a baker has 27 wheat bagels and 36 plain bagels that will be divided into boxes. Each box must have the same number of wheat bagels and the same number of plain bagels. What is the greatest number of boxs the baker can make using all of the bagels?
What is 8.675 as a mixed number in simplified formation
Et f(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 5)j + zk. find the flux of f across s, the part of the paraboloid x2 + y2 + z = 11 that lies above the plane z = 2 and is oriented upward.
The flux of [tex]\vec f(x,y,z)[/tex] across S is given by the surface integral
[tex]\displaystyle \iint_S \vec f(x,y,z) \cdot d\vec s[/tex]
Join to S the disk D of radius 3 in the plane z = 2, for which we have
[tex]x^2+y^2+2=11 \implies x^2+y^2=9=3^2[/tex]
Let S' = S U D (the union of S and D). Since S' is closed, we can use divergence theorem to compute the flux of [tex]\vec f[/tex] through S' :
[tex]\displaystyle \iint_{S'} \vec f \cdot \vec s = \iiint_R \mathrm{div}\vec f \, dV[/tex]
Compute the divergence of [tex]\vec f[/tex] :
[tex]\mathrm{div}\vec f = \dfrac{\partial\left(z\tan^{-1}(y^2)\right)}{\partial x} + \dfrac{\partial\left(z^3\ln(x^2+5)\right)}{\partial y} + \dfrac{\partial(z)}{\partial z} = 1[/tex]
Compute the volume integral by converting to cylindrical coordinates. Take
[tex]\begin{cases}x=r\cos(\theta) \\ y = r\sin(\theta) \\ z = \zeta \\ dV = dx\,dy\,dz = r\,dr\,d\theta\,d\zeta\end{cases}[/tex]
Then the flux of [tex]\vec f[/tex] across S' is
[tex]\displaystyle \iint_{S'} \vec f \cdot \vec s = \int_{-3}^3 \int_{-\sqrt{9-x^2}}^{\sqrt{9-x^2}} \int_2^{11-x^2-y^2} dV = \int_0^{2\pi} \int_0^3 \int_2^{11-r^2} r \, d\zeta \, dr \, d\theta = \frac{81\pi}2[/tex]
To get the flux across S alone, we subtract from this integral the flux of [tex]\vec f[/tex] across D.
Parameterize D by the vector function
[tex]\vec\sigma(\rho,\phi) = \rho \cos(\phi) \, \vec\imath + \rho \sin(\phi) \, \vec\jmath + 2\, \vec k[/tex]
with [tex]0\le\rho\le3[/tex] and [tex]0\le\phi\le2\pi[/tex].
Get the downward-pointing normal vector to D :
[tex]\vec n = \dfrac{\partial\vec\sigma}{\partial\phi} \times \dfrac{\partial\vec\sigma}{\partial \rho} = -\rho\,\vec k[/tex]
Compute the flux across D :
[tex]\displaystyle \iint_D \vec f\cdot d\vec s = \int_0^{2\pi} \int_0^3 \vec f(\vec\sigma) \cdot \vec n \, d\rho\,d\phi = \int_0^{2\pi} \int_0^3 (-2\rho) \, d\rho \, d\phi = -18\pi[/tex]
So the flux of [tex]\vec f[/tex] across S is
[tex]\displaystyle \iint_S \vec f \cdot d \vec s = \frac{81\pi}2 - (-18\pi) = \boxed{\frac{117\pi}2}[/tex]
To find the flux of f across the part of the paraboloid that lies above the plane z = 2 and is oriented upward, we can use the formula for flux and evaluate the integral.
Explanation:To find the flux of f across the part of the paraboloid that lies above the plane z = 2 and is oriented upward, we can use the formula for flux: flux = ∫∫(f•n)dA. Here, f(x,y,z) = z tan⁻¹(y²)i + z³ ln(x² + 5)j + zk.
The equation of the paraboloid is x² + y² + z = 11. Using these equations, we can set up the double integral and solve for the flux.
After evaluating the integral, we can find the flux of f across the given surface.
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"write the expression in radical form and then evaluate"
A total of $2100 for a house painting job is to be divided between two painters in the ratio of 3 to 4. How much does each painter receive?
How many years would it take Jim to earn interest equal to half of his original principal at 10% simple interest?
A. 6 months
B. 12 months
C. 5 years
D. 10 Years
Jim would need 5 years to earn interest equal to half of his original principal at a 10% simple interest rate.
To find out how many years it would take for Jim to earn interest equal to half of his original principal at a 10% simple interest rate, we use the formula for simple interest: I = PRT, where I is the interest, P is the principal, R is the rate of interest per year, and T is the time in years.
