the pitch, or frequency, of a vibrating string varies directly with the square root of the tension. if a string vibrates at a frequency of 300 hertz due to a tension of 8 pounds, find the frequency when the tension is 72 pounds.

Answers

Answer 1

[tex]\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \begin{array}{llll} \stackrel{frequency}{f}\textit{ of a vibrating string varies directly}\\ \qquad \qquad \textit{with the square root of the tension }\stackrel{tension}{t} \end{array}[/tex]

[tex]\bf f=k\sqrt{t}\quad \textit{we also know that } \begin{cases} f=300\\ t=8 \end{cases}\implies 300=k\sqrt{8} \\\\\\ \cfrac{300}{\sqrt{8}}=k\implies \cfrac{300}{\sqrt{2^2\cdot 2}}=k\implies \cfrac{300}{2\sqrt{2}}=k\implies \cfrac{150}{\sqrt{2}}=k \\\\\\ \textit{and we can \underline{rationalize} it to }\cfrac{150\sqrt{2}}{2}\implies 75\sqrt{2}=k[/tex]

[tex]\bf thus\qquad f=\stackrel{k}{75\sqrt{2}}\sqrt{t}\implies \boxed{f=75\sqrt{2t}}\\\\ -------------------------------\\\\ \textit{now, when t = 72, what is \underline{f}?}\qquad f=75\sqrt{2(72)}[/tex]

Answer 2

Answer:

when the tension is 72 pounds , the frequency is 900 hertz

Step-by-step explanation:

Hello, I think I can help you with this.

you can easily solve this by using a rule of three.

According to the question data:

the pitch, or frequency, of a vibrating string varies directly with the square root of the tension.in mathematical terms it is:

f ∝ √T

where f is the pitch or frequency and T is the tension

Step 1

if a string vibrates at a frequency of 300 hertz due to a tension of 8 pounds

300 hertz ∝ √8 pounds

300⇔√8

what is the frequency when the tension is 72 pounds

x⇔√72

Step 2

Let

300⇔√8

x⇔√72

the relation is

[tex]\frac{300}{\sqrt{8} } =\frac{x}{\sqrt{72} }\\\\ Now, solve\ for\ x\\\\\\\frac{300*\sqrt{72} }{\sqrt{8} } =x\\x=\frac{300*\sqrt{72} }{\sqrt{8} } \\x=\frac{300*\sqrt{8*9}}{\sqrt{8}} \\x=\frac{300*\sqrt{8}*\sqrt{9}}{\sqrt{8}} \\x=300*\sqrt{9}\\x=300*3\\x=900[/tex]

when the tension is 72 pounds , the frequency is 900 hertz

have a good day.

Related Questions

Find the length and width of a rectangle that has the given perimeter and a maximum area. perimeter: 128 meters

Answers

P = 128 meters = 2W + 2L. We want to maximize the area: A = L*W

Solve 128 meters = 2W + 2L for either W or L:

64 meters = W + L, so W = 64-L
and subst. your result into

A = L*W: A = L*(64-L). Then A(L) = 64L - L^2. You could graph this and find the approx value of L at which A(L) is at its max.

Or, if you know calculus, differentiate A(L) and set the result = to 0. Solve for L.

L + W = 64, so you can subst. your value for L into this eqn to find W.

If s = {r, u, d} is a set of linearly dependent vectors. if x = 5r + u + d, determine whether t = {r, u, x} is a linearly dependent set

Answers

Consider any arbitrary linear combination of the vectors [tex]\mathbf r,\mathbf u\,\mathbf x[/tex]. We have

[tex]c_1\mathbf r+c_2\mathbf u+c_3\mathbf x=c_1\mathbf r+c_2\mathbf u+c_3(5\mathbf r+\mathbf u+\mathbf d)[/tex]
[tex]=(c_1+5c_3)\mathbf r+(c_2+c_3)\mathbf u+c_3\mathbf d[/tex]
[tex]=c_4\mathbf r+c_5\mathbf u+c_6\mathbf d[/tex]

We know [tex]\mathbf r,\mathbf u,\mathbf d[/tex] are linearly dependent, which means there must exist some choice of not all zero constants [tex]c_4,c_5,c_6[/tex] such that the combination above gives the zero vector. So [tex]T=\{\mathbf r,\mathbf u,\mathbf x\}[/tex] is a set of linearly dependent vectors.

1. which expression is equivalent to 8 × 8 × 8 × 8?

