1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
tatiyna
3 years ago
6

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola

Mathematics
1 answer:
kodGreya [7K]3 years ago
5 0

Answer:

Width =√10 and Height = \frac{10}{4}

Step-by-step explanation:

Let the coordinates of the vertices of the rectangle which lie on the given parabola y = 5 - x² ........ (1) are (h,k) and (-h,k).

Hence, the area of the rectangle will be (h + h) × k

Therefore, A = h²k ..... (2).

Now, from equation (1) we can write k = 5 - h² ....... (3)

So, from equation (2), we can write A =h^{2} [5-h^{2} ]=5h^{2} -h^{4}

For, A to be greatest , \frac{dA}{dh} =0 = 10h-4h^{3}

⇒ h[10-4h^{2} ]=0

⇒ h^{2} =\frac{10}{4} {Since, h≠ 0}

⇒ h = ±\frac{\sqrt{10} }{2}

Therefore, from equation (3), k = 5 - h²

⇒k=5-\frac{10}{4} =\frac{10}{4}

Hence, Width = 2h =√10 and Height = k =\frac{10}{4}. (Answer)

You might be interested in
In a number with at least two digits, the last number was removed. The resulting number was n smaller than ghe previous one.
BartSMP [9]

Answer:

The largest possible value of n is 11.

(A) is correct option.

Step-by-step explanation:

Given that,

The number with at least two digits,the last number was removed. The resulting number was n smaller than the previous one.

We need to find the largest possible value of n

Using given data,

The smallest number of two digit is 10.

Now, we removed last digit then we get 1 which is equal to 10 divided 10.

So, n = 10

But the largest number of two digit is 99.

We removed last digit then we get 9 which is equal to 99 divided 11.

So, n = 11

Hence, The largest possible value of n is 11.

(A) is correct option.

5 0
3 years ago
For Thanksgiving Break Nykouth and her family is going to visit relatives in Nebraska. Her dad has found a hotel room at the Hil
taurus [48]

Answer:

109n + 35

Step-by-step explanation:

I'm not sure what you are asking because you have no question in there

8 0
2 years ago
Pls help I will give you brainiest
tekilochka [14]
What do you need help with?
4 0
2 years ago
A car travels 568km in 8 1/2 hours. What is the average speed in meters/second?
GaryK [48]

Answer:

The speed would be 60kph

60/60=1

Step-by-step explanation:

60x24=1,440

It would at a speed of 1,440km per day.

In a year it would go 525,600 km.

Every nanosecond it would go 0.0001 cm.

3 0
2 years ago
Read 2 more answers
If each dozen cost $3.70 what should be the selling price be if he wants to make an 80% profit?​
klemol [59]
Answer: $6.66

Explanation:
3.70 multiplied by 0.80 = 2.96.
3.70 + 2.96 = $6.66
7 0
3 years ago
Read 2 more answers
Other questions:
  • A handler loads one item every 10 ?minutes, so 48 items are completed in his first day of work. his manager checks his work by r
    5·1 answer
  • What’s the rate of change of this graph?
    11·2 answers
  • Zarat Zim sells refrigerators. He earns 8% commission on sales. How much does he earn on sales of $3000 !!!!!!!!!!!!!!!!BIG POIN
    13·2 answers
  • Model and record 2 digit addition
    14·2 answers
  • Which statement correctly describes the click on the letter to your answer only
    5·2 answers
  • The diameter of fishing line varies. Fishing lines can have a diameter as small as 2 x 102 inch and as large as 6 x 10-2 inch. H
    14·1 answer
  • Help me I did not get this part so can you<br> All help me
    15·1 answer
  • When solving -1/3 (x − 15) = −4, what is the correct sequence of operations?
    13·1 answer
  • The table below shows the ticket rates for whale watching trips offered by Beluga Fun Tours:
    11·1 answer
  • PLZ HALP I NEED HALP YA IM TALKING TO YOU (25 points)
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!