In this case, Jim wants the interest I to be half of the principal P. So the equation becomes :
[tex]\frac{P}{2} = P \times 0.10 \times T[/tex] or T
= [tex]\frac{P}{2 \times P \times 0.10}[/tex], which simplifies to T =[tex]\frac{1}{2 \times 0.10}[/tex]or T = 5 years. Therefore, the correct answer is C. 5 years.
The lengths of the legs of a right triangle are 3 cm and 4 cm. What is the length of the hypotenuse?
To find the length of the hypotenuse of a right triangle with legs measuring 3 cm and 4 cm, use the Pythagorean theorem formula c = √(a² + b²). Plugging in the values gives c = √(9 + 16), which results in a hypotenuse of 5 cm.
The student is asking how to find the length of the hypotenuse of a right triangle when the lengths of the other two sides are given. In this case, the legs of the triangle are 3 cm and 4 cm long. To find the hypotenuse, we use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). This can be expressed as a formula: a² + b² = c². Solving for c, we can find the hypotenuse by taking the square root of the sum of the squares of the other two sides:
c = √(a² + b²)
Plugging in the values for a and b:
c = √(3 cm)² + (4 cm)²
c = √(9 cm² + 16 cm²)
c = √25 cm²
c = 5 cm
Therefore, the length of the hypotenuse is 5 cm.
Me Ramirez bought 1/4 pounds of cashews. He divided the cashews equally among his 3 children. How much did each child get?
M(6, 6) is the midpoint of . The coordinates of S are (8, 9). What are the coordinates of R?
A dentist is making identical dental care bags for patients using 56 tubes of toothpaste, 112 packets of floss, and 85 toothbrushes. What is the greatest number of identical dental care bags the dentist can make with the least amount of items leftover
Answer: There would be 56 tubes, 112 packets and 85 toothbrushes in the dental care bags.
Step-by-step explanation:
Since we have given that
Number of tubes of toothpaste = 56
Number of packets of floss = 112
Number of toothbrushes = 85
We need to find the greatest number of identical dental care bags that dentist can make with the least amount of items leftover.
So, we will find "H.C.F." of 56, 112, 85 which is equal to 1.
So, there would be 56 tubes, 112 packets and 85 toothbrushes in the dental care bags.
what is the difference? 5/3-1/2
A. 4
B. 7
C. 7/6
D. 7/0 = undefined
four-fifths of a number minus two is greater than three-tenths of twice that number
Andrew make six dollars an hour +9 dollars an hour for every hour of overtime overtime hours are any hours more than 40 hours for the week. Create an equation that shows the amount of wages earned S for working why hours of overtime. Can’t remember to include in the equation the amount earned from working 40 hours
Suppose that there were a strong correlation between the variables g and h. Which of these is a true statement?
a. g must cause h
b. g must not cause h
c. g may cause h
d. h must cause g
Answer: c. g may cause h
Step-by-step explanation:
Correlation: It represents the relation between any two or more than two variable.
Causation: It is a kind of correlation where one variable if affected by the other variable.
Therefore , Causation implies correlation.
But correlation does not imply causation.
Hence, if there were a strong correlation between the variables g and h, then g may cause h.
What is 3.313 Rounded to the nearest tenth
If a bolt of fabric measuring 20 yards 8 inches is divided into 26 equal sections how long is each section
F the experimental value for the percentage of o is 37%, the accepted value of the percentage of oxygen is 40%, what is the percentage error in the experiment?
One safe investment pays 10% per year, and a more risky investment pays 18% per year. A woman who has $139,700 to invest would like to have an income of $18,930 per year from her investments. How much should she invest at each rate?
To achieve an annual income of $18,930, the woman should invest $77,700 at the 10% rate and $62,000 at the 18% rate.
To determine how much a woman should invest at each rate to achieve an income of $18,930 per year, we can set up a system of linear equations. Assuming she invests x dollars at the 10% rate and y dollars at the 18% rate, we can use the following equations:
x + y = $139,700: This equation represents the total amount of money she has to invest.
0.10x + 0.18y = $18,930: This equation represents the annual income from the investments.
To solve:
Multiply the first equation by 0.10:
0.10x + 0.10y = $13,970
Subtract this from the second equation:
0.18y - 0.10y = $18,930 - $13,970
0.08y = $4,960
Divide by 0.08 to find y:
y = $62,000
Substitute y back into the first equation to find x:
x + $62,000 = $139,700
x = $77,700
Therefore, the woman should invest $77,700 at the 10% rate and $62,000 at the 18% rate to achieve her desired income.
