Allison drive 30 mph through the city and 55 mph on the New Jersey Turnpike she drove 90 miles from battery Park to the Jersey shore how much of the time was city driving if she needs about 1.2 hours on the turnpike
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Please help with homework (it's not 40 or 60) also please say how to work out if you can
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Suppose w=xy+yz, where x=e2t, y=2+sin(4t), and z=2+cos(7t).
a. use the chain rule to find dwdt as a function of x, y, z, and t. do not rewrite x, y, and z in terms of t, and do not rewrite e2t as x.
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i.e
dx/dt = 2e^2t
dy/dt= 4cos 4t
dZ/dt = -7sin 7t
now
from
W=xy+yz
dw/dx = y ( by partial differentiation)
dw/dy= x+z
dw/dz= y
now Dw/dt = ⅓{ (dx/dt×dw/dx) + (dy/dt×dw/dy)+(dz/dt×dw/dz)
dw/dt = ⅓{ (2e^2t×y) + (4cos4t×(x+z) + (-7sin7t×y)}
= ⅓{ 2ye^2t + 4(x+z)Cos4t - 7ySin7t}
pheww
that should help...
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).
6× 532 expanded form
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There are five shelves of video games in a video store. There are six video games on each shel. how many video games are there on the shelves?
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Answer:
I think its 30 as well
Step-by-step explanation:
solve the equationX=15/x+1/4
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Answer:
x = -3.75 or 4
Step-by-step explanation:
Multiply by 4x and solve the resulting quadratic in any of the usual ways.
... 4x² = 60 +x
... 4x² -x -60 = 0 . . . . . . . . . . . subtract 60+x
... (x -4)(4x +15) = 0 . . . . . . . . .factor the equation
... x = 4 . . . or . . . -15/4 . . . . . . the values that make the factors zero
_____
Comment on the graph
It is convenient to use a graphing calculator to find the zeros of a function, so it works well to rewrite the equation to be something that is equal to zero. Here, we've subtracted the right side, so we have ...
... f(x) = x - (15/x +1/4) = 0
How do I solve 9a-7=110
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Please add 7 to both sides of the eqn, obtaining 9a = 117.
Solve for a by dividing both sides by 9: a = 117/9 = 13 (answer)
[tex]9a=110+7 [/tex]
[tex]9a=117 [/tex]
[tex]a= \dfrac{117}{9} [/tex]
[tex]a=13[/tex]
What must the distance be between charges of +2.35 and −1.96 for the attractive force between them to be the same as that between charges of +4.06 and −2.11 separated by a distance of 2.26 pm?
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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.
Explanation: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)))
find the missing value in the ratio table .
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5 x 3 = 15, therefore, 3 x 3 = 9
because you multiplied 3 for 5, you will be doing the same for 3, which means 3 x 3
hope this helps
3/5 = 9/15 = 12/20...so ur missing number is 9
Find the linear equation of the plane through the point (2,4,9) and parallel to the plane x+4 y+5 z+4 =0.
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Which equation shows how (-10, 8) can be used to write the equation of this line in point-slope form?
subtract the fractions and simplify the answer 7 8/9-5 3/5
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To subtract 3/5 from 8/9, you'd need to find the lowest common denominator (LCD) of 3/5 and 8/9, convert both fractions to have this LCD, and then subtract.
The LCD is (5)(9)=45. Then 8/9 and 3/5 become 40/45 and 27/45.
Subtracting 27/45 from 40/45 results in the fraction 13/45.
Then the full solution is 2 13/45.
You could also do this problem by converting 7 8/9 and 5 3/5 into improper fractions:
71/9 - 28/5. Again, the LCD is 45. Can you rewrite both fractions with 45 as the common denominator and then perform the subtraction?
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.
Explanation: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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How many 5-digit numbers (including leading 0s) are there with no digit appearing exactly two times?
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30240 are 5-digit numbers (including leading 0s) are there with no digit appearing exactly two times
What is Number system?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 carpenter uses 65 shelves to make 13 bookcases. she uses the same number of shelves for each bookcase. are 32 shelves enough to build 6 more shelves?
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65 ÷ 13 = 5
Now we know, it takes 5 shelves to build a single bookcase. The next step would be to find out how many shelves it would take to build 6 more bookcases. To find the answer, you would multiply the number of shelves it takes to build 1 bookcase by the number of bookcases that need to be built.
