad 0=(1+2x)$

and solve for x in each case to find your critical points.

Apply your First Derivative Test to further classify these points. You should end up finding that x=-1/2 is an relative extreme value, while x=0 is not.

Let's come back to this,

$\rm f'(x)=2x^{-2/3}+4x^{1/3}$

and take our second derivative.

$\rm f''(x)=-\frac43x^{-5/3}+\frac43x^{-2/3}$

Looking for inflection points,

$\rm 0=-\frac43x^{-5/3}+\frac43x^{-2/3}$

Again, pulling out the smaller power of x, and fractional part,

$\rm 0=-\frac43x^{-5/3}\left(1-x\right)$

And again, apply your Zero-Factor Property, setting each factor to zero and solving for x in each case. You should find that x=0 and x=1 are possible inflection points.

Applying your Second Derivative Test should verify that both points are in fact inflection points, locations where the function changes concavity.

8 0

3 years ago

The perimeter of a stop sign has a perimeter of 16x2 - 80x. What is the length of one side?

uranmaximum [27]

Since a stop sign is an octagon it has eight sides. So the perimeter will be:

p=8x, p=perimeter and x=side length. We are told that the perimeter is equal to:

16x^2-80x so we can say:

16x^2-80x=8x subtract 8x from both sides

16x^2-88x=0 factor out 8x

8x(2x-11), since we know x>0

x=11/2

x=5.5 units

7 0

3 years ago

Rút gọn biểu thức x^2-3/x+√3

zzz [600]

Answer:

i dont understand

Step-by-step explanation:

7 0

2 years ago

Solve for the value of x. ABC 20 28 9x-8

Marizza181 [45]

28+20+9x-8=180

48+9x-8=180

9x=180-40

9x=140

×=15.56

6 0

2 years ago

Based on the circle graph how many pounds of milk and eggs does the average American consume each year PLS EXPLAIN FOR BRAINLEST

Gnoma [55]

Answer:

H. 552

Step-by-step explanation:

Circle graph information:

Milk and eggs = x%
Fruits and vegetables = 38%
Cereals = 10%
Meat and fish = 10%
Sugar = 8%
Fats and oils = 4%

Total consumption = 1840 pounds per person

First, calculate the percentage of milk and eggs (the value of x).

Total percentages = 100%

⇒ x + 38 + 10 + 10 + 8 + 4 = 100

⇒ x + 70 = 100

⇒ x = 30

Therefore, 30% of food consumption is milk and eggs.

To calculate the number of pounds of milk and eggs the average American consumes each year, simply find 30% of the total consumption:

= 30% of 1840

= 30% × 1840

$=\sf \dfrac{30}{100} \times 1840$

= 552

Therefore, the average American consumes 552 pounds of milk and eggs each year.

5 0

2 years ago

Read 2 more answers