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3 years ago

The variable z is inversely proportional to x. When x is 16, z has the value 0.9375. What is the value of z when x= 26?

Mathematics

1 answer:

Lyrx [107]3 years ago

5 0

The problem belongs to indirect variation.

formula for indirect variation is $z*x=k$

we have $x=16$

$z=0.9375$

we know that $k=z*x$

$k=0.9375*16=15$

now we need find $z$ when $x=26$

$z=k/x$

$z=15/26=0.57$

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How do you do this question?

ElenaW [278]

x*y' + y = 8x

y' + y/x = 8 .... divide everything by x

dy/dx + y/x = 8

dy/dx + (1/x)*y = 8

We have something in the form

y' + P(x)*y = Q(x)

which is a first order ODE

The integrating factor is $u(x) = e^{\int P(x)dx} = e^{\int (1/x) dx} = e^{\ln(x)} = x$

Multiply both sides by the integrating factor (x) and we get the following:

dy/dx + (1/x)*y = 8

x*dy/dx + x*(1/x)*y = x*8

x*dy/dx + y = 8x

y + x*dy/dx = 8x

Note the left hand side is the result of using the product rule on xy. We technically didn't need the integrating factor since we already had the original equation in this format, but I wanted to use it anyway (since other ODE problems may not be as simple).

Since (xy)' turns into y + x*dy/dx, and vice versa, this means

y + x*dy/dx = 8x turns into (xy)' = 8x

Integrating both sides with respect to x leads to

xy = 4x^2 + C

y = (4x^2 + C)/x

y = (4x^2)/x + C/x

y = 4x + Cx^(-1)

where C is a constant. In this case, C = -5 leads to a solution

y = 4x - 5x^(-1)

you can check this answer by deriving both sides with respect to x

dy/dx = 4 + 5x^(-2)

Then plugging this along with y = 4x - 5x^(-1) into the ODE given, and you should find it satisfies that equation.

6 0

3 years ago

The length of a rectangular garden is 17 feet longer than its width. If the area of the garden is 234 square feet, what are the

kifflom [539]

Answer:

The garden is 9 feet wide and 26 feet long.

Step-by-step explanation:

L = W+17

area = LW = 234

(W+17)W = 234

W²+17W-234 = 0

Quadratic formula

W = [-17 ± √(17² – 4·1(-234))] / [2·1]

= [-17 ± √1225] / 2

= [-17 ± 35] /2

= -26, 9

-26 is an extraneous solution

W = 9

L = W+17 = 26

The garden is 9 feet wide and 26 feet long.

3 0

3 years ago

The admission fee at a carnival fair is $4.50 for children

Romashka-Z-Leto [24]

Answer:

Adult=1,385.71

Children=814.29

Approximately

Adult=1386

Children=814

Step-by-step explanation:

c= number of children

a= number of adults

Admission fee for children=$4.50

Admission fee for adults=$8.00

Total attendees=2200

Total amount realized=$5050

We need two equations to solve the two unknowns

c + a=2200 (1)

4.50c + 8.00a=5,050 (2)

From (1)

c + a=2200

c=2200 - a

Substitute c=2200 - a into (2)

4.50c + 8.00a=5,050

4.50(2200 - a) + 8.00a=5050

9900 - 4.50a +8.00a=5050

Collect like terms

9900-5050= -4.50a+8.00a

4,850=3.5a

Divide both sides by 3.5

1,385.71=a

Substitute a=1,385,71 into (1)

c + a=2200

c+1385.71=2200

c=2200-1385.71

=814.29

c=814.29

4 0

3 years ago

Read 2 more answers

Can someone simplify this equation and solve for x and y? (2x-5)+(y-1)+x=169

goldenfox [79]

Answer:

Answer

2x+3y=14,2x−3y=2

Adding :

2x+3y=14

2x−3y=2

__________

4x=16

x=4

∴xy=4×2

2×4+3y=14

8+3y=14

3y=6

y=2

Step-by-step explanation:

here you go

6 0

3 years ago

Read 2 more answers

Refer to the data set of body temperatures in degrees Fahrenheit given in the accompanying table and use software or a calculato

Mariulka [41]

The mean of the dataset is the average, while the median is the middle element.

The mean and the median of the given dataset is 98.2
The results support the common belief that the mean body temperature is 98.6F

The mean of the dataset is calculated using:

$\bar x = \frac{\sum x}{n}$

So, we have:

$\bar x = \frac{99.2+ 99.2 +98.2+............+97.7}{48}$

$\bar x = \frac{4715}{48}$

$\bar x = 98.2$

The median position is:

$Median = \frac{1}{2}(n + 1)$

$Median = \frac{1}{2}(48 + 1)$

$Median = \frac{1}{2}(49)$

$Median = 24.5$

This means that the median is the average of the 24th and 25th element

Using the sorted dataset, we have:

$Median = \frac{1}{2}(98.2 + 98.2)$

$Median = 98.2$

Because the calculated mean and the common belief (98.6) are close, then we can conclude that the results support the common belief that the mean body temperature is 98.6F