In science class, Savannah measures the temperature of a liquid to be 34 ∘ 34∘ Celsius. Her teacher wants her to convert the temperature to degrees Fahrenheit. What is the temperature of Savannah's liquid to the nearest degree Fahrenheit?
Answer:
The temperature of Savannah's liquid to the nearest degree Fahrenheit is 93.1°.
Step-by-step explanation:
Given : In science class, Savannah measures the temperature of a liquid to be 34° Celsius. Her teacher wants her to convert the temperature to degrees Fahrenheit.
To find : What is the temperature of Savannah's liquid to the nearest degree Fahrenheit?
Solution :
The general formula to convert Celsius into Fahrenheit is
[tex]F = (C\times \frac{9}{5}) + 32[/tex]
Substitute C=34°,
[tex]F = (34\times \frac{9}{5}) + 32[/tex]
[tex]F = (34\times 1.8) + 32[/tex]
[tex]F = 61.2+ 32[/tex]
[tex]F =93.1[/tex]
Therefore, The temperature of Savannah's liquid to the nearest degree Fahrenheit is 93.1°.
Which expression is equivalent to 10x2y + 25x2? 5x2(2y + 5) 5x2y(5 + 20y) 10xy(x + 15y) 10x2(y + 25)
we have
[tex]10x^{2}y+ 25x^{2}[/tex]
we know that
[tex]10=2*5\\25=5*5[/tex]
substitute
[tex](2*5)x^{2}y+ (5*5)x^{2}[/tex]
Factor [tex]5x^{2}[/tex]
[tex](5x^{2})(2y+ 5)[/tex]
therefore
the answer is
[tex](5x^{2})(2y+ 5)[/tex]
The equivalent expression of 10x^2y + 25x^2 is 5x^2(2y + 5)
What are equivalent expressions?Equivalent expressions are expressions that have equal values
The expression is given as:
10x^2y + 25x^2
Factor out 5x^2 from the expression
5x^2(2y + 5)
Hence, the equivalent expression of 10x^2y + 25x^2 is 5x^2(2y + 5)
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There are three more apple trees than pear trees in the yard. Altogether there are 35 trees. How many apple trees and how many pear trees are there?
35-3 =32
32/2 = 16
there are 16 pear trees and 19 apple trees
Consider the graph of Cx + Ay = B where A, B, and C are all positive constants. Find the coordinates of the x-intercept.
The coordinates of the x-intercept are (B/C,0)
What is the x-intercept of a graph?The x-intercept of a graph is defined as the places where the graph crosses the x-axis or the locations where the coordinate of the y-axis equals 0, which are known as the x-intercept of a graph.
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
Consider the graph of Cx + Ay = B
Here A, B, and C are all positive constants.
To determine the coordinates of the x-intercept
⇒ Cx + Ay = B,
Substitute the value of y = 0 and solve for x
⇒ Cx + A(0) = B,
⇒ Cx = B,
Divide both sides by C
⇒ x = B/C
Hence, the coordinates of the x-intercept are (B/C,0).
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Sue has $2.10 in dimes and nickels. If she has 12 more dimes than nickels, how many of each coin does she have?
A determine the center of gravity location for the destinations and shipping quantities shown below: destination (x,y) quantity d1 3,5 600 d2 5,1 400 d3 6.7 300 d4 8.4 500
Find the reciprocal of 1 1/11. Find the reciprocal of 11/12.
An elevator steadily descends 500 feet in 20 seconds. How would you express the change in the elevator's height per second? The change in the elevator's height per second is____ nothing feet per second.
Answer:
The elevators descends at the rate of 25 feet per second or we can write the change in height of elevator is -25 feet per second, since the elevator is moving in opposite direction.
Step-by-step explanation:
We are given the following information in the question:
The elevator descends 500 feet in 20 seconds.
Now, we know that at 0 second the lift was at 0 feet.
To calculate the change in the height of elevator per second, we use the following formula:
[tex]\text{Change in height per second} = \displaystyle\frac{y_2-y_1}{x_2-x_1}\\\\= \displaystyle\frac{500-0}{20-0} = \frac{500}{20} = 25\text{ feet per second}[/tex]
Hence, the elevators descends at the rate of 25 feet per second or we can write the change in height of elevator is -25 feet per second, since the elevator is moving in opposite direction.
The change in the elevator's height per second is -25 feet per second. This is calculated by dividing the total descent (500 ft) by the time taken (20 s). The negative value indicates a descent.
