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
marishachu [46]
3 years ago
8

Suppose the path of a baseball follows the path graphed by the quadratic function ƒ(d) = –0.6d2 + 5.4d + 0.8 where d is the hori

zontal distance the ball traveled in yards, and ƒ(d) is the height, in yards, of the ball at d horizontal yards. Identify the domain and range that matches this situation.

Mathematics
2 answers:
dezoksy [38]3 years ago
7 0

Answer:

Domain:

[0,9.146]

Range:

[0,12.95]

Step-by-step explanation:

we are given

a baseball follows the path graphed by the quadratic function

f(d)=-0.6d^2+5.4d+0.8

where

d is the horizontal distance the ball traveled in yards

ƒ(d) is the height, in yards, of the ball at d horizontal yards

Domain:

we know that domain is all possible values of x for which any function is defined

So, for finding domain , we will take smallest x-value to largest x-value

so, we can set f(d)=0 and find zeros

-0.6d^2+5.4d+0.8=0

we can use quadratic formula

d=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

d=\frac{-54\pm \sqrt{54^2-4\left(-6\right)8}}{2\left(-6\right)}

d=-\frac{\sqrt{777}-27}{6},\:d=\frac{27+\sqrt{777}}{6}

d=-0.14579,d=9.146

we know that d is a horizontal distance

and distance can never be negative

so, domain will be

[0,9.146]

Range:

Since, this is quadratic equation

so, it is also equation of parabola

so, firstly we will find vertex of parabola

Suppose, we have

ax^2+bx+c=0

Vertex is

x=\frac{-b}{2a}

so, we can compare

a=-0.6

b=5.4

c=0.8

now, we can find vertex

x=\frac{-5.4}{2\times -0.6}

d=4.5

now, we can find y-value

f(4.5)=-0.6(4.5)^2+5.4(4.5)+0.8

f(4.5)=12.95

we can see

that leading coefficient is -0.6

which is negative

so, parabola opens downward

so, range will be

[0,12.95]

Vinil7 [7]3 years ago
5 0

Answer:


Domain is all real numbers


Range is


y\le 12.95



Step-by-step explanation:


The given function is


f(d)=-0.6d^2+5.4d+0.8


This is a maximum quadratic function therefore the domain is all real numbers.


Let us complete the square to find the vertex.



f(d)=-0.6(d^2-9d)+0.8



f(d)=-0.6(d^2+9d)+-0.6(\frac{9}{2})^2- -0.6(\frac{9}{2})^2+ 0.8




f(d)=-0.6(d-\frac{9}{2})^2+\frac{243}{20}+ 0.8





f(d)=-0.6(d-\frac{9}{2})^2+\frac{259}{20}






Therefore the range is




y\le \frac{259}{20}



y\le 12.95


See graph




You might be interested in
Which situation can be represented by the 40x + 20 = 200?
garik1379 [7]

Answer: The first situation fit the equation and it will take Mitch 4.5 weeks to pay back

Step-by-step explanation:

4 0
3 years ago
HELPPPP
drek231 [11]
Second option. 1.5% of 2,700 is 40.5. Multiply that by 5 and you get 202.5 add that to 2,700 and you get 2,902.5. Round that and you get 2,903. Hence, the second option is correct.
3 0
3 years ago
What is an equation of the line that passes through the point (-5, -1) and is
Radda [10]

Answer:

y = -4/5 x - 5

Step-by-step explanation:

3 0
3 years ago
brad built 1/4 of a model airplane on monday and 2/3 of it on tuesday. he finished building the airplane on wednesday. what frac
Inessa05 [86]
Teh answer is 1/12. 1/4+ 2/3 is 11/12. First, you need to find the common denominator of 4 and 3, and that is 12.Then, you multiply 1*3 because 4*3 is 12.You then have the fraction of 3/12. Then, you multiply 2*4 because again, what you do to the top, you also do to the bottom, so you would also have the fraction of 8/12.The rest is easy. 3/12 + 8/12 is 11/12.And the missing piece of 11/12 is 1/12, because that made it whole.
Hope that helps!
6 0
3 years ago
I really need help pls
Vladimir79 [104]
Is there answer choices ? If so i need to see the answer choices so i can answer for you
4 0
2 years ago
Other questions:
  • A square poster has a side length of 26 in. Drawn on the poster are four identical triangles. Each triangle has a base of 8 in.
    6·2 answers
  • A city zoo builds an enclosure for birds in the shape of a cone with the dimensions shown. There are 42 birds contained in the e
    10·2 answers
  • Solve x 2 + 6x - 5 = 0 by completing the square. Which equation is used in the process?
    14·1 answer
  • ______ x ________ = 16
    13·1 answer
  • Roy has bought two square photo frames. The ratio of their sides is 4:1. If PQ = 12 inches, what is AB? A. 12 in. B. 9 in. C. 6
    7·1 answer
  • What type of number is 3/2
    8·2 answers
  • 9. Which of the following fractions is equivalent to 1.68?
    11·1 answer
  • Please help! I will give brainly!
    7·1 answer
  • What is the intermediate step in the form square for the following equation? (x + a) ^ 2 = b as a result of completing the squar
    14·1 answer
  • Andrew writes the algebraic expression 2s + 2.79 to represent the cost of his lunch. He bought 2 sandwiches and a large drink. I
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!