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Olenka [21]
1 year ago
13

What is the maximum vertical distance between the line y = x + 56 and the parabola y = x2 for −7 ≤ x ≤ 8?

Mathematics
1 answer:
atroni [7]1 year ago
5 0
-7 and 8 are the solutions to the given equation system.
Therefore, the maximum distance between the y values of the two equations must lie exactly between their points of intersection. That is on x value:
x = (-7 + 8)/2 = 0.5
The maximum distance is:
y = 0.5 + 56 = 56.5
y = 0.5² = 0.25
56.5 - 0.25 = 56.25 units
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Subtract 1.05 from a certain number. Multiply the difference by 0.8, add 2.84 to the product then divide the sum by 0.01 and get
bazaltina [42]
Answer:
The number is 6.25

Explanation:
Assume that the number we are looking for is x

First, we will set up the equations as follows:
1- Subtract 1.05 from the number (assume the result is y):
x - 1.05 = y

2- Multiply the difference by 0.8 (assume the product is z):
0.8(y) = z

3- add 2.84 to the product (assume the result is w):
z + 2.84 = w

4- divide the sum by 0.01, the quotient is 700:
w / 0.01 = 700

Now, we will work backwards as follows:
4) w / 0.01 = 700
    w = 0.01 * 700
    w = 7

3) z + 2.84 = w
    z + 2.84 = 7
    z = 7 - 2.84
    z = 4.16

2) 0.8y = z
    0.8y = 4.16
    y = 4.16 / 0.8
    y = 5.2

1) x - 1.05 = y
    x - 1.05 = 5.2
    x = 5.2 + 1.05
    x = 6.25

Hope this helps :)
8 0
2 years ago
Read 2 more answers
A mile-runner’s times for the mile are normally distributed with a mean of 4 min. 3 sec. (This would have to be expressed in dec
Vinvika [58]

Answer: 0.0668

Step-by-step explanation:

Given: Mean : \mu=\text{4 min. 3 sec.=4.05 minutes}

Standard deviation : \sigma = \text{2 seconds=0.033333 minutes }

The formula to calculate z-score is given by :_

z=\dfrac{x-\mu}{\sigma}

For x= 4 minutes  , we have

z=\dfrac{4-4.05}{0.03333}\approx-1.5

The P-value = P(z\leq-1.5)=0.0668072\approx0.0668

Hence, the probability that on a given run, the time will be 4 minutes or less = 0.0668

8 0
1 year ago
(n) ________ is a variable that affects both variables of interest and may falsely give the impression of a cause-and-effect rel
gtnhenbr [62]

Answer: CONFOUNDING VARIABLES

Step-by-step explanation: Confounding variables are

unexpected external factor that affects both variables of interest, confounding variables usually gives the false impression that changes in one variable leads to changes in the other variable, when, in Actual, it is the external factor that caused the change being investigated. Confounding variables usually leads to wrong conclusions during research and experiments and are capable of causing biased outcomes when the real cause and effect relationship is not determined.

4 0
2 years ago
11. In a gym the ratio of men to women with membership is 5:2. If the gym has 735 persons with membership, how many men will the
Doss [256]

The ratio is 5:7 when you are dealing with total membership. In other words, out of every 7 members, 5 will be men and 2 will be women

The ratio will look like this

5:7 = x:735             change to a proportion

5/7 = x / 735          Cross Multiply

7*x = 5 * 735          Combine the right

7*x = 3675             Divide by 7

x = 3675/7             Divide

x = 525

Answer: 525 men

6 0
2 years ago
A recipe for guacamole uses 12% lime juice, if a batch contains 0.75 cup of lime juice, how large is the batch of guacamole?
FinnZ [79.3K]
0.75/0.12=6.25

the batch is 6.25 cups

8 0
1 year ago
Read 2 more answers
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