A. 8 × 4
B. 8^5
C. 8^4
D. 4^8

2. which expression is equivalent to 4 × 4 × 4 × 4 × 4 × 4 × 4?

3. which expression is equivalent to 7 × 7 × 7 × 7 × 7 × 7?

4. which expression is equivalent to 4 × 4 × 4?

5. which expression is equivalent to 3 × 3?

Answers

question 1: c. ) 8^4 question 2: 4^7 question 3: 7^6 question 4: 4^3 question 5: 3^2

1. A. 8×4
2. 4×7
3. 7×6
4. 4×3
5. 3×1 or 3×2 it's probably 3×2 tho

The driver of a car traveling at 54ft/sec suddenly applies the brakes. The position of the car is s=54t-3t^2, t seconds afyer the driver applies the brakes.
How many seconds after the driver applies the brakes does the car come to a stop

Answers

s = 60t - 3t^2
v = ds/dt = 60 - 6t

when it comes to rest, v = 0,
so t = 10 sec

now distance travelled = time taken x average velocity
= 10 x (60 + 0)/2
= 300 ft

After time [tex]t = 9[/tex] seconds the driver applies the brakes does the car come to a stop.

What is time?

" Time is defined as the measurable slot of period in which required action is done."

Formula used

[tex]y = x^{n} \\\\\implies \frac{dy}{dx} = nx^{n-1}[/tex]

According to the question,

Position of the car [tex]'s' = 54t - 3t^{2}[/tex]

[tex]'s'[/tex] represents the distance

[tex]'t'[/tex] is the time in seconds

When driver applies break [tex]v= 0[/tex],

[tex]v = \frac{ds}{dt}[/tex]

Calculate the first derivative with respect to time we get,

[tex]'s' = 54t - 3t^{2}\\\\\implies \frac{ds}{dt} = 54- 6t[/tex]

As [tex]\frac{ds}{dt} =0[/tex] we get the required time as per given condition,

[tex]54-6t =0\\\\\implies 6t =54\\\\\implies t = 9[/tex]

Hence, after time [tex]t = 9[/tex] seconds the driver applies the brakes does the car come to a stop.

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The GCF of any two even numbers is always even. true or false?

Answers

your answer is false.

True because if you use prime factorization of even numbers you will always get a 2. If a number has 2 as a factor then it is even.

Given e(x + 4) = 10 and e[(x + 4) 2 ] = 116, determine (a) var(x + 4), (b)μ= e(x), and (c)σ 2 = var(x).

Answers

a. [tex]\mathbb V(X+4)=\mathbb E((X+4)^2)-\mathbb E(X+4)^2=116-10^2=16[/tex]

b. [tex]\mathbb E(X+4)=\mathbb E(X)+\mathbb E(4)=\mathbb E(X)+4=10\implies\mathbb E(X)=6[/tex]

c. [tex]\mathbb V(X)=\mathbb E(X^2)-\mathbb E(X)^2[/tex]

[tex]\mathbb E((X+4)^2)=\mathbb E(X^2+8X+16)=\mathbb E(X^2)+8\mathbb E(X)+\mathbb E(16)[/tex]
[tex]\implies116=\mathbb E(X^2)+48+16\implies\mathbb E(X^2)=52[/tex]

[tex]\implies\mathbb V(X)=52-6^2=16[/tex]

Final answer:

In the given statements, first 'x' is derived from the equation e(x + 4) = 10, then it is plugged into e(x) to find μ and the variance formula to obtain σ².

Explanation:

The question presents a scenario with two equations: e(x + 4) = 10 and e[(x + 4) 2 ] = 116 .To solve these equations, you would need to employ various algebraic and statistical concepts. Given this information, let's procede as follows:

To find (a) var(x + 4), we first need to determine the value of 'x' which can be derived from the given e(x + 4) = 10. After calculating 'x', we can work out (b)μ= e(x) by inserting our calculated 'x' into the e(x) formula. Finally, σ 2 = var(x) can be computed by applying 'x' in the variance formula.

Please note, this solution requires a good understanding of the properties of exponential functions and the statistical representation of variance (var), mean (μ), and standard deviation (σ²). Due to the complexity of these equations, I recommend using a calculator to accurately work out each part.

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We wish to choose 7 cards from a usual deck of 52 playing cards. In how many ways can this be done if we are required to choose the cards in the following ways?
(a) with no restriction.
(b) all cards come from the same suit.
(c) exactly 3 Aces and exactly 3 Kings are chosen.
(d) all 7 cards have values between 2 and 7 inclusive.
(e) all 7 cards all have different values (where Jacks are different from Queens, etc.).

