Answer:
x = 81
Step-by-step explanation:
y = k√x
56 = k√49
56 = k(7)
Divide both sides by 7
8 = k
k = 8
------------------------
When y = 72
72 = 8√x
Divide both sides by 8
9 = √x
Square both sides
81 = x
x = 81
Consider the differential equation dy/dx=xy^4.
(b) Find ⅆ2yⅆx2 in terms of x and y. Determine the concavity of all solution curves for the given differential equation in Quadrant II. Give a reason for your answer.
(c) Find the particular solution y=f(x) to the given differential equation with initial condition f(4)=−1.
The differential equation [tex]\frac{dy}{dx} = xy^{4}[/tex] is considered and the solutions for the following questions are found.
What is a differential equation?
A differential equation is an equation that links the derivatives of one or more unknown functions. Differential equations contain derivatives, which might be either partial derivatives or ordinary derivatives.
The differential equation describes a relationship between the variable that is constantly varying with respect to the change in another quantity, and the derivative represents a rate of change.
Given,
[tex]\frac{dy}{dx} = xy^{4}[/tex]
a) Now finding [tex]\frac{d^{2} y}{dx^{2} }[/tex] = [tex]y^{4} + 4xy^{3} \frac{dy}{dx}[/tex] = [tex]y^{4} + 4xy^3 (xy^4) = y^4 + 4x^2y^7[/tex]
In quadrant II, the values of x < 0 and the values of y >0.
So [tex]\frac{d^{2} y}{dx^{2} }[/tex] = [tex]y^4 + 4x^2y^7[/tex] > 0 for all values of x and y in quadrant II.
Therefore the concavity is up for of all solution curves of the given differential equation.
b)
[tex]\frac{dy}{dx} = xy^{4}\\\\\frac{dy}{y^4} =x dx\\\\\int {\frac{dy}{y^4} } \, = \int {x} \, dx \\\\\frac{y^{-4+1} }{-4+1} = \frac{x^{2} }{2} + c\\\\\frac{y^{-3} }{-3} = \frac{x^{2} }{2} +c[/tex]
Now it is given that initial condition is f(4) = -1
So substituting x =4 and y = -1 is the above equation to find c, we get
[tex]\frac{-1^{-3} }{-3} = \frac{4^2}{2} +c \\\\\frac{1}{3} = 8 + c\\\\c = \frac{1}{3} - 8 = \frac{-23}{8}[/tex]
Therefore the solution y = f(x) is to the given differential equation with initial condition f(4)=−1.
[tex]\frac{y^{-3} }{-3} = \frac{x^{2} }{2} -\frac{23}{8}\\ \\ \frac{1}{3y^3} = \frac{46 - 8x^2 }{16} = \frac{23 - 4x^2 }{8}\\\\y = \sqrt[3]{\frac{8}{3(23-4x^2)} }[/tex]
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Use the equation below to find the selling price m of one marker
What is the Volume of this Prism?
Answer:
240
Step-by-step explanation:
Juanita changed $20 into euros when the exchange rate was €1=$1.2685.
How many euros did she receive?
Give your answer correct to 2 decimal places.
The radius of a circle is 3.5 m. Find the circumference to the nearest tenth.
Answer:
22cm
the ans is in the picture with the steps
(hope it helps can i plz have brainlist :D hehe)
Step-by-step explanation:
Answer:
21.98 rounded = 22
Step-by-step explanation:
There are two formulas to find circumference either C=2πr or C=πd.
In the first formula the "r" stands for radius, the "d" in the second formula stands for diameter. Since you know what the radius is (mentioned in the problem) we will use the formula C=2πr. You will substitute "r" for 3.5, it will look like this C=2π3.5. Now you will multiply 3.5x2=7. Now you are left with C=7π. Now you would multiply 7 times π (you could use 3.14 as a substitution for π) 7x3.14=21.98. Since you need to round to the nearest tenth, your answer would be 22.
