Answer:
Step-by-step explanation:c
If an equation, Y varies directly as X varies. If Y equals 208 when X equals 13, what is the value of X when Y equals -144?
Answer: X = -9
Step-by-step explanation:
You can set up a ratio to solve this.
208/13 = -144/x
208x=-1872
x = -9
\(\mathbb{ANSWER:}\)
Step 1: Write the equation of variation
\(\sf y \propto x\)\(\sf y = kx\)Step 2: Solve for k or the constant of proportionality
\(\sf 208 = k(13)\)\(\sf \frac{208}{13} = \frac{k(13)}{13}\)\(\sf k = 16\)Step 3: Solve for x
\(\sf -144 = 16x\)\(\sf \frac{-144}{16} = \frac{16x}{16}\)\(\sf x = \boxed{\sf -9}\)find the volume of the solid generated by revolving the region bounded above by y = 16 cos x and below by y - 3 sec x, about the x-axis.
The volume of the solid generated by revolving the region bounded above by y = 16 cos(x) and below by y - 3 sec(x) about the x-axis can be found by using the method of cylindrical shells. The volume of the solid is approximately 89.9 cubic units.
To find the volume of the solid, we can integrate the cross-sectional area of the infinitesimally thin cylindrical shells that make up the solid.
The cross-sectional area of a cylindrical shell can be approximated by multiplying the circumference of the shell by its height. In this case, the circumference is given by 2πx (since we are revolving around the x-axis), and the height is given by the difference between the upper and lower functions: 16 cos(x) - (3 sec(x)).
Therefore, the differential volume of each cylindrical shell is given by:
dV = 2πx(16 cos(x) - (3 sec(x))) dx
To find the total volume, we integrate this expression over the appropriate interval. Since the region is bounded by the given functions, we integrate with respect to x from the point where the two functions intersect to the point where they intersect again. The intersection points can be found by setting the two functions equal to each other and solving for x.
After performing the integration, we find that the volume of the solid is approximately 89.9 cubic units.
It's worth noting that the integral in this case may be difficult to evaluate analytically and may require numerical methods or software to obtain an approximate solution.
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Example 4 A closed box has a fixed surface area A and a square base with side x. (a) Find a formula for the volume, V. of the box as a function of x. What is the domain of V? (b) Graph V as a function of x. (c) Find the maximum value of V.
use the work in example 4 in this section of the textbook to find a formula for the volume of a box having surface area 10.
The volume of the box with surface area 10 is given by the formula V = 2.5x^2 - 0.25x^4, where x is the length of a side of the square base.
To find a formula for the volume of the box with surface area A and square base with side x, we first need to find the height of the box. Since the box has a square base, the area of the base is x^2. The remaining surface area is the sum of the areas of the four sides, each of which is a rectangle with base x and height h. Therefore, the surface area A is given by:
A = x^2 + 4xh
Solving for h, we get:
h = (A - x^2) / 4x
The volume V of the box is given by:
V = x^2 * h
Substituting the expression for h, we get:
V = x^2 * (A - x^2) / 4x
Simplifying, we get:
V = (Ax^2 - x^4) / 4
The domain of V is all non-negative real numbers, since both x^2 and A are non-negative.
To graph V as a function of x, we can use a graphing calculator or plot points using a table of values. The graph will be a parabola opening downwards, with x-intercepts at 0 and sqrt(A) and a maximum at x = sqrt(A) / sqrt(2).
To find the maximum value of V, we can take the derivative of V with respect to x and set it equal to 0:
dV/dx = (2Ax - 4x^3) / 4
Setting this equal to 0 and solving for x, we get:
x = sqrt(A) / sqrt(2)
Plugging this value of x into the formula for V, we get:
V = A^1.5 / (4sqrt(2))
Therefore, the maximum value of V is A^1.5 / (4sqrt(2)).
To find the formula for the volume of a box having surface area 10, we simply replace A with 10 in the formula we derived earlier:
V = (10x^2 - x^4) / 4
Simplifying, we get:
V = 2.5x^2 - 0.25x^4
Therefore, the volume of the box with surface area 10 is given by the formula V = 2.5x^2 - 0.25x^4, where x is the length of a side of the square base. The domain of V is all non-negative real numbers.
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Ms. Sze is grading math tests. A student’s work on a problem is given
below
Answer:
No the student is not correct because the answer is 0.4761. All the student did was wrong was the adding up the zeros.
