Find StartFraction dy Over dx EndFraction for y equals StartFraction negative 5 x cubed minus 5 x squared plus 3 Over negative 5 x Superscript 4 Baseline plus 2 EndFraction . Do not simplify.
Answers
Answer:
\(\dfrac{dy}{dx}=\dfrac{(-5x^4+2)(-15x^2-10x)+(-5x^3-5x^2+3)(-20x^3)}{(-5x^4+2)^2}\)
Step-by-step explanation:
Given: \(y=\dfrac{-5x^3-5x^2+3}{-5x^4+2}\)
We are required to find the derivative of y with respect to x, \(\dfrac{dy}{dx}\) .
We apply the quotient rule:
For a fractional expression,
\(\dfrac{u}{v},$ \dfrac{dy}{dx}=\dfrac{vu'+uv'}{v^2}\)
\(u=-5x^3-5x^2+3,$ $u'=-15x^2-10x\\\\v=-5x^4+2, v'=-20x^3\)
\(\dfrac{dy}{dx}=\dfrac{(-5x^4+2)(-15x^2-10x)+(-5x^3-5x^2+3)(-20x^3)}{(-5x^4+2)^2}\)
Since we are asked not to simplify, we simply leave our answer in the substituted form above.
Related Questions
The pH scale measures how acidic or basic a substance is. Lemon juice is said to have a pH of less than 4 and greater than 1.5. Model the normal range of pH values of lemon juice, using a compound inequality.
1.5 > x > 4
1.5 < x < 4
1.5 ≤ x ≤ 4
1.5 ≥ x ≥ 4
Answers
The normal range using a compound inequality is 1.5 < x < 4
How to model the normal range using a compound inequality.From the question, we have the following parameters that can be used in our computation:
pH values less than 4
pH values greater than 1.5
Represent the pH values with x
Using the above as a guide, we have the following:
x is less than 4
x is greater than 1.5
When represented as inequality, we have
x < 4 and x > 1.5
Combine the inequalities
1.5 < x < 4
Hence, the normal range is 1.5 < x < 4
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Write the equation of the line that has slope 3 and passes through the point
(-2,5).
Answers
y=mx +c
where m is the slope, c is a constant, and x and y are variables,
we know the slope is 3 so m=3
rewriting it
y=3x +c
to find c we substitute values x=-2 and y=3 into the equation y=3x +c
so
3= 3(-2) + c
c=9
thus, y=3x+ 9
Explanation:
y = kx+m is the equation of a line. The coefficient of x is the slope i.e 3. So we know that a part of the equation is y = 3x + m.
How to find M?
Well, we already have a point on the equation. Meaning we already have an x and a y. -2 = x and 5 = y.
The equation then becomes 5 = (3 x -2) + m.
Solve for m and the answer will be m = 11.
Now we have both m and K meaning that the whole equation is solved and it’s y = 3x + 11
Val's whole-house central air conditioner uses 3,000 watts when running. Val runs the AC 4 hours per summer day. Electricity costs (15 cents)/(1 kilowatt-hour). How much does Val's AC cost to run for a summer month of 30 days?
Answers
Answer:
Step-by-step explanation:
3000 W = 3 kW
3 kW(4hr/day)(30 day/month) = 360 kWh/month
360 kWh/month($0.15 / kWh) = $54
So about $75 when you add all the taxes and other fees that get added to a typical electric bill.
A punch recipe calls for 1 1/2 quarts of sparking water and 3/4 of a quart of grape juice.
How much grape juice would you need to mix with 3 3/4 quarts of sparkling water?
Answers
Answer:
15/8 quarts is needed.
Step-by-step explanation:
Hoped this helped.
Roger wants to make a deposit into his savings account. He is depositing 2 checks, one for $125.62 and the other for
$532.50. He would like to receive $40.00 in cash after the deposit. Calculate the amount that he will be depositing into
his savings account.
a. $658.12
b. $618.12
C.
$743.74
d $698.12
Answers
Answer:
B
Step-by-step explanation:
Add $125.62 and $532.50 and then subtract 40 from the total
The amount that he will be depositing into his savings account is, $618.12
We know that;
The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
We have to given that;
Roger wants to make a deposit into his savings account. He is depositing 2 checks, one for $125.62 and the other for $532.50. He would like to receive $40.00 in cash after the deposit.
