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2 years ago

Find a polynomial function of degree 3 such that f(10)=17 and the zeros of f are 0, 5 and 8

Mathematics

1 answer:

fomenos2 years ago

3 0

Step-by-step explanation:

Since f(0) = f(5) = f(8) = 0, we have f(x) = Ax(x - 5)(x - 8), where A is a real constant.

We know that f(10) = 17.

=> A(10)(10 - 5)(10 - 8) = 17

=> A(10)(5)(2) = 17

=> 100A = 17, A = 0.17.

Hence the answer is f(x) = 0.17x(x - 5)(x - 8).

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A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 166 feet and a maximum height of 40 feet. Find

scoray [572]

Answer:

38.27775 feet

Step-by-step explanation:

The bridge has been shown in the figure.

Let the highest point of the parabolic bridge (i.e. vertex of the parabola) be at the origin, $O(0,0)$ in the cartesian coordinate system.

As the bridge have the shape of an inverted parabola, so the standard equation, which describes the shape of the bridge is

$x^2=4ay\;\cdots(i)$

where $a$ is an arbitrary constant (distance between focus and vertex of the parabola).

The span of the bridge = 166 feet and

Maximum height of the bridge= 40 feet.

The coordinate where the bridge meets the base is $A(83, -40)$ and $B(-83, -40).$

There is only one constant in the equation of the parabola, so, use either of one point to find the value of $a$ .

Putting $A(83,-40)$ in the equation (i) we have

$83^2=4a(-40)$

$\Rightarrow a=-43.05625$

So, on putting the value of $a$ in the equation (i), the equation of bridge is

$x^2=-172.225y$

From the figure, the distance from the center is measured along the x-axis, x coordinate at the distance of 10 feet is, $x=\pm 10$ feet, put this value in equation (i) to get the value of y.

$(\pm10)^2=-172.225y$

$\Rightarrow y=-1.72225$ feet.

The point $P_1(10,-1.72225)$ and $P_2(-10,-1.72225)$ represent the point on the bridge at a distance of 10 feet from its center.

The distance of these points from the x-axis is $d=1.72225$ feet and the distance of the base of the bridge from the x-axis is $h=40$ feet.

Hence, height from the base of the bridge at 10 feet from its center

$= h-d$

$=40-1.72225=38.27775$ feet.

8 0

3 years ago

PLEASE HELP 40 POINTS & BRAINLIEST!

Setler79 [48]

The correct answer is b. The domain of the function is in terms of x, so we are looking at the x-axis. The line stretches from 3 to 7 on the x-axis, so we know that b is our answer.

8 0

3 years ago

Read 2 more answers

Please help, I’ll mark who’s ever right the Brainiest

sukhopar [10]

Answer:

0; 1/4; 1/2; 1.5; 1.75 and 1 and 3/4 are the same.

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

The volleyball team at West View High School is comparing T-shirt companies where they can purchase their practice shirts. The t

Alex73 [517]

Answer:

Q#1.total number of T-shirts for total cost to be equal=10

Q#2.For the total cost to be the same for both companies, the volleyball team would need to purchase 10 T-shirts from each company

Q#3.total of $105 for each company.

Step-by-step explanation:

Q#1

two functions are given

y=10.5x

y=7.5x+30

where y represents cost and x represents number of shirts

we have to find number of shirts to be purchased from each company keeping cost equal

hence we will write

10.5x=7.5x+30

10.5x-7.5x=30

3x=30

x=30/3

x=10

Number of shirts to be equal cost price is 10

Q#2

two functions are given

y=10.5x

y=7.5x+30

where y represents cost and x represents number of shirts

we have to find number of shirts to be purchased from each company keeping cost equal

hence we will write

10.5x=7.5x+30

10.5x-7.5x=30

3x=30

x=30/3

Number of shirts =x=10

Q#3

total cost=y=?

for y=10.5x

put x=10

y=10.5*10

cost=y=105

and for other function

for y=7.5x+30

put x=10

y=7.5(10)+30

y=75+30=105

8 0

3 years ago

Read 2 more answers

A luxury resort is offering an incentive discount. If you book your room six months in advance, you will save 15% off the price

Anna [14]

Answer:the total discounted cost for your stay is $1948.2

Step-by-step explanation:

If you book your room six months in advance, you will save 15% off the price of the room. You decide to take advantage of the offer and book a room for 6 nights. If the original price per night for the room is $382, this means that the value of the discount would be

15/100 × 382 = 0.15 × 382 = $57.3

The cost of the room for a night would be

382 - 57.3 = $324.7

Since you are staying for six nights,

the total discounted cost for your stay would be

324.7 × 6 = $1948.2

8 0

3 years ago