Step-by-step explanation:
Given the ordered pair, (1,1/2) what is the constant of proportionality
The constant of proportionality is y divided x so in this case will be:
\(\frac{\frac{1}{2}}{1}=\frac{1}{2}\)What is the slope of the line passing through the points
A(-4,-3) and B (-5, -6)?
-11/3
1/3
1
════════ ∘◦❁◦∘ ════════
Answer = 1════════════════════
Knownx1 = (-4)
y1 = (-3)
x2 = (-5)
y2 = (-6)
════════════════════
Questionslope = gradient (m)
════════════════════
Way to do\(m = \frac{y2 - y1}{x2 - x1} = \frac{( - 6) - ( - 4)}{( - 5) - ( - 3)} = \frac{( - 2)}{( - 2)} = 1 \)
════════════════════
Write an expression equivalent to
4 - (-7)
help
Answer:
7 - (-4)
Step-by-step explanation:
You can turn the numbers.
if 2p°and ( p+15)are a pair of complementary angles find them.
Answer:
angles r 50°&40°
Step-by-step explanation:
2p+p+15=90°3p=90°-15°3p=75°p=75°/3p=25°2p=2×25=50°
p+15=25+15=40°
stay safe healthy and happy.41- 3/4 x < 53
please help!
Answer:
x > - 16
Step-by-step explanation:
41- 3/4 x < 53
Subtract 41 from each side
41-41- 3/4 x < 53-41
-3/4x < 12
Multiply each side by -4/3, remembering to flip the inequality
-4/3 * -3/4x > 12 * -4/3
x > - 16
Administering wages and salaries
The values in the columns which completes the table for the COLA salary adjustments are as follows;
\(\begin{tabular}{|c|c|c|c|} \cline{1-4}&Amount & Amount&New Salary\\ \cline{1-4}1& \$1,672&\$1,584&\$47,256 \\ \cline{1-4} 2 & \$1,312&\$3,116&\$45,428 \\ \cline{1-4}3&\$1,483&\$1,425&\$34,408 \\ \cline{1-4}\end{tabular}\)
4. The COLA Increase and New Salaries are presented as follows;
\(\begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} & J. Spar&T. Beggins & R. Stokes &D. Garcia& J. Stiles\\ \cline{1-6}COLA Increase & 6.5\%&6.5\%&6.3\%&7.5\%&6.3\% \\ \cline{1-6} New Salary & \$20,430&\$23,925&\$35,480.04&\$15,792.3&\$31,385.64 \\ \cline{1-6} \end{tabular}\)
5. Ron Fortini's weekly salary prior to the increase was about $899.12
What is a COLA?
COLA is an acronym for Cost-Of-Living-Adjustment, which is an increase in salary or income to keep pace with the current inflation rate or trend and increased societal cost of living.
The amount C. North received based on COLA is; $44,000 × 2.80% = $1,232
The amount received as merit is; $44,000 × 3.60% = $1,584
The New Salary amount = $1,232 + $1,584 + $44,000 = $47,256
The amount N. Vanders received as COLA is; $41,000 × 3.20% = $1,312
The amount received as merit is; $41,000 × 7.60% = $3,116
The New Salary is; $41,000 + $1,312 + $3,116 = $45,428
The amount M. Clark received as COLA is; $31,500 × 4.70% = $1,480.5
The amount M. Clark received as merit is; $31,500 × 4.50% = $1,417.5
M. Clark's New Salary is; $31,500 + $1,480.5 + $1,417.5 = $34,397
Please find above the completed columns that complete the questions 1, 2, and 3 above.
4. The COLA received based on the sliding scale for the cost-of-living adjustment are;
J. Spar; 6.5%
T. Beggins; 6.5%
R. Stokes; 6.3%
D. Garcia; 7.5%
J. Stiles; 6.3%
The New Salaries based on the total increase are;
\({}\) New Salary
J. Spar; $18,000 + $18,000 × 12.50% = $20250
T. Beggins; $21,750 + $21,750 × 10.00% = $23,925
R. Stokes; $31,860 + $31,860 × 11.4% = $35,492.04
D. Garcia; $14,615 + $14,615 × 8.20% = $15,813.43
J. Stites; $27,916 + $27,916 × 12.525% = $31,412.479
Please find included the completed rows for the COLA Increase and the New Salary above
5. Let x represents Ron Fortini's prior weekly salary
Ron Fortini's weekly salary after 5.20% merit increase and 2.75% cost-of-living increase, Ron Fortini's new salary is $968.80
Therefore;
New weekly salary = Prior weekly salary + (Prior weekly salary × (5.20% + 2.75%))
$968.80 = x + x × 0.0775 = 1.0775·x
1.0775·x = $968.80
x = $968.80/1.0775 ≈ $899.12
Therefore, Ron Fortini's weekly salary prior to the increases was $899.12
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What is the measure of angle KMH?