Hence, The amount that he will be depositing into his savings account is,
⇒ $125.62 + $532.50 - $40
⇒ $658.12 - $40
⇒ $618.12
Thus, The amount that he will be depositing into his savings account is, $618.12
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Select the correct answer.
What is the range of the function graphed below?
у
8
6
-
2
-4
HX
- 2
2
4
6
2
4
-6
OA - < y < -2
Answers
Answer:
B
Step-by-step explanation:
The range of the function is - ∞ < y < 2
How to determine the range?The range of the function are the set of output values of the function.
From the given graph, the values of the graph increases from negative infinity and ends at 2
So, the range of the function is - ∞ < y < 2
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a) Calculate the length of Road C in the image below. Show your work.
b) If a student rides her bike at an average speed of 19.5 km/h, how long will it take her to travel to school using Road C and Road B? Show your work.
c) How much quicker will it be for this student to travel to school along Road A? Show your work.
Answers
Using Pythagoras' Theorem, we found the length of Road C and the respective time taken to travel along each road.
What is meant by Pythagoras' theorem?
The Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse. In essence, Pythagoras' theorem is used to determine a triangle's angle and length of an unknown side. This theorem allows us to obtain the hypotenuse, perpendicular, and base formulas.
The given figure is a right triangle.
The length of road A = 16.01 km
The length of road B = 10 km
a) The length of road C can be found using Pythagoras' theorem.
From figure,
A² = B² + C²
16.01 ² = 10² + C²
C² = 156.32
C = 12.5 km
b) Speed of bike = 19.5 km/h
Length of road C = 12.5 km
Time = Length/speed = 12.5/19.5 = 0.64 hours
Length of road B =10 km
Time = Length/speed = 10/19.5 = 0.51 hours
c) Length of road A = 16.01
Time taken = Length/speed = 16.01/19.5 = 0.82 hours.
Therefore using Pythagoras' Theorem, we found the length of Road C and the respective time taken to travel along each road.
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For use in a linear regression model, categorize which of the following variables should be represented as dummy variables and which can be represented as quantitative variables.
Answers
Dummy variables:
Ice Clean Flavor, Gender, Shoe Color, Number on an Athlete's Jersey, Ice Cream Flavor
Quantitative Variables:
Time to run a marathon, Flat-Screen TV, Height, Hours Spent Researching Core, Calories in Desserts
A dummy variable, often known as an indicator variable or simply a dummy, is a variable in regression analysis that accepts the values 0 or 1 to signify the lack or presence of a category effect that would be anticipated to change the outcome.
Any variable where the data indicate amounts is referred to be a quantitative variable (e.g. height, weight, or age). Any variable where the data represent groupings is referred to as a categorical variable. This comprises categories (like where people placed in a race), rankings (like cereal brands), and binary results (e.g. coin flips).
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The complete question is:
For use in a linear regression model, categorize which of the following variables should be represented as dummy variables and which can be represented as quantitative variables.
ITEMS
TIME TO RUN A MARATHONSHOE COLORHEIGHTNUMBER ON AN ATHLETE'S JERSEYGENDERSIZE OF FLAT-SCREEN TELEVISIONHOURS SPENT STUDYING COREICE CREAM FLAVORCALORIES IN DESSERTSCATEGORY
Dummy VariablesQuantitative VariablesWhich rule explains why these triangles are
congruent?
U
T
V
W
AAS
ASA
SAS
SSS
These triangles
cannot be proven
congruent.
Answers
These triangles can be proven congruent by using ASA RULE.
What is congruent triangles and its rules ?
When two triangles are congruent, their three sides and their three angles match precisely.
If there is a turn or a flip, the equal sides and angles might not be in the same place, but they are still present.
ASA rule stands for Angle-Side-Angle rule which means two angles and a side of both triangles are equal.