Explanation:To determine the change in an object's height per second, we can use the formula for velocity, which is the displacement (change in position) divided by the time. In this case, the elevator descends 500 feet in 20 seconds. Therefore, the change in the elevator's height per second is 500 feet divided by 20 seconds.
The change in the elevator's height per second is -25 feet per second
The negative sign indicates that the elevator is descending, as opposed to ascending. It's important to note that this is an average rate of change because the question doesn't specify that the elevator's speed is constant.
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Barry’s Bagel Emporium sells a dozen bagels for $5.00. This price is no longer high enough to create a profit. The owner decides to raise the price. He does not want to alarm his customers with too large of an increase. He is considering four different plans. Plan A: Raise the price by $0.05 each week until the price reaches $8.00. Plan B: Raise the price by 10 percent each week until the price reaches $8.00. Plan C: Raise the price by the same amount each week for 6 weeks, so that in the sixth week the price is $8.00. Plan D: Raise the price by $0.25 each week until the price reaches $8.00. Which plan will result in the price of the bagels reaching $8.00 fastest? plan A plan B plan C plan D
Answer:
Plan B
Step-by-step explanation:
Plan B and plan C start out at the same increase: 10% ($0.50) for the first week. The increase under plan C stays at 10% of the original value, but the increase under plan B increases according to the value the week before, which keeps getting larger.
Hence, plan B gets to $8.00 the fastest — after about 5 weeks.
Find the price of a $35 basketball that is on sale for 50% off the regular price.
The price of the basketball on sale is $17.50.
To calculate this:
1. Calculate 50% of $35:
$35 x 0.50 = $17.50
2. Subtract the discount from the original price:
$35 - $17.50 = $17.50
When an item is on sale for a percentage off, you first find what that percentage represents of the original price. In this case, 50% of $35 is $17.50. Then, you subtract that amount from the original price to find the sale price. So, the basketball, originally priced at $35, would be $17.50 when it's on sale for 50% off.
Complete question:
Find the price of a $35 basketball that is on sale for 50% off the regular price.
What is 5 to the 0.75 power?
The answer is [tex]\( 5^{0.75} = 5^{\frac{3}{4}} = \sqrt[4]{5^3} \)[/tex].
To solve[tex]\( 5^{0.75} \)[/tex], we first express 0.75 as a fraction in its simplest form. The number 0.75 is equivalent to [tex]\( \frac{3}{4} \)[/tex]. Therefore, [tex]\( 5^{0.75} \)[/tex] can be rewritten as [tex]\( 5^{\frac{3}{4}} \)[/tex].
Now, we can break down [tex]\( 5^{\frac{3}{4}} \)[/tex] using the properties of exponents. The exponent [tex]\( \frac{3}{4} \)[/tex] indicates that we are looking for the fourth root of 5 raised to the power of 3. Mathematically, this is expressed as [tex]\( \sqrt[4]{5^3} \)[/tex].
To find the value, we first calculate [tex]\( 5^3 \)[/tex], which is [tex]\( 5 \times 5 \times 5 = 125 \)[/tex]. Then we take the fourth root of 125. The fourth root of a number is the number that, when raised to the power of 4, gives the original number. In this case, we are looking for a number that, when raised to the power of 4, equals 125.
The fourth root of 125 is not an integer, but we can approximate it. We know that [tex]\( 2^4 = 16 \)[/tex]and [tex]\( 3^4 = 81 \)[/tex], so the fourth root of 125 must be between 2 and 3. Through calculation or using a calculator, we find that [tex]\( \sqrt[4]{125} \)[/tex] is approximately 3.3019.
Therefore, [tex]\( 5^{0.75} \)[/tex] is approximately 3.3019.
Pam read 126 pages of her summer reading book in 3 hours. Zack read 180 pages of his summer reading book in 4 hours. If they continue to read at the same speeds, will they both finish the 215 page book after 5 total hours of reading?
Answer:
Zack can finish the 215 page book after 5 total hours of reading but Pam cannot.
Step-by-step explanation:
Pam read 126 pages of her summer reading book in 3 hours.
[tex]\texttt{Speed of Pam =}\frac{126}{3}=42page/hour[/tex]
Zack read 180 pages of his summer reading book in 4 hours. [tex]\texttt{Speed of Zack =}\frac{180}{4}=45page/hour[/tex]
Number of pages Pam read in 5 hours = 5 x 42 = 210 pages
Number of pages Zack read in 5 hours = 5 x 45 = 225 pages
We need to find will they both finish the 215 page book after 5 total hours of reading,
Here number of pages read by Zack is greater than 215 and number of pages read by Pam is less than 215.
So Zack can finish the 215 page book after 5 total hours of reading but Pam cannot.