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Harman [31]
3 years ago
5

Solve the system. Please help!

Mathematics
1 answer:
Rufina [12.5K]3 years ago
4 0

Answer:

y = 3, -3

x = 6, -6

Step-by-step explanation:


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A circular swimming pool has a diameter of 40 meters. The depth of the pool is constant along west-east lines and increases line
Nataliya [291]

Answer:

Volume is 2000\pi\ m^{3}

Solution:

As per the question:

Diameter, d = 40 m

Radius, r = 20 m

Now,

From north to south, we consider this vertical distance as 'y' and height, h varies linearly as a function of y:

iff

h(y) = cy + d

Then

when y = 1 m

h(- 20) = 1 m

1 = c.(- 20) + d = - 20c + d              (1)

when y = 9 m

h(20) = 9 m

9 = c.20 + d = 20c + d                  (2)

Adding eqn (1) and (2)

d = 5 m

Using d = 5 in eqn (2), we get:

c = \frac{1}{5}

Therefore,

h(y) = \frac{1}{5}y + 5

Now, the Volume of the pool is given by:

V = \int h(y)dA

where

A = r\theta

A = rdr\ d\theta

Thus

V = \int (\frac{1}{5}y + 5)dA

V = \int_{0}^{2\pi}\int_{0}^{20} (\frac{1}{5}rsin\theta + 5) rdr\ d\theta

V = \int_{0}^{2\pi}\int_{0}^{20} (\frac{1}{5}r^{2}sin\theta + 5r}) dr\ d\theta

V = \int_{0}^{2\pi} (\frac{1}{15}20^{3}sin\theta + 1000) d\theta

V = [- 533.33cos\theta + 1000\theta]_{0}^{2\pi}

V = 0 + 2\pi \times 1000 = 2000\pi\ m^{3}

7 0
3 years ago
Solve 7n + 4 < 9n – 3.
soldier1979 [14.2K]
I hope this helps you

6 0
3 years ago
A person must score in the upper 8% of the population on an IQ test to qualify for membership in MENSA, the international high-I
Cloud [144]

Answer:

A person must get an IQ score of at least 138.885 to qualify.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 115, \sigma = 17

(a). [7pts] What IQ score must a person get to qualify

Top 8%, so at least the 100-8 = 92th percentile.

Scores of X and higher, in which X is found when Z has a pvalue of 0.92. So X when Z = 1.405.

Z = \frac{X - \mu}{\sigma}

1.405 = \frac{X - 115}{17}

X - 115 = 17*1.405

X = 138.885

A person must get an IQ score of at least 138.885 to qualify.

5 0
3 years ago
Read 2 more answers
The box plot below represents some data set. What is the value of the median?
OLEGan [10]

Answer:

80

Step-by-step explanation:

Look at the box plot and look at each line.

The first line that is all the way to the left, that is the Quartile 1.

The last line all the way to the right, that is Quartile 3.

Now lets look at the box part.

The beggining of the box is the minimum.

The ending of the box is the maximum.

The middle line is the median.

How I remember it is Median=Middle

Hopw this hels :D

8 0
2 years ago
Determine whether each exponential equation is a decay or a growth.
kolezko [41]

Answer:

OHHH THE ANSWER IS 1 would be pie 7 and the last one is .9 ok thanks for 15 points

Step-by-step explanation:

STEP 1: GO GET A CALULATOR

STEP 2 GO F UR STEP SIS

5 0
2 years ago
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