a patient is to take 2 4/5 tablespoons of medicine per day in 2 equally divided doses. how much medicine is to be taken in each dose?

Final answer:

To find dwdt using the chain rule, differentiate w=xy+yz, where x=e^2t, y=2+sin(4t), and z=2+cos(7t), as functions of t, apply partial derivatives and multiply by dx/dt, dy/dt, and dz/dt.

Explanation:

The student asked how to use the chain rule to find dwdt as a function of x, y, z, and t, without rewriting x, y, and z in terms of t, and keeping e2t as x. Given w=xy+yz, where x=e2t, y=2+sin(4t), and z=2+cos(7t), we apply the chain rule to differentiate w for t, remembering that x, y, and z are all functions of t. To find debt, we derive each component individually and sum their contributions. The calculation involves taking partial derivatives of w to x, y, z, multiplied by their respective derivatives to t (dx/dt, dy/dt, dz/dt).

Subtract the first day of the month from the date of the last Wednesday and divide by 7 to find the remainder. Count backwards from Wednesday to determine the day of the week for the first day of the month, which is Saturday in this case.

The subject of this question pertains to dates and the calendar, which fall under the domain of Mathematics. To answer the question, we need to calculate how many days have passed from the 26th (the last Wednesday) to the 1st day of the same month. A week has seven days so we use the principles of modular arithmetic, a branch of number theory. The 26th day is a Wednesday, and for every seven days we go back, it will still be Wednesday. Thus, the difference from 26 to 1 is 25. Dividing 25 by 7, we get a quotient of 3 and a remainder of 4. This tells us that four days before the last Wednesday, which was the 26th, would be the first day of the month. Going backwards from Wednesday, we count Tuesday (1), Monday (2), Sunday (3), and Saturday (4). Therefore, the first day of that month falls on a Saturday.

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Answer:

A. 5/8 = h/20

Step-by-step explanation:

Topic: Triangle Similarity

As you can see in the image you can paint the problem that way, it means that each side of the triangle is a multiplier from the other one same side, so you can build a relation as follows:

[tex]\frac{5}{h} = \frac{8}{20} \\[/tex]

you can re arrange the equality as

[tex]\frac{5}{8} = \frac{h}{20}[/tex]

as you can ssee you just reached the option A. 5/8 = h/20

3/20, or 0.15 of the shirts each evening

1 - 1/4 = 3/4

(3/4) / 5 = (3/4) / (5/1) = (3/4) x (1/5) = 3/20 = 0.15

In a 30-60-90 triangle, the side opposite the 30-degree angle (s) has a length of "s," and the hypotenuse has a length of "2s."

The side opposite the 60-degree angle is "s√3."

We have,

In a 30-60-90 triangle, the sides are in a specific ratio:

x, x√3, and 2x,

where x is the length of the shortest side (opposite the 30-degree angle).

Step 1:

Identify the shortest side (opposite the 30-degree angle).

Let's assume the length of the shortest side (opposite the 30-degree angle) is "s."

Step 2:

Find the other side lengths.

The side opposite the 60-degree angle is s√3.

The hypotenuse is twice the length of the shortest side, so it is 2s.

Thus,

In a 30-60-90 triangle, the side opposite the 30-degree angle (s) has a length of "s," and the hypotenuse has a length of "2s."

The side opposite the 60-degree angle is "s√3."

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To subtract the fractions 7 8/9 and 5 3/5, first convert them into improper fractions. Then, adjust them to the common denominator (45 in this case) and subtract to get the answer of 2 13/45.

To begin, we need to convert these mixed fractions (7 8/9 and 5 3/5) into improper fractions. 7 8/9 equals 71/9 (since 7*9 + 8 = 71) and 5 3/5 equals 28/5 (since 5*5 + 3 = 28). Now, we can subtract these fractions by finding a common denominator or a number that 9 and 5 mutually divide into. This number is 45. Therefore, we adjust these fractions to have the denominator of 45, getting 355/45 and 252/45. The subtraction of these adjusted fractions equals 103/45. That can be simplified into 2 13/45.

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Answer:

I think its 30 as well

Step-by-step explanation:

The distance between charges of +2.35 and −1.96,  should be approximately 1.566 picometers (pm).

Coulomb's law states that the force (F) between two point charges is given by:

F =[tex]\dfrac{(k \times q1 \times q2)}{r^2}[/tex]

Where:

The electrostatic force between the charges is F

k is Coulomb's constant, approximately equal to 8.99 × 10^9 N m²/C².

The magnitudes of the two charges are [tex]q_1[/tex] and [tex]q_2[/tex].

The distance between the charges is r.

Given that the charges are +2.35 and −1.96, we'll call the distance between them x (in pm). Similarly, for charges +4.06 and −2.11, the distance is given as 2.26 pm.