On amazon, you found the same shoe for $108. What is the percent difference between the price of the original and the price of the amazon shoe
Answer:
Step-by-step explanation:
Here's the complete question:
It cost Nike $55.00 to make the Kyrie 5, but it is selling for $130.19. Calculate the markup/percent Increase for the shoe. On Amazon, you found the same shoe for $108. What is the percent difference between the price of the original shoe and the price of the amazon shoe
The percentage Increase of the shoe will be:
= Selling price - Cost/ Cost × 100
= (130.19 - 55.00) / 55.00 × 100
= 75.19 / 55.00 × 100
= 136.71%
The percent difference between the price of the original shoe and the price of the amazon shoe will be:
= (130.19 - 108)/130.19 × 100
= (22.19 / 130.19) × 100
= 17%
How do you write 4 7/8 as a decimal
Answer:
4.88
Step-by-step explanation:
Turn 4 7/8 as an improper fraction Divide The FractionDone!Hops This Helps!
To convert 4 7/8 into a decimal, we first need to turn the mixed number into an improper fraction.
In order to turn the mixed number into an improper fraction, we need to multiply the whole number by the denominator and add it up with the numerator.
[tex]4\dfrac{7}{8}[/tex]
[tex]4\times8=32+7=39[/tex]
Now, put that sum over the denominator:
[tex]\dfrac{39}{8}[/tex] (improper)
Now, to turn the improper fraction into a decimal, we need to divide the numerator by the denominator:
[tex]39\div8[/tex]
[tex]=\fbox{4.875}[/tex] (final answer)
Given the parent functions f(x) = 5x - 1 and g(x) = 3^x-
9, what is g(x) - f(x)?
Answer:
g(x) - f(x) = 3^x - 9 - (5x - 1) = 3^x -5x - 8
4. Automotive Trades At the beginning of the day on Monday, the parts
department has on hand 520 spark plugs. Mechanics in the service depart-
ment estimate they will need about 48 plugs per day. A new shipment of
300 will arrive on Thursday. Write out a mathematical statement that gives
the number of spark plugs on hand at the end of the day on Friday. Calcu-
late this total.
StS estimate
Therefore , the solution of the given problem of equation comes out to be 580 spark plugs will be left.
Describe the equation.Using the equals symbol (=), a mathematical equation appears to be a formula that connects two statements and denotes equality. A scientific assertion that supports the equality of two mathematical abstraction is known as an equation in algebra. For instance, the equal sign is present between the variables ptdc + 6 and 12 in the output obd + 6 = 12. The link between the syllable on either side of either a letter is described by a mathematical formula. In many cases, the logo and the say — are identical.
Here,
Given: A new supply of 300 spark plugs will come on Thursday,
and 520 spark plugs require 48 plugs per day.
To determine an equation to determine however many plugs will just be left at the end of Friday:
So,
where n is the no of days
=> 520 - 48*n + 300
=> 520 - 48*5 + 300
=> 520 - 240 + 300
=> 520 + 60
=> 580
Therefore , the solution of the given problem of equation comes out to be 580 spark plugs will be left.
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I need help this makes no sense
Answer:
∠ SQT = 63°
Step-by-step explanation:
since QS bisects ∠ RQT , then
∠ RQS = ∠ SQT = 7x + 7
then
∠ RQS + ∠ SQT = ∠ RQT , that is
7x + 7 + 7x + 7 = 9x + 54
14x + 14 = 9x + 54 ( subtract 9x from both sides )
5x + 14 = 54 ( subtract 14 from both sides )
5x = 40 ( divide both sides by 5 )
x = 8
Then
∠ SQT = 7x + 7 = 7(8) + 7 = 56 + 7 = 63°
Apply In Bhutanese architecture, the faces of
buildings are trapezoids. If the row of decorative
brick shown is 28.5 feet wide, what is the width
of the base of the building?
Answer:
Understand Given kite ABCD and isosceles trapezoid WXYZ, complete a two-column proof to show that ... 9. △ADW ≅ △CDZ. 9. SAS. 9. Apply In Bhutanese architecture, the faces of buildings are trapezoids. If the row of decorative brick shown is 28.5 feet wide, what is the width of the base of the building? 25 ft. 16 ft. 16 ft.