5 x 6 = 30
So, yes, 32 shelves would be more than enough to build 6 more bookcases.
I hope this helps!
Franks quarter grades are 82.5, 94.7, and 87.9 what grade rounded to the nearest percent will frank need to recieve at least a an 89 % final course grade A.92% B.90% C.91% D.89% please show work
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Frank would have to get a 92% on his final course grade in order to get above an 89%.
The probability that Jinelle’s bus is on time is 2/3 , and the probability that Mr. Corney is driving the bus is 4/5. What is the probability that on any given day Jinelle’s bus is on time and Mr. Corney is the driver?
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The probability that on any given day Jinelle’s bus is on time and Mr. Corney is the driver is (8/15).
What is probability?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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A total of 14000 votes were cast to two opposing candidates. Adam and Karl.Adam won by ratio of 4:3 how many votes were cast to karl?
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The number of votes cast to Karl is
[tex]6000[/tex]
EXPLANATION
The total votes cast is
[tex]14000[/tex]
We were given that Adam and Karl won by ratio of
[tex]4:3[/tex]
This means the number of votes cast to Adam corresponds to 4, while that of Karl corresponds to 3.
The total ratio is
[tex] = 4 + 3 = 7[/tex]
Number of votes cast to Karl is
[tex] = \frac{Karl's\:ratio}{Total\:ratio} \times Total\:votes \:cast[/tex]
[tex] = \frac{3}{7} \times 14000[/tex]
This simplifies to,
[tex] = 3 \times 2000[/tex]
[tex] = 6000[/tex]
Therefore 6000 votes were cast in favour of Karl.
If the food is good or if I eat too much, I'll exercise. How do you write this compound statement in symbols.
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Y=the food is yummy
O=overeat
E=exercise
Note:
∪ = or
-> if ... then
(Y∪O)->E
A book has a front and a back and 400 pages. The front and back cover are each 0.9mm thick measured to 1 decimal place. Each page is 0.13 mm thick measured to 2 decimal places. Calculate the minimum thickness of the book.
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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.
The last wednesday in a certain month is on the 26th day of that month. What day of the week is the first day of that month?
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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.
Explanation: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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80 miles per hour is how many feet per minute?
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[tex]\bf \cfrac{80~\underline{mile}}{\underline{hr}}\cdot \cfrac{5280~feet}{\underline{mile}}\cdot \cfrac{\underline{hr}}{60~min}\implies \cfrac{80\cdot 5280~feet}{60~min}\implies \cfrac{422400~feet}{60~min} \\\\\\ 7040\frac{feet}{min}[/tex]
is 30 x 10 to the 3rd power equal 30000
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Yes,[tex]\(30 \times 10^3\)[/tex] is equal to 30,000.
When we have a number written in scientific notation, such as [tex]\(10^3\),[/tex] it means we are multiplying the base (which is 10 in this case) by itself a certain number of times, indicated by the exponent (which is 3 in this case).
So, [tex]\(10^3\)[/tex] means [tex]\(10 \times 10 \times 10\)[/tex], which equals 1,000.
Therefore, when we multiply 30 by [tex]\(10^3\)[/tex], it's equivalent to multiplying 30 by 1,000, which results in 30,000.
What age was the mean of all the guesses (rounded to the nearest whole number)? 57 59 63 68 74?
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To get this, you just have to add all the numbers up, and then divide your answer by the amount of numbers you added (just for future reference in problems like these!). To round to the nearest whole number, you look at the decimal: .2. It's closer to 0 than it is to 10, so the 64.2 would round down to 64.
I hope this helps!
An investment firm recommends that a client invest in bonds rated AAA, A, and B. The average yield on AAA bonds is 4%, on A bonds 6%, and on B bonds 11%. The client wants to invest twice as much in AAA bonds as in B bonds. How much should be invested in each type of bond under the following conditions?
A. The total investment is $26,000, and the investor wants an annual return of $1,620 on the three investments.
B. The values in part A are changed to $38,000 and $2,360, respectively
A. The client should invest $(?) in AAA bonds, $(?)in A bonds, and $(?)in B bonds.
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1) Variables:
X: amount invested in AAA bonds
Y: amount invested in A bonds
Z: amount invested in B bonds.