Answers

In a usual deck of 52 cards, there are 4 suits with 13 card for each suit.

(a) with no restriction.
If there is no restriction and different order is not important, then the possible way should be: 52!/ (52-7)!7!= 52!/45!7!= (52* 51* *50*49*48*47*46)/(7*6*5*4*3*2*1) = 674274182400/5040= 133,784,560 ways

(b) all cards come from the same suit.
If all card has to come from the same suit, that means you will only have 13 possible cards for each suit.
Then the possible ways for each suit: 13!/(13-7)!7!= (13*12*11*10*9*8*7)/ (7*6*5*4*3*2)= 8648640/5040= 1716 ways per suit.
Since there are 4 suits then the possible way= 1716 * 4= 6864

(c) exactly 3 Aces and exactly 3 Kings are chosen.
In this case, we will have 3 aces, 3 kings, and one random card. There are 4 aces/kings in one deck and we have to choose 4.
The possible ways for 3 aces or 3 kings would be: 4!/3!(4-3)!= 4 ways.
After choosing the 3 aces and 3 kings, the deck should have 52-3-3 = 46 card left. That mean there will be 46 possible ways for the random card.
The total possibilities should be: 4 * 4* 46= 736 ways

(d) all 7 cards have values between 2 and 7 inclusive
There are four cards with each value. The value between 2 and 7 inclusive should be 7-2+1= 6 different value. Since each value has 4 cards and we have 6 different value, then the total possible card is 6*4= 24
Then, we take 7 cards from those 24 cards. The possible should be: 24!/7!(24-7)!= (24*23*22*21*20*19*18) / 5040= 1744364160/5040= 346104

(e) all 7 cards all have different values (where Jacks are different from Queens, etc.).
There is 4 card with same value. For the first take, you will have 52 different ways. But for the second take, you will only have 52-4=48 different ways. That was because you can use:
1. one card that you take earlier.
2. three cards with the same value.
Then the possible ways become like this: 52*48*44*40*36*32*28/ 7!= 28,114,944

explain how you could find 3/8% of 800

Answers

3/8 of 800 is 300.. 3/8 of 800 is really 300.To check, take 3/8 and convert it to .375. Then, find what .375 of 800 is... 300!
Also, you can see that 3/8 and 800 can easily be converted to a common denominator... 800. So, just add 2 zeros to 3, and you get 300!

First turn 3/8 into a decimal, which would be .375 Next the key word of in 3/8% of 800 tells us to multiply 3/8% and 800 so since we know 3/8% = .375 in decimal form, lets multiply .375 x 800 = 300 so 3/8% of 800 is 300

The ____ function can be used to ensure that a number has the appropriate number of decimal places.

Answers

The round function can be used to ensure that a number has the appropriate number of decimal places.

Two small fires are spotted by a ranger from a fire tower 60 feet above ground. The angles of depressions re 11.6° and 9.4°. How far apart are the fires? (The fires are in the same general direction from the tower.)

Answers

The two fires are about 70 feet from each other. The assumption is that the ground is relatively level and that a right triangle will be made with the three points of the triangle being the ranger, the spot on the ground directly beneath the ranger, and the fire itself. So the distance to the first fire will be: Calculate the angle. That will be 90° - 11.6° = 78.4° The distance will be tan(78.4) = X/60 60 tan(78.4) = X 60 * 4.871620136 = X 292.2972082 = X And that's how far the 1st fire is from the ranger's station. Now for the 2nd angle = 90° - 9.4° = 80.6° 60 tan(80.6) = X 60 * 6.040510327 = X 362.4306196 = X And the distance between the two fires will be the difference in distance from the tower, so 362.4306196 - 292.2972082 = 70.13341146 Rounding to 2 significant figures gives 70 feet.

Toby exercises 14 hours a week. John exercises 20% more than Toby and Jenny exercises two more hours than John. Which expression represents how much Jenny exercises? (w represents weeks)

Answers

John exercised 20% more than Toby. So the number of hours that John exercises per week is 14 + 0.2(14) = 14 + 2.8 = 16.8.

Jenny exercises two more hours than John. So the number of hours that Jenny exercises per week is 16.8 + 2 = 18.8.

