Isaac drinks 8 glasses of water each day. He says he will drink 2,920 glasses of water in a year that has 365 days. Is the exact answer reasonable

Given: f(x) = 9 cos (2x)

The differential equation is df = - 18 sin(2x) dx

When x contrasts from π/6 to π/6 + 01, then dx = 0.1.
The variation in f is δf = - 18 sin(π/3) *(0.1) = -1.5588 ≈ -1.559

The computation in the change in f directly:

f(π/6) = 9 cos(π/3) = 4.5
f(π/6 + 0.1) = 9 cos(π/3 + 0.2) = 2.6818
δf = 2.6818- 4.5 = -1.6382 ≈ -1.638

Direct computation of δf is near to the real value but in error. 
The two outcomes will be closer as dx gets smaller.

Answer would be:
δf = -1.559  (correct answer)
δf = -1.638 (approximate answer)

Answer:

a

Step-by-step explanation:

The value of x is 12 and this can be determined by using the arithmetic operations and the given data.

Given :

40% is equal to the fraction x/30.

The following steps can be used in order to determine the value of 'x':

Step 1 - The arithmetic operations can be used in order to determine the value of 'x'.

Step 2 - According to the given data, the 40% is equal to the fraction x/30.

Step 3 - So, the value of X is calculated as:

[tex]\dfrac{40}{100}=\dfrac{x}{30}[/tex]

Step 4 - Simplify the above expression.

x = 12

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Final answer:

The unit rate, or average speed, for traveling 4543.08 km in 52.4 hours is calculated by dividing the distance by the time, resulting in an average speed of 86.70 km/h.

Explanation:

The question asks for the unit rate of 4543.08 km traveled in 52.4 hours, which is essentially asking for the average speed in kilometers per hour (km/h). To find this, you would divide the total distance traveled by the total time taken.

Mathematically, this is expressed as:

Substituting the given values:

Therefore, the unit rate or average speed is 86.70 km/h. It's important to note that when calculating such problems, it's essential to maintain consistency in the units (in this case, km for distance and hours for time) to ensure the accuracy of your result.

Answer:

Option D is correct

Solution = (-1, -2)

Step-by-step explanation:

Given the equation:

y = x – 1               ....[1]

y = 3x + 1            ....[2]

Equate equation [1] and [2] to solve for x.

[tex]x-1=3x+1[/tex]

Subtract x from both sides we have;

[tex]-1=2x+1[/tex]

Subtract 1 from both sides we have;

[tex]-2=2x[/tex]

Divide both sides by 2 we have;

x = -1

Substitute the value of x = -1 in [1] we have;

y=-1-1 = -2

Graphically:

Graph the system of equations as shown below.

The intersection point of these lines is the solution for the given system of equation

⇒ (-1, -2)

Therefore, the solution for the given system of equation is, (-1, -2)

The length of each side of the church window is 20 inches.

To find the length of each side, we need to determine the perimeter of the square. The perimeter is the sum of all four sides of the square. In this case, it is given that the perimeter is 80 inches. Since all sides of a square are equal in length, we can divide the perimeter by 4 to find the length of each side. So, each side of the church window will be 80 inches divided by 4, which is 20 inches.

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Answer:

its  A

Step-by-step explanation:

Answer:

The distance traveled in 13.6 light year is [tex]7.9968\times 10^{13}\text{ miles}[/tex]      

Step-by-step explanation:

Given : Astronomers measure large distances in light-years. One light-year is the distance that light can travel in one year, or approximately 5,880,000,000,000 miles. Suppose a star is 13.6 light-years from Earth.

To find : In scientific notation, how many miles away is it?

Solution :

According to question,

The distance can travel in 1 light year is

[tex]1 \text{ light year} = 5,880,000,000,000 \text{ miles}[/tex]

We have to find the distance traveled in 13.6 light-years.

