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2 years ago

A building has an entry the shape of a parabolic arch 74 ft high and 28 ft wide at the base as shown below.

Mathematics

2 answers:

sergiy2304 [10]2 years ago

6 0

The equation of a parabola with vertex at (h,k) is
y=a(x-h)²+k

vertex isi at (0,0)

y=a(x-0)²+0
y=a(x)²
y=ax²
find a

we see that one point is (14,-74)
x=14 and y=-74

-74=a(14²)
-74=196a
divide both sides by 196
-37/98=a

the equation is

$y= \frac{-37}{98} x^2$

Cerrena [4.2K]2 years ago

3 0

If a building has an entry shape of a parabolic arch 74 ft high and 28 ft wide at the base as shown in the figure and then the vertex is at (0,0). The parabola is opening downward, so the equation to be used is x² = -4ay. 4a is equal to 28 and so the equation is x² = -28y

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The coordinates of the midpoint of line GH are M(−132,−6) and the coordinates of one endpoint are G(−4, 1). The coordinates of t

Darina [25.2K]

Answer:

Since, the coordinates of the midpoint of line GH are M(\frac{-13}{2}, -6)(

−13

,−6) .

The coordinates of endpoint G are (-4,1)

We have to determine the coordinates of endpoint H.

The midpoint of the line segment joining the points (x_1, y_1)(x

) and (x_2, y_2)(x

) is given by the formula (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})(

) .

Here, The endpoint G is (-4,1) So, x_1 = -4 , y_1=1x

=−4,y

Let the endpoint H be (x_2,y_2)(x

)

The midpoint coordinate M is (\frac{-13}{2}, -6)(

−13

,−6) .

So, \frac{-13}{2} = \frac{-4+x_2}{2}

−13

−4+x

{-13} = {-4+x_2}−13=−4+x

{-13}+4 = {x_2}−13+4=x

{x_2}=9x

Now, -6 = \frac{1+y_2}{2}−6=

1+y

-12 = {1+y_2}−12=1+y

y_2= -13y

=−13

So, the other endpoint H is (-9,-13).

7 0

1 year ago

Maury and Tyra are making phone calls to state representatives' offices to lobby for an issue. Muary can call all 120 state repr

oee [108]

Maury = 120/10 (12 calls/hour)
Tyra = 120/8 (15 calls/hour)

Together they are 27 calls per hour.
120 / 27 = 4.4444444444

So it'd take them 4.44444444 (recurring) hours to make 120 calls.

6 0

1 year ago

Find the length of the segment indicated. Round your answer to the nearest tenth if necessary.

Elena-2011 [213]

Given:

The length of the segment of the chord DB is 8.2 units.

The length of the segment AB is 6.9 units.

The length of the radius AC be x units.

We need to determine the value of x.

Length of BC:

Since, we know the property that, "if a radius is perpendicular to the chord, then it bisects the chord".

Thus, applying the above property, we have;

DB ≅ BC

8.2 = BC

Thus, the length of BC is 8.2 units.

Value of x:

Since, ∠B makes 90°, let us apply the Pythagorean theorem to determine the value of x.

Thus, we have;

$AC^2=AB^2+BC^2$

Substituting the values, we have;

$x^2=6.9^2+8.2^2$

$x^2=47.61+67.24$

$x^{2} =114.85$

$x=10.7$

Thus, the value of x is 10.7 units.

Hence, Option A is the correct answer.

4 0

1 year ago

Stefan's family rented a rototiller to prepare an area in their backyard for spring planting. The rental company charged an init

BaLLatris [955]

Answer: the hourly fee for the rototiller is $3

Step-by-step explanation:

Let h represent the hourly fee for renting the rototiller.

The rental company charged an initial fee of $43 with an additional fee per hour. Assuming that they rented the rototiller for x hours. This means that if they rented the rototiller for x hours, the total amount that they would pay is

43 + hx

If they paid $64 after renting the rototiller for 7 hours, the equation that models this problem would be

43 + 7h = 64

7h = 64 - 43 = 21

h = 21/7 = $3

8 0

2 years ago

Read 2 more answers

Grandma Millie is shrinking! Her height decreases by 1 4 cm 4 1 cmstart fraction, 1, divided by, 4, end fraction, start text,

solmaris [256]

Question

Grandma Millie is shrinking! Her height decreases by 1/4 cm each year. What is her total change in height over 3 years?

Answer:

Total change in her height is ¾cm

Step-by-step explanation:

At the end of each year, her height would have decreased by ¼cm

Now we have to determine the total change in her height over 3 years

If the height of Grandma decreases by ¼ in one year

The. Her height would decrease by 3 * ¼ in 3 years

3 * ¼

= ¾ cm

Thus, the total change in her height over 3 years is ¾

7 0

1 year ago