So an expression representing the number of hours that Jenny exercises after w weeks is 18.8w.

the answer is 18.8w

Toby 14w

John 14(1.2)w

Jenny 14(1.2)w + 2w

thus, Jenny exercise

14(1.2)w + 2w

16.8w + 2w

18.8w

what is the equation for a line that passes through (-7, 2) and is perpendicular to the graph of y=-1/2x+3

Answers

first off, what is the slope of say y = -1/2x+3? well, let's take a peek

[tex]\bf y=\stackrel{slope}{-\cfrac{1}{2}}x+3[/tex]

well, then, a line perpendicular to that line, will have a slope that is negative reciprocal to that one, so if the slope of that graph is -1/2, then

[tex]\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad -\cfrac{1}{2}\\\\ slope=-\cfrac{1}{{{ 2}}}\qquad negative\implies +\cfrac{1}{{{ 2}}}\qquad reciprocal\implies + \cfrac{{{ 2}}}{1}\implies 2[/tex]

so, we're really looking for the equation of a line whose slope is 2, and runs through -7, 2.

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ -7}}\quad ,&{{ 2}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies 2 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-2=2[x-(-7)] \\\\\\ y-2=2(x+7)\implies y-2=2x+14\implies y=2x+16[/tex]

A perpendicular line will have a negative reciprocal slope (-1/2 → 2/1)
Use the given point to find the y-intercept "b" in y = mx+b

y = 2x + b
2 = 2(-7) + b
2 = -14 + b
2 + 14 = b
16 = b

final equation :
y = 2x + 16

Find all values of x that are simultaneously a solution to the congruences x ≡ 2 (mod 3), x ≡ 1 (mod 5), x ≡ 3 (mod 29).

Answers

[tex]\begin{cases}x\equiv2\pmod3\\x\equiv1\pmod5\\x\equiv3\pmod{29}\end{cases}[/tex]

Let's start by supposing [tex]x=2+3+3=11[/tex]. Modulo 3, we end up with 2 as needed.

But modulo 5, we want to get 1, so we'd need to multiply the first and last terms by 5 and the second term by the inverse of 3 modulo 5. We have [tex]3\times2\equiv6\equiv1\pmod5[/tex], so we multiply by 2:

[tex]x=2\times5+3\times2+3\times5=31[/tex]

But now modulo 3, the first term gives a remainder of 1, so simply multiply by 2:

[tex]x=2\times5\times2+3\times2+3\times5=41[/tex]

Next, modulo 29, we can force the first two terms to vanish by multiplying them by 29, but the last term still yields 15. We want to get 3 on its own, so we could just multiply the third term by the inverse of 5 modulo 29. We have [tex]5\times6\equiv30\equiv1\pmod{29}[/tex].

[tex]x=2\times5\times2\times29+3\times2\times29+3\times5\times6=844[/tex]

Now, [tex]844\equiv1\pmod3[/tex], so we need to multiply the first term by 2 one more time; [tex]844\equiv4\pmod5[/tex], so we need to multiply the second term by the inverse of 4 modulo 5, which would be 4 since [tex]4^2\equiv16\equiv1\pmod5[/tex]; and [tex]844\equiv3\pmod{29}[/tex], so the last term is okay.

[tex]x=2\times5\times2\times29\times2+3\times2\times29\times4+3\times5\times6=1946[/tex]

We know 1946 is a possible solution because we engineered it that way, but it's not the smallest positive solution. We have

[tex]1946\equiv206\pmod{3\times5\times29}\equiv206\pmod{435}[/tex]

The general solution to the system is then [tex]x=206+435n[/tex], where [tex]n\in\mathbb Z[/tex].

What percent of 9.2 is 43.7

Answers

if we take 9.2 to be the 100%, what is 43.7 off of it in percentage then?

[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 9.2&100\\ 43.7&p \end{array}\implies \cfrac{9.2}{43.7}=\cfrac{100}{p}\implies p=\cfrac{43.7\cdot 100}{9.2}[/tex]

The requried 475% of 9.2 is 43.7, as of the given percentage situation.

What is the percentage?

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
In the question, we are asked to determine the 43.7 is what percent of 9.2.

So, let the percent be x,
x % of 9.2 = 43.7
x/100 × 9.2 = 43.7
x = 43.7/9.2 × 100%
x = 475%

Thus, the requried 475% of 9.2 is 43.7, as of the given percentage situation.