G
84°
M 4x
K
H
Your answer
A net of a triangular prism is shown below.
What is the surface area, in square feet, of the triangular prism
A.44
B.96
C.108
D.120
Answer:
Step-by-step explanation:
broski do length x height
Length x Width
height x width
and then multiply each product by 2 becue of 2 sides then add
Answer: C: 108 feet squared
Step-by-step explanation:
To figure out surface area, you must find the area of all sides and then add them.
The area of the top rectangle is 24 feet squared.
8x3=24
The area of the second rectangle is 32 feet squared.
8x4=32
The area of the third rectangle is 40 feet squared.
5x8=40
The area of the triangle to the left is 6 feet squared.
3x4=12
12/2=6
The area of the triangle to the right is 6 feet squared.
3x4=12
12/2=6
Add them all up: 6+6+40+24+32=108
Therefore, the area is 108 feet squared.
3. On Wednesday, a sudden snowfall delayed school busses and caused
12 of Ms. Jackson's 25 students to arrive late to class. What percent of
students made it on time? *
Select the choice that translates the following verbal phrase correctly to algebra:
the product of k and m
km
k + m
k − m
k ÷ m
Answer:
km that is k×m means k is multiplied by m
Simplify fraction 4/28 and 24/80
Answer:
1. 1/7
2. 3/10
Step-by-step explanation:
4/28 can be divided by 4
24/80 can be divided by 8
Please Help, Im having trouble with this
Answer:
1 7/8 can be written as 8*1+7/8=15/8=1.875
Step-by-step explanation:
Dee has $120 to spend. She went to the grocery store and spent $55. She then bought 3 potted flowers for $18 each at the nursery. How much money did Dee have left? Select each correct equation or set of equations that could be used to answer the question. 4.AR.1.1 $120 - $55 = N; N-(3x $18) = M $120 - $55 - (3 × $18) = M (3 x $18) - $55 - $120 = M ($120-$55)-(3x $18)= M $120+ $55 - (3 × $18) = M
Answer:
To find out how much money Dee had left after her purchases, we can use the equation: $120 - $55 - (3 × $18) = M. This equation represents the initial amount of money Dee had ($120) minus the amount she spent at the grocery store ($55) minus the cost of the three potted flowers ($18 each, so 3 × $18). By simplifying this equation, we can find the value of M, which represents the money Dee had left.
what is an equation for the line that passes through the coordinates (2,7) and (0,1)
Answer:
(x1,y1) is (2,7)
(x2,y2) is (0,1)
Step-by-step explanation:
Points:
(x1,y1) is (2,7)
(x2,y2) is (0,1)
Point-slope form is:
(y-y1) = ( (y2-y1) / (x2-x1) )(x - x1)
y - 7 =( (-6)/(0-2) )(x-2)
y - 7 = 3x - 6
y = 3x + 1 [slope-intercept form]
Check:
Is (2,7) on the line:
7 = 3(2) + 1 ?
y = 7 ?yes
Is (0,1) on the line:
1 = 3(0) + 1 ?
1 = 1 ?yes
what is the first 5 terms of n cubed
Answer:
i dont knoweeee imitherrr
Ahab pays 1.15 x 10^3 dollars for one year's tuition ay naylor's university his sister attends north central university and pays 2.8 x 10^3 dollars in tuition for her first year what is the difference in tuition paid by ahab and his sister? answer in scientific notation without units the coefficient may be exact or rounded to 2 decimal places
Difference between the fees of Ahab and his sister is \(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)
Review the following subtraction rules and properties:
The subtraction identity property (also known as the zero subtraction rule): Any number minus zero is equal to itself. \((2-0=2)\)The rule of subtraction by one: any number minus one will decrease that number by one. \((5- 1 = 4)\)Rule of subtraction number minus itself: any number minus itself is equal to zero. \((2 - 2 = 0)\)Number minus the number immediately before the Subtraction rule: any number minus the number immediately before it is equal to one. \((3 -2 = 1)\)Inverse operation: reverses the effect of another operation. Subtraction reverses addition. (Because \(3 + 2 = 5\), then \(5 - 2 = 3\) and \(5 - 3 = 2\))Given: Ahab pays dollars for one year's tuition fees and his sister pays dollars fees in tuition for the first year
To find: Difference in tuition fees paid by Ahab and his sister?
