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
steposvetlana [31]
3 years ago
12

The base of a rectangle lies on the x-axis, while the upper two vertices lie on the parabola y = 13 − x2. Suppose that the coord

inates of the upper right vertex of the rectangle are (x, y). Express the area of the rectangle as a function of x.
Mathematics
1 answer:
Misha Larkins [42]3 years ago
5 0

Answer:

Area of Rectangle = 26x - 2x^3

Step-by-step explanation:

Rectangle two vertices lie on x axis ; two vertices lie on parabola y = 13 - x^2.

Supposing coordinates of upper right vertex of rectangle are P = x , y

Due to parabola symmetry, width of rectangle is twice the distance  horizontal (X) axis distance between Y axis & point P.

Width of rectangle = 2x

Length of rectangle = y  ; y = 13 - x^2

Area of Rectangle = Length x Width

= 2x (y)

= 2x (13 - x^2)

= 26x - 2x^3

You might be interested in
The graphs below are both quadratic functions. The equation of the red graph is
Natali5045456 [20]

Answer:

D. g(x)=\frac{1}{5}x^2

Step-by-step explanation:

  • The equation of the red quadratic graph is f(x)=x^2.
  • This is the parent quadratic function or the base of the quadratic functions.
  • This red quadratic graph has been dilated by a certain scale factor  to obtain the blue graph. Recall that, when the scale factor is a fraction, such that 0\: the graph is stretched horizontally.
  • The dilated graph then becomes wider than the parent function.
  • From the given function equations, the possible value of k can only be k=\frac{1}{5}.
  • Therefore the blue graph has equation: g(x)=\frac{1}{5}x^2
  • The correct answer is D.
6 0
3 years ago
What are the zeros of the polynomial function? f(x)=x^3+x^2−9x−9
ella [17]

Answer:

1: x = -1

2: x = 3

3: x = -3

Step-by-step explanation:

f(x)=<u>x^3+x^2</u>−9x−9

f(x)=x^2<u>(</u>x+1) <u>−9x−9</u>

f(x) = x^2<u>(x+1)</u> - 9<u>(x+1)</u>

f(x)= (x+1)<u>(x^2-9)</u>

f(x) =(x+1)(x-3)(x+3)

8 0
3 years ago
Read 2 more answers
Is it congruent or not ? Remember that the diagram may not be drawn to scale . justify your conclusion.
Leno4ka [110]

Yes, we can see each triangle has congruent angle, side, angle, respectively (SAD). When two triangles have these correlating congruences, they can be determined as congruent.

4 0
3 years ago
Rose watches a circular ornament that has 6 equally spaced stones. identify x
Feliz [49]

Answer:

x = 60°

Step-by-step explanation:

It is given that the stones are equally spaced. As the circle is divided into 6 parts by 6 split points and there are 360∘ in the circle, each part equals 360∘/6 = 60∘. So,

mAB◠ = 60∘

mBC◠ = 3 (60∘)  = 180∘

If a tangent and a secant intersect in the exterior of a circle, then the measure of the angle formed is half the difference of the measures of its intercepted arcs.

x = 1/2 (mBC◠ − mAB◠)

Substitute the known values into the formula.

x = 1/2 (180∘ − 60∘)

= 1/2 (120∘)

= 60∘

Therefore, x = 60∘.

8 0
3 years ago
I live for walks at a rate of 4 mph she lives 2 miles from the news station how long will it take her to walk home from the news
Tresset [83]

um half hour? because at 4mph youll get 4 miles in an hour so 2 miles, is half the rate which makes it half hour

3 0
3 years ago
Other questions:
  • How do you draw 1/2 of 1/4
    10·2 answers
  • 4x-8x divided by 2
    15·1 answer
  • scientist measured water pressures of different depths she measured the table showing her findings the X values represents the d
    9·2 answers
  • Convert 13 over 2 to a decimal using long division.
    15·1 answer
  • Solve a/10 - 1/2=1/2 for a
    14·2 answers
  • The polygons are similar but not necessarily drawn to scale find the value of X. Show the steps you use to solve the problem (im
    6·2 answers
  • HELP HERE PLEASEEEEEEEEEEEE
    13·1 answer
  • Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving
    9·1 answer
  • Can someone pls tell me this answer which I have shown in the screenshot pls
    12·1 answer
  • So I'm giving away 100 points I'm in a good mode so make the best of them.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!