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Find the difference: 16.25 - 7.92

Answers

Your answer is going to be 8.33

the difference is 8.33.
give me the best plz

what is the least common denominator for 5/6 and 3/8

Answers

The least common denominator is 24.

Mr. Carandang sold a total of 1,790 prints of one of his drawings. Out of all 1,273 unframed prints that he sold, 152 were small and 544 were medium-sized. Out of all of the framed prints that he sold, 23 were small and 42 were extra large. Of the large prints that he sold, 188 were framed and 496 were unframed. Small Medium Large Extra Large Total Framed 23 264 188 42 ? Unframed 152 544 496 81 1,273 Total 175 808 684 123 1,790 Which number is missing from the two-way table?'

Answers

framed unframed total
small 23 152 175
medium 264 544 808
large 188 496 684
ex-large 42 81 123
total 517 1273 1790

The missing number in the two-way table is the total number of framed prints, which is 517. This is calculated by subtracting the total unframed prints from the total prints sold and then summing the known framed prints.

To find the missing number of prints in the table, we need to determine the total number of framed prints sold by Mr. Carandang. We know the following from the table:

Total prints sold: 1,790Unframed prints: 1,273

To find the total number of framed prints:

Total framed prints = Total prints - Total unframed prints

Total framed prints = 1,790 - 1,273 = 517

Now we need to sum the known framed prints:

Framed small: 23Framed medium: 264Framed large: 188Framed extra large: 42

The total of known framed prints is:

23 + 264 + 188 + 42 = 517

Thus, the total framed prints value was missing and it is 517.

What is the value of |−25|?

Answers

Hi there!!

The answer to this is |-25| = 25.

Hope this helped!! ☺♥

the answeeeeerrrr is positive 25!!,!

A machine is set to fill the small-size packages of m&m candies with 56 candies per bag. a sample revealed: three bags of 56, two bags of 57, one bag of 55, and two bags of 58. to test the hypothesis that the mean candies per bag is 56, how many degrees of freedom are there?

Answers

In statistics, the amount of degrees of freedom is the quantity of values in the final computation of a statistic that are free to differ. In this case, you can get the answer by adding the number of bags and subtracting 1.

So in computation, this would look like: 3 + 2 + 1 + 2 - 1 = 7

Therefore, 7 is the degrees of freedom.

Final answer:

The number of degrees of freedom for the hypothesis test that the mean candies per bag is 56 is 7, calculated by subtracting one from the total number of sampled bags.

Explanation:

To calculate the number of degrees of freedom for the hypothesis test that the mean candies per bag is 56, we use the sample size minus one. The sample size is the number of observations, which is the total count of bags sampled. In this case, we have a total of 8 bags (three bags of 56, two bags of 57, one bag of 55, and two bags of 58). Therefore, the degrees of freedom for this test would be 8 - 1 = 7.

PLEASE HELP 15 POINTS WILL GIVE BRAINLIEST The following formula, F = ma, relates three quantities: Force (F), mass (m), and acceleration (a). A: Solve this equation, F = ma for a. B If F = -24 units and m = 10 units, what is the acceleration, a? Use the equation from Part (a) to answer the question. C: If F = 24 units and a = 12 units, what is the mass, m? Use the equation, F = ma, to plug in the known values and solve for m

Answers

Part A

The expression "ma" is the same as "m*a" (m times a). To isolate 'a', we divide both sides by m. Division is the inverse operation of multiplication. Think of it as undoing multiplication

F = ma
F = m*a
F/m = m*a/m
F/m = a
a = F/m

Answer: a = F/m
Note: the slash "/" without quotes means "divide"

===========================================
Part B

Use the result from part A. We will plug F = -24 and m = 10 into that equation

a = F/m
a = -24/10
a = -2.4

Answer: -2.4

===========================================
Part C

We will use the equation F = m*a

F = m*a
24 = m*12 ... plug in F = 24 and a = 12
24/12 = m*12/12
2 = m
m = 2

Answer: 2

In Miss Marshalls classroom 6/7 of the students play sports of the students who play sports for fifth also play instruments if there are 35 students in her class how many play sports and instruments

Answers

6/7 time 4/5 = 24/35
24 students do both.