2) Return:
4%* X + 6% * Y + 11% * Z = 1620
3) Investment:
X + Y + Z = 26,000
4) Ratio between AAA and B bonds.
X = 2*Z
5) Solution of the system of equations:
Replace X with 2Z in the two first equations:
2Z * 4% + Y * 6% + Z * 11% = 1620
=> 0.08Z + 0.06Y + 0.11Z = 1620
=> 0.19Z + 0.06Y = 1620
2Z + Y + Z = 26,000
=> 3Z + Y = 26,000 => Y = 26,000 - 3Z
Replace Y with 26,000 - 3Z
0.19Z + 0.06(26,000 - 3Z) = 1620
0.19Z + 1560 - 0.18Z = 1620
0.01Z = 1620 - 1560
0.01Z = 60
Z = 60 / 0.01 = 6000
=> X = 2*6000 = 12,000
=> Y = 26,000 - 12,000 - 6,000 = 8,000
Answer: 12,000 in bonds AAA, 8,000 in bonds A, and 6000 in bonds B.
Part B.
2) Return:
0.04X + 0.06 Y + 0.11Z = 2360
3) Investment:
X + Y + Z = 38,000
4) Ratio between AAA and B bonds.
X = 2Z
5) Solution of the system of equations:
Replace X with 2Z in the two first equations:
=> 0.08Z + 0.06Y + 0.11Z = 2360
=> 0.19Z + 0.06Y = 2360
2Z + Y + Z = 38,000
=> 3Z + Y = 38,000 => Y = 38,000 - 3Z
Replace Y with 38,000 - 3Z
0.19Z + 0.06(38,000 - 3Z) = 2360
0.19Z + 2280 - 0.18Z = 2360
0.01Z = 2360 - 2280
0.01Z = 80
Z = 80 / 0.01 = 8000
=> X = 2*8000 = 16,000
=> Y = 38,000 - 16,000 - 8000 = 14,000
Answer: 16,000 in AAA bonds, 14,000 in A bonds, and 8,000 in B bonds.
Manuel stores his favorite CDs in a box like the one shown
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round 7300 correct to one significant figure.
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Any zero that isnt trapped between two non-zero numbers (on the left side of the decimal) is insignificant, therefore the 3 rounds down. hope this helped!
Significant figure means you should have x amounts of numbers that aren't zero.
In this case you are required to have one number that isn't a zero.
Therefore you round down to give you 7000 as your final answer.
To get a better idea follow through the rest:
E.g Round 64, 492 to two significant figures.
This means you'd have two numbers that aren't a zero.
So you're final answer would have been 64000.
Hope This Helps You!
Good Luck :)
- Hannah ❤
What is the greatest perfect square that is a factor of 396? Explain
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Factors of 396 are: 1,2,3,4,6,9,11,12,18,22,33,36,44,66,99,132,198,396
Now we check which is the greatest perfect square in these.
396, 198, 132, 99, 66,44 are not perfect square,
so 36 is the largest perfect square from the factors of 396, 6 x 6 = 6² = 36
In the 30-60-90 triangle below side s has a length of ___ and the hypotenuse has a length of
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so, h^2 = s^2 + 1
However, if we have two sides of the same length, we should have a isosceles triangle, meaning that two of the angles are the same. However, this is not the case here.
the only possible answer is , s = sqrt(3) and h = 2
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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Lenox ironed 1/4 of the shirts over the weekend. She plans to split the remainder of the work equally over the next 5 evenings.
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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
What is the value of k? 0.5k+6=4k-8
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6+8=4k-.5k
14=3.5k
So K=4
Jackie's watch loses two minutes every hour. Adam's watch gains one minute every hour. They both set their watches at the radio at 6:00 am, then start their journey to the airport. When they arrive (at the same time) their watches are twelve minutes apart. What is the real time they arrive at the airport?
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Let the number of hour ellapsed at the time they are twelve minutes apart be x, then
2x + x = 12
⇒ 3x = 12
⇒ x = 12 / 3 = 4
Thus, after 4 hours Jackie's watch has lost 8 minutes and Adam's watch has gained 4 minutes.
Therefore, the real time at the time they arrive at the airport is 10:00 am.
Find the x-intercept of the graph of the equation: x + 6y = 7
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x + 6(0) = 7
x + 0 = 7
x = 7
so x intercept is (7,0)