Solution:
To find the difference in their fees we have to perform simply normal subtraction
Subtract the fees of his sister from Ahab's fees which is as follows:
\(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)
Hence the difference between the fees of Ahab and his sister is \(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)
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susie paid $6 for 8 pounds of potatoes what is the cost per pond of potatoes
Answer: $.075 per pound
Step-by-step explanation:
You divide $6 (total cost) by 8 pounds to find the cost per pound
Give the perimeter and the area of a square with sides that measure 9 cm.
Answer:
Perimeter = 36
Area = 81
Step-by-step explanation:
Perimeter of a square is side length * 4.
9*4 = 36
Area of a square is L*L,
9*9 = 81
can you help me with this question plss.
Answer:
5/12
Step-by-step explanation:
I used a calculator
Look at screenshot; I need answer you don't have to explain
In the given graph with the function, x = -9 if f(x) = 7
What is graph?An illustration of a relation is a function graph. In set theory and modern mathematical foundations, a function is actually equal to its graph. It is often helpful to think of functions as mappings, which include the sets that constitute the domain and the codomain in addition to the relationship between input and output.
A codomain should be considered, for instance, when determining whether a function is onto (surjective) or not. The codomain is not determined by the graph of a function alone. The terms "function" and "graph of a function" are frequently used because, although they refer to the same thing, they express different viewpoints on it.
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1)What is the value of x?
drawing not to scale
A)-19
B)125
C)19
D)55
2) M<3=37 find m<1
drawing not to scale
A)37
B)143
C)127
D)153
Answer:
A. C) x = 19
B. A) 37
Step-by-step explanation:
A. 7x - 8 = 6x + 11
7x - 8 - 6x = 6x + 11 - 6x
x - 8 = 11
x - 8 + 8 = 11 + 8
x = 19
B.
If m<3 = 37
<1 = <3
Therefore, m<1 must equal 37
Solve the inequality: -6n - 12 >= 3(-n + 12)
Answer:
-16 > n or n < -16
Step-by-step explanation:
First, we can write the inequality and distribute.
-6n-12 > 3(-n+12)
-6n-12 > -3n+36
Get rid of a variable first (it makes solving a lot easier). We can add 6n to both sides.
-6n-12 > -3n+36
+6n +6n
-12 > 3n+36
Now, we can subtract 36 on both sides.
-12 > 3n+36
-36 -36
-48 > 3n
Divide by 3 on both sides.
-48 > 3n
/3 /3
-16 > n or (if it's easier) n < -16
Hope this helps!! Have a wonderful day C:
Please Please please please help help help help!!!!!!!!!!!!!!!!!!!
Find the product of 3 times the difference of 30 and 25 and 4 times the sum of12 and 15.
And please don't send the links and all please just answer step by step please!!.
Answer:
Step-by-step explanation:
30 30 x 3 = 90
x 3
90
first multiply 4 x 5 = 20 bring down 0 then multiply 4 x 2 = 8 then add+2= 10
25 x 4 = 100
12 x 15 = 180
pls do this!!!!
worth 80 points!!
Answer:
a. x > -1
b. x >= -2
c. x <= 3
d. x <= 0
Step-by-step explanation:
PLEASE HELP, THIS IS A BENCHMARK. WILL GIVE BRAINLIEST!
Use the description of AABC below to solve Parts A and B.
m
Part A: Which of the following is the value of x?
A. x = 10
B. x= 5
B. x = 4
D. x = 2
Part B: Order the sides of ABC from shortest to longest. Drag and drop the displayed choices to order.
a diver was collecting water samples from a lake. he collected a sample at every 3m, starting at 5m below water surface. the final sample was collected at a depth of 35m.how many sample did he collected
The diver collected water samples at every 3 meters, starting from 5 meters below the water surface, up to a final depth of 35 meters.
We can find the number of samples collected by dividing the total depth range by the distance between each sample and then adding 1 to include the first sample.
The total depth range is:
35 m - 5 m = 30 m
The distance between each sample is 3 m, so the number of samples is:
(30 m) / (3 m/sample) + 1 = 10 + 1 = 11
Therefore, the diver collected a total of 11 water samples.