[tex]13.6 \text{ light year} =13.6\times 5,880,000,000,000 \text{ miles}[/tex]

[tex]13.6 \text{ light year} =79,968,000,000,000 \text{ miles}[/tex]

In scientific notation,

[tex]13.6 \text{ light year} =7.9968\times 10^{13}\text{ miles}[/tex]

Therefore, The distance traveled in 13.6 light year is [tex]7.9968\times 10^{13}\text{ miles}[/tex]

Answer:  The required value of x is 16.

Step-by-step explanation:  Given that the value of y is 7 when the value of x is 8.

We are to find the value of x when y is 14.

The ratio of y to x is given by

[tex]y:x=7:8.[/tex]

Therefore, when y = 14, we must have

[tex]14:x=7:8\\\\\\\Rightarrow \dfrac{14}{x}=\dfrac{7}{8}\\\\\\\Rightarrow x=\dfrac{14\times8}{7}\\\\\Rightarrow x=16.[/tex]

Thus, the required value of x is 16.

36/2 = 18

80/2=40

36/80 = 18/40

18/2 =9

40/2 = 20

36/80 = 9/20

the straight line would be 3^2 + 4^2 = X^2

9+16 = x^2

25 = x^2

x = sqrt(25)

x = 5

it is 5 miles

16,400 x (1 + 0.051)^20 =

16400 x (1.051)^20 =

16400 x 2.70429659 =

$44,350.46 

subtract the distance she traveled from the total distance she has to go

4 2/3 - 3 1/3 = 1 1/3 miles to go 

Answer:

-9x+y=82

Step-by-step explanation:

hope this helped!

The equation y-10=9(x+8) can be transformed into standard form by distributing, simplifying, and rearranging terms to get 9x - y = -82.

The given equation is y-10=9(x+8), and we're asked to change this slope-intercept form into the standard form. First, we'll start by distributing the 9 to both x and 8 which will result in y-10 = 9x + 72. Then, we'll bring terms involving x and y to one side of the equation, leading to -9x + y = 82. This is almost in standard form, but typically we want the leading coefficient (the coefficient of x) to be positive, so we'll multiply the equation by -1. This gives us 9x - y = -82, which is the equation in standard form.

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Answer:

[tex]r[/tex]≈[tex]5.2 in[/tex]

Step-by-step explanation:

It is given that a circle is required to inscribe an equilateral triangle with an area of [tex]35.074 in^2[/tex] and an altitude of [tex]7.794 in[/tex],

Also, we know that the centroid divides the altitude into 2:1 form, thus

[tex]r=\frac{2}{3}(h)[/tex]

Substituting the value of an altitude, we have

[tex]r=\frac{2}{3}(7.794)[/tex]

[tex]r=5.196 in[/tex]

[tex]r[/tex]≈[tex]5.2 in[/tex]

Therefore, the radius of the circle is [tex]5.2 inches[/tex].

Answer:

Step-by-step explanation:

Answer: Option (2) and (5) are the correct options.

Step-by-step explanation:

Since, the given expression, x+3.6= -1.7

If we add -3.6 in both sides then we get x+3.6+(-3.6)=1.7-3.6⇒x= -1.9

while,

If we subtract 3.6 from both sides then we get x+3.6-3.6=1.7-3.6⇒x= -1.9

Thus, In the above by adding -3.6 and by subtracting 3.6 we get the value of x in one step.(because after this only x remains in LHS of the given expression)

Therefore, Option (2) and (5) are correct.

Note: Except these two options we can not get x in one step. (we can not get single x in LHS of the given expression by the other options.)

Answer:

b e

Step-by-step explanation:

Answer: Circumference = 25.1 meters.

Area = 50.2 square meter.

Step-by-step explanation:

The circumference of a circle is given by :-

[tex]C=2\pi r[/tex]

Area of circle is given by :-

[tex]A=\pi r^2[/tex], where r is the radius.

Given : Radius = 4 meters

Then circumference of the circle will be :-

[tex]C=2(3.14) (4)=25.12\approx25.1\text{ meters}[/tex]

Area of circle is given by :-

[tex]A=(3.14)(4)^2=50.24\approx50.2\text{ meters}^2[/tex]

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