Setting up the equation:

For the first pair of charges (q1 = +2.35 C and q2 = −1.96 C):

F1 =[tex]\dfrac{(k \times |2.35 \times (-1.96)|)}{x^2}[/tex]

For the second pair of charges (q1 = +4.06 C and q2 = −2.11 C):

F2 =[tex]\dfrac{(k \times |4.06 \times (-2.11)|)}{(2.26)^2}[/tex]

Since the forces are said to be equal, we have:

F1 = F2

The solution of the expression for x is given by:

[tex]\dfrac{(k \times |2.35 \times (-1.96)|}{x^2}[/tex] =[tex]\dfrac{(k \times |4.06 \times (-2.11)|)}{(2.26)^2}[/tex]

|[tex]\dfrac{(2.35 \times (-1.96)}{x^2}[/tex]| =[tex]\dfrac{|4.06 \times (-2.11)|}{ (2.26)^2}[/tex]

[tex]{(2.35 \times 1.96)} {x^2}[/tex] = [tex]\dfrac{(4.06 \times 2.11)} { (2.26)^2}[/tex]

[tex]x^2[/tex] =[tex]\dfrac{(2.35 \times 1.96 \times (2.26)^2} {(4.06 \times 2.11)}[/tex]

[tex]x^2[/tex] = 2.450206485

x ≈ [tex]\sqrt{2.450206485[/tex]

x ≈ 1.566 pm

Therefore, the distance between charges of +2.35 and −1.96,  should be approximately 1.566 picometers (pm).

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To find the distance between charges of +2.35 and -1.96 for the attractive force to be the same, use Coulomb's Law to calculate the force between charges of +4.06 and -2.11 separated by a distance of 2.26 pm. Then solve for the distance using the same formula and the calculated force value.

To find the distance between charges of +2.35 and -1.96 for the attractive force to be the same as between charges of +4.06 and -2.11, we can use Coulomb's Law. The formula for calculating the force between two charges is F = k * (|q1 * q2| / (d^2)) where k is the proportionality constant and d is the distance between the charges.

First, we calculate the force between charges of +4.06 and -2.11. Let q1 = +4.06, q2 = -2.11, and d = 2.26 pm. Plugging these values into the formula, we get:

F = (1/47e) * (|4.06 * -2.11| / (2.26^2))

Next, we can find the distance between charges of +2.35 and -1.96 such that the attractive force is the same. Let q1 = +2.35, q2 = -1.96, and F = the value we calculated earlier. Rearranging the formula to solve for d, we get:

d = sqrt((|q1 * q2| / (F * k)))

The probability that on any given day Jinelle’s bus is on time and Mr. Corney is the driver is (8/15).

Probability is the chance of happening an event or incident.

Given, the probability that Jinelle’s bus is on time is 2/3.

The probability that Mr. Corney is driving the bus is 4/5.

Therefore, the probability that on any given day Jinelle’s bus is on time and Mr. Corney is the driver is:

= (2/3) × (4/5)

= (8/15)

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30240 are 5-digit numbers (including leading 0s) are there with no digit appearing exactly two times

A number system is defined as a system of writing to express numbers.

By means of Permutation we solve this

The term permutation refers to a mathematical calculation of the number of ways a particular set can be arranged.

The formula for permutation is [tex]^{n}P_{r} =\frac{n!}{(n-r)!}[/tex]

n is total number of objects

r is number of objects selected

We need to find 5-digit numbers (including leading 0s) are there with no digit appearing exactly two times

¹⁰P₅=10!/(10-5)!

=10!/5!

=10×9×8×7×6×5!/5!

=30240

Hence, 30240 are 5-digit numbers (including leading 0s) are there with no digit appearing exactly two times

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a. Let x  represent the number of questions finished.
b. The equation is  x + 37 = 78 , and solving yields  x = 41 .
c. The student finished 41 questions.

a. Define a variable for the unknown value. Let  x  represent the number of questions the student has finished.

b. Write and solve the equation. The total number of questions is the sum of the questions finished and the questions left:  x + 37 = 78 . Now solve for  x :

x = 78 - 37 = 41

So, the student has finished 41 questions.

c. Answer the question with the correct units. The student has finished 41 questions out of the total 78. Therefore, the student has [tex]\( \frac{41}{78} \)[/tex] of the test complete. To express this as a percentage, multiply by 100:

[tex]\[ \frac{41}{78} \times 100 \approx 52.56\% \][/tex]

The student has finished approximately 52.56% of the test.

Que. A student is taking a test. He has 37 questions left. If the test has 78 questions, how many questions has he finished? a. Define a variable for the unknown value. Let ...........represent............
b. Write and solve the equation.
c. Answer the question with the correct units........

Answer:

The answer is actually 5.17 centimeters

Step-by-step explanation:

The question is asking you to calculate the minimum thickness so you have to find the lowest bounds.

The covers are 0.9 mm to 1 d.p so the minimum thickness is 0.85 because that is the lowest bound.

The pages are 0.13 mm to 2 d.p so the minimum thickness is 0.125 as that is the lowest bound.

0.85  x 2 = 1.7 and 0.125 x 400 = 50

50 + 1.7 = 51.7 which is the minimum length.

Final answer:

The minimum thickness of a book with 400 pages, each 0.13mm thick, and two covers, each 0.9mm thick, is calculated to be 53.8mm.

Explanation:

The minimum thickness of a book can be calculated by summing the thickness of the covers and all the pages. We are given that each cover is 0.9mm thick and each page is 0.13mm thick. To find the minimum thickness of the book, we multiply the thickness of each page by the total number of pages and then add the thicknesses of the front and back covers.

To calculate:

Thickness of all pages: 400 pages × 0.13 mm/page = 52 mm

Thickness of both covers: 2 covers × 0.9 mm/cover = 1.8 mm

Total minimum thickness: 52 mm + 1.8 mm = 53.8 mm

The minimum thickness of the book is therefore 53.8 mm.