Step-by-step explanation:
find the volume please help! Use 3.14 for pi, and round to the nearest hunredth when necessary.
Answer:
Explanation is^{}
in a file
bit.^{}
ly/3gVQKw3
Which of the parabolas has a maximum?
(1) y = 8x² + 6x + 6
(2) y = -2x² + 6x - 6
(3) y = 2x² - 6x + 6
(4) y = 6x² - 6x-6
Answer:
(2) y = -2x² + 6x - 6
Step-by-step explanation:
Notice that the only leading coefficient that is negative is in the 2nd equation. Hence, the shape of the parabola will be upside down, making it have a maximum.
Limx→0 e^x -e^5/ x-5
Answer:e5
Step-by-step explanation:
Here you go
The figure below is divided into 100 squares of equal size.
What percent of the figure is shaded?
Answer:
45%
Step-by-step explanation:
45 boxes are shaded
so percentage shaded is 45 out of the total which is 100
so 45 / 100 X 100
=45%
Find the value of
5x? if x =
- 3
Answer:
-15
Step-by-step explanation:
5x-3=-15
Step-by-step explanation:
Simon builds this podium on a platform.
What is the combined volume of the podium and the platform?
Enter your answer in the box
The combined volume of the podium and the platform is 64 cubic feet.
This sort of figure offers several choices. We really only need to consider how to divide the front face into appropriate rectangles, since the depth of the figure is 2 feet everywhere.
The volume is the area of the front face times that depth.
1) A 2 ft × 4 ft upright atop a 12 ft × 2 ft horizontal base. The frontal area is
(2 ft)(4 ft) +(12 ft)(2 ft) = 8 ft² +24 ft² = 32 ft
so, the total volume is:
V = frontal area × depth
V= (32 ft²)(2 ft)
V=64 ft³
2) A vertical post of 2 ft × 6 ft at the left side with a horizontal protrusion of 10 ft × 2 ft from its bottom.
The frontal area calculated this way is:
(2 ft)(6 ft) +(10 ft)(2 ft) = 12 ft² +20 ft² = 32 ft²
Again, the total volume is (32 ft²)(2 ft) = 64 ft³.
3) A 6 ft × 12 ft rectangle with a 4 ft × 10 ft cutout from the upper right corner. The area calculated this way is
(6 ft)(12 ft) -(4 ft)(10 ft) = 72 ft² -40 ft² = 32 ft² . . . . . same as above
Again, the total volume is (32 ft²)(2 ft) = 64 ft³.
V=64 ft³.
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How many one-half cubes with dimensions of One-half times 1 times 1 fit in a unit cube?
1
2
4
6
Answer:
4 i think
Step-by-step explanation:
i think 2 but i dont know for sure ahahahaha
Which expression is equivalent
Answer:
10^14
Step-by-step explanation:
The expression (10^2)^7 uses an exponent rule known as power raised to a power.
The rule states that when you multiply a base and its exponent to a power, you multiply the inner exponent and the outer exponent:
[tex](a^m)^n\\a^m^n[/tex]
Thus, we have
[tex](10^2)^7\\10^2^*^7\\10^1^4[/tex]
Helpppp plzzz it’s so hard
AABC~ ADEF. What is the scale factor?
Help please
Answer:
3:1 or 3
Step-by-step explanation:
the left triangle is scaling up to the right triangle. 5/15 is 1/3
7/21 is 1/3
4/14 is 1/3
since it is scaling UP, the scale factor is 3:1
Determine the range of f(x) = x + 51.
A-{yl-00
B-{y 1-5
C-{y|0 ≤y <∞0}
D-{y | 5 ≤y < 00}
Answer:
90670998.89999999999999
Solve for all values of x by factoring.
x^2−6x+20=6x
Answer:
x = 10 and x = 2
Step-by-step explanation:
x² - 6x + 20 = 6x
x² - 12x + 20 = 0
We should have values of p and q that multiply and give the answer as 20 and if added give -12.