How many different 4-digit sequences can be formed using the digits 0, 1,..., 6 if repetition of digits is allowed

Answers

0 through 6 is 7 total numbers

1st digit can be 0-6 = 7 numbers

2nd digit can be 0-6 = 7 numbers

3rd digit can be 0-6 = 7 numbers

4th digit can be 0-6 = 7 numbers

7 * 7 *7 *7 = 2401 different combinations

I keep getting 13. It's supposed to be 3. Can you show me how it's done? 3(a-5) = -6

Answers

First, divide both sides by 3. I think your mistake was that you were multiplying -3. Please note that in order to cancel something out you need to do the reverse operation. The reverse operation of subtraction is addition and the reverse of multiplication is division.

3(a - 5) = -6
a - 5 = -2

Now add 5 to both sides

a - 5 = -2
+5 +5
a = 3

Hope this helps!

3(a-5) = -6

Start by distributing...

3a - 15 = - 6

Add 15 to both sides...

3a = 9

Divide both sides by 3 to get a by its self

a = 3

If f(x) = 3x + 6, which of the following is the inverse of f(x)?

A. f –1(x) = 3x – 6
B. f –1(x) =
C. f –1(x) =
D. f –1(x) = 6 – 3x

Answers

Final answer:

To determine the inverse of the function f(x) = 3x + 6, you need to switch 'x' and 'f(x)', isolate f-1(x) on one side of the equation, then solve for f-1(x). The resulting inverse function is f-1(x) = (x - 6)/3.

Explanation:

The function given is f(x) = 3x + 6. To find the inverse of this function, we first need to switch 'x' and 'f(x)', giving us: x = 3f-1(x) + 6. Next, we want to isolate f-1(x) on one side of the equation. To do this, we subtract 6 from both sides of the equation resulting in: x - 6 = 3f-1(x). Finally, we divide all terms by 3 to solve for f-1(x), which gives us f-1(x) = (x - 6)/3. So, the correct answer from the options given is not listed.

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Suppose 8 out of every 20 students are absent from school less than 5 days a year.Predict how many students would be absent less than 5 days a year out of 40,000 students.

Answers

Answer:
8/20 * 40,000 = 16,000

5x^7y^4+25xy^2+15xy^3/5xy^3

Answers

The answer is
5x^7y^4+3x^2y^6+25xy^2

Find the rate of change of the area of a square with respect to the length z , the diagonal of the square. what is the rate when z=2?

Answers

The diagonal of a square is equal to the side x times square root of 2, xSqrt(2)
z = xSqrt(2), its rate of change is just Sqrt(2)

The rate of change of Area, A with respect to the diagonal length, z and the rate of change when z = 2 is :

[tex]\frac{dA}{dz} = z [/tex]

[tex]\frac{dA}{dz} = 2 \: when \: z = 2 [/tex]

The area of a square is rated to its diagonal thus :

Area of square = A

Length of diagonal = z

The relationship between Area and diagonal of a square is : [tex]A \: = 0.5 {z}^{2} [/tex]

The rate of change of area with respect to the length, z of the square's diagonal ;

This the first differential of Area with respect to z

[tex] \frac{dA}{dz} = 2(0.5)z \: = z[/tex]

Therefore, the rate of change of area, A with respect to the length, z of the diagonal is [tex]\frac{dA}{dz} = z [/tex]

The rate of change [tex]\frac{dA}{dz} [/tex] when z = 2 can be calculated thus :

Substitute z = 2 in the relation [tex]\frac{dA}{dz} = z [/tex]

Therefore, [tex]\frac{dA}{dz} = 2 [/tex]

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Use an algebraic rule to describe a translation right 4 units and down 2 units.

Answers

In the conventional Cartesian plane, horizontal coordinates increase to the right and vertical coordinates increase up. Hence the described translation adds 4 to each horizontal coordinate and -2 to each vertical one:
(x, y)⇒(x+4, y-2)

Express 9.21212121212... as a rational number, in the form pq

Answers

[tex]x=9.212121\ldots=9.\overline{21}[/tex]
[tex]100x=921.212121\ldots=921.\overline{21}[/tex]
[tex]99x=921.\overline{21}-9.\overline{21}=921-9=912[/tex]
[tex]\implies x=\dfrac{912}{99}=\dfrac{304}{33}[/tex]

12 PTS!!!

John ordered two kinds of pizza for a party: sausage pizzas and veggie pizzas. He ordered three pizzas of each kind. The pizzas cost a total of $99. If the cost of each veggie pizza is $18, what is the cost of a sausage pizza?

Answers

99-18= 81/3=27
Answer: 27

1 veggie pizza cost 18 so 3 cost 18*3 = 54

99-54 = 45 for the 3 sausage pizzas

45/3 = 15 dollars each for sausage

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