The height of a cylinder is twice the radius of its base.

. A bridge over a river is built in the shape of a parabolic arch. The bridge has a span of 100 feet. The height of the arch is

katen-ka-za [31]

Answer:

The height of the arch at its center is 250/9 or about 27.78 feet.

Step-by-step explanation:

We can write an equation to model the parabolic arch.

Let the left-most point of the arch be the origin (0, 0).

Since the bridge has a span of 100 feet, the right-most point must be (0, 100).

We can use the factored form of a quadratic:

$y=a(x-p)(x-q)$

Where p and q are the x-intercepts.

Our x-intercepts are x = 0 and x = 100. Hence:

$y=ax(x-100)$

At a point 40 feet from the center, the height of the arch is 10 feet.

The center is x = 50. So, a point 40 feet from the center can be either x = 10 or x = 90.

So, for instance, when x = 10, y = 10. Substitute and solve for a:

$10=10a(10-100)$

So:

$\displaystyle a=-\frac{1}{90}$

The same value will result if we let x = 90 and y = 10.

Hence, our equation is:

$\displaystyle y=-\frac{1}{90}x(x-100)$

The height of the arch at its center will be when x = 50. Hence:

$y(50)=\displaystyle -\frac{1}{90}(50)((50)-100)=\frac{250}{9}\approx 27.78\text{ feet}$

4 0

3 years ago

!! PLEASE HELP, TIMED!!Multiple choice, BRAINLIEST for correct answer!

dexar [7]

Answer:

I'm not going to lie I'm not 100% sure but I think it's c

5 0

3 years ago

Read 2 more answers

The perimeter of a rectangular park is 200 feet. The length of the park is 40 feet longer than the width.Find the length of the

Leto [7]

$\green{ \boxed{\sf \: length \: \: = 70 \: \: feet}}$

Step-by-step explanation:

Let assume that,

Wide = x

So,

length = x + 40

Given,

perimeter = 200 feet

We know that,

Perimeter = 2(length + wide)

So,

$200 = 2(x + 40 + x) \\ = > \frac{200}{2} = 2x + 40 \\ = > 2x + 40 = 100 \\ = > 2x = 100 - 40 = 60 \\ = > x = \frac{60}{2} \\ = > x = 30 \: feet$

So length = x + 40 = 30 + 40 = 70 feet

6 0

3 years ago

At Delia’s company, the purchases are recorded at net amounts. On August 5, $40,000 worth of merchandise was purchased on accoun

Kay [80]

Answer:

$2,940

Step-by-step explanation:

Data provided in the question:

Cost of merchandise purchased = $40,000

Cost of merchandise returned = $3,000

Terms = 2/10, n/30

Now,

The amount that will be recorded as the purchase return

= Cost of merchandise returned - Discount on cost of merchandise

= $3,000 - ( 2% of $3,000 )

= $3,000 - ( 0.02 × $3,000 )

= $3,000 - $60

= $2,940

6 0

4 years ago

A survey of 46 college athletes found that 24 played volleyball, while 22 played basketball. a) If we pick one athlete survey pa

PSYCHO15rus [73]

Answer:

A) $\dfrac{11}{23}$

B) $\dfrac{88}{345}$

Step-by-step explanation:

A survey of 46 college athletes found that

24 played volleyball,
22 played basketball.

A) If we pick one athlete survey participant at random, the probability they play basketball is

$P_1=\dfrac{22}{46}=\dfrac{11}{23}$

B) If we pick 2 athletes at random (without replacement),

the probability we get one volleyball player is $\dfrac{24}{46}=\dfrac{12}{23};$
the probability we get another basketball player is $\dfrac{22}{45}$ (only 45 athletes left).

Thus, the probability we get one volleyball player and one basketball player is

$P_2=\dfrac{12}{23}\cdot \dfrac{22}{45}=\dfrac{88}{345}$

5 0

4 years ago