=> p * q = -10 * -2 = 20
=> p + q = -10 + (-2) = -12
Therefore, we can factor it now:
(x - 10) (x - 2) = 0
We can say:
x - 10 = 0, and x - 2 = 0
=> x = 0 + 10, and x = 0 + 2
=> x = 10 and x = 2
Hope this helps!
Elizabeth buys 50 meters of ribbon to make bows for the cheer squad. Each bow uses 1.3 meters of ribbon. How many bows can Elizabeth make? *
Answer:
38 bows
Step-by-step explanation:
50 ÷ 1.3 ≡ 38 6/13
38 × 1.3 = 49.4
Since you cant make 6/13 of a ribbon, Elizabeth would be able to make 38 bows.
How is the number of Electoral College seats per state determined? A. by the number of party delegates assigned to the state B. by the total number of
Each state is given a specific amount of "votes" under the "Electoral College" system. The amount of "votes" each state receives is proportionate to its size.
What is the makeup of the Electoral College? There are 538 electors in all. The number of electors allotted to each state is equal to the sum of its two Senate seats plus the number of representatives in the House of Representatives.Three electoral votes are granted to the District of Columbia under the 23rd Amendment. According to the amount of each State's population as established by the Census, each State is given a certain number of electors equal to the sum of its U.S. Senators (which are always two) and U.S. Representatives.There are two steps involved in selecting each State's electors. The political parties in each State first select elector candidate slates before the general election. Second, during the general election, each State's voters choose its electors by voting ballots.To learn more about Electoral College refer to :
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Is the first side “SW=XW” or “ST=XU”?
Answer:
SW =XW and ST=XU and UW=TW
Step-by-step explanation:
All are true and correct since the two triangles are congruent
Given triangle ABC, which equation could be used to find the measure of ∠C?
a
tan m∠C = one half
b
sin m∠C = square root of 5 over 5
c
sin m∠C= square root of 5 over 2
d
tan m∠C = 2
The measure of the angle ∠C in the triangle ABC can be gotten using tan m∠C = 2
What is an equation?An equation shows how two or more numbers and variables are related to each other.
On the other hand, trigonometric ratios are used to show the relationship between the sides and angles of a right angled triangle.
The basic equations of the trigonometry ratios are
sinФ = opposite/hypotenuse; cosФ = adjacent/hypotenusetanФ = opposite/adjacentUsing the above as a guide, and the given triangle:
We have:
tan m∠C = opposite/adjacent
Substitute the known values in the above equation, so, we have the following representation
tan m∠C = 6/3
Evaluate
tan m∠C = 2
Hence, the true equation is (d) tan m∠C = 2
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If 7/8 is multiplied by 4/5, will the product be greater than wait her of the two factors Explain.
Answer:
[tex] \frac{7}{8} \times \frac{4}{5} = \frac{7 \times 1}{2 \times 5} \\ = \frac{7}{10} [/tex]
4. LA and B form a linear pair. If MZA = (6x - 19) and mZB = (11x-22), find mZB. A. 59" B. 65 C. 115 D. 121
Answer:
<B =121
Step-by-step explanation:
If the angles form a linear pair, they add to 180
6x-19 + 11x-22 = 180
Combine like terms
17x -41 = 180
Add 41 to each side
17x-41+41 = 180+41
17x = 221
Divide by 17
17x/17 =221/17
x =13
<b = 11x-22 = 11*13 -22 = 143-22 =121
what is f for 1/8f = 3
Answer:
F = 24
Step-by-step explanation:
simplify 1/8
(1/8 x F) - 3 = 0
3 = 3/1 = 3 x 8/ 8
F x (3 x 8) / 8 F - 24/ 8
F - 24/ 8 = 0
F - 24/ 8 = 0 x 8
Answer:
24
Step-by-step explanation:
You want to know f for 1/8f = 3.
UndoMultiply the given equation by 8 to undo the multiplication by 1/8:
8(1/8f) = 8(3)
f = 24 . . . . . . . . simplify
The value of f is 24.
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