Main Body:
In ΔTUV and ΔTWV
VT =VT ----(1)
∠VTU=∠TVW -----(2)
As TUVW is a parallelogram
so, ∠T = ∠U
hence, ∠TVU =∠VTW ----(3)
taking equation 1, 2,3
therefore, ΔTUV ≅ ΔTWV by ASA rule which means by Angle- Side- Angle rule.
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Which sentence can represent the inequality 5x+ 257?O The sum of half of a number and three-fourths is at least five and one quarter.O Half the sum of a number and three-fourths is not more than five and one quarter.O The sum of half of a number and three-fourths is at most five and one quarter.O Half the sum of a number and three-fourths is not less than five and one quarter.
Answers
The inequality consist of two terms 1/2 x and 3/4, in which 1/2 x is half of a number x and 3/4 is expressed as three-fourth, so 1/2x + 3/4 is sum of half of a number and three fourth.
The mixed fraction 5 1/4 can be expressed as five and one-fourth.
The inequality sign,
\(\ge\)represents the left hand side value of sign is more than or equal to the value on right hand side of equation or left hand side value is atleast equal to right hand side equation.
So sum of half of a number and three-fourth is atleast five and one fourth.
Hi can any one teach me this constant difference
Answers
The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).
How do you find the constant difference in a sequence of numbers?In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.
Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.
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A computer costs £968. A tax of 16.5% is then added to the cost of the computer. Work out the amount of tax that is added to the cost of the computer.
Answers
The amount of tax that is added to the cost of the computer is 159.72
How to determine the amount of tax that is added to the cost of the computer.From the question, we have the following parameters that can be used in our computation:
Computer cost = 968
Tax percentage = 16.5%
Using the above as a guide, we have the following:
Tax amount = Computer cost * Tax percentage
substitute the known values in the above equation, so, we have the following representation
Tax amount = 968 * 16.5%
Evaluate
Tax amount = 159.72
Hence, the amount of tax that is added to the cost of the computer is 159.72
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At Paul's Pet Palace, 3/16 of the animals are dogs and 5/24 of the animals are cats. What fraction of the animals are neither dogs nor cat?
Answers
You have that 3/16 of the animals are dogs and 5/24 of the animals are cat.
To determine the fraction of animals that are neither dogs nor cat, consider the following:
If 3/16 are dogs, then 13/16 are other animals, but from this fraction, 5/24 are cats. Then, the subtraction 13/16 - 5/24 results in the fraction of animals that are neither dogs nor cat:
\(\frac{13}{16}-\frac{5}{24}=\frac{312-80}{384}=\frac{232}{384}\)simplify the last fraction:
\(\frac{232}{384}=\frac{116}{192}=\frac{58}{96}=\frac{29}{48}\)Hence, 29/48 of the animal are neither dogs nor cats
3x^2+5x+25 when x =3
Answers
The value of the quadratic equation when x = 3 is 67.
What is a quadratic equation?
Any algebraic equation that can be expressed in standard form as where x represents an unknown number and where a, b, and c represent known values, with a ≠ 0, is a quadratic equation.
We are given a quadratic equation as 3\(x^{2}\) + 5x + 25.
Now, when x = 3, we get
⇒ 3* \(3^{2}\) + 5 (3) + 25
⇒ 3 (9) + 5 (3) + 25
⇒ 27 + 15 + 25
⇒ 67
Hence, the value of the quadratic equation when x = 3 is 67.
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Question: Evaluate : 3x² + 5x + 25 when x = 3.
If they were originally 12 apples at home, the number of apples after a 50% increase would be:
Answers
The number of apples after the increase will be 18.
How many apples would there be?Percentage is the fraction of an amount that is usually expressed as a number out of hundred. The sign that is used to represent percentage is %. In order to change a number to a percentage, multiply by 100.
After the apples are increased, the new number of apples would be half more than the initial number of apples.
The formula that can be used to determine the new number of apples is: New number of apples = original number of apples x (1 + increase/100)
= 12 x (1 + 50/100)
= 12 x (1 + 0.5)
= 12 x 1.5 = 18
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Determine if the product of 3V2 and 8V17 is rational or irrational. Explain your answer.
Answers
Answer:
Step-by-step explanation:
3√2×8√17=24√(2×17)=24√(34)
it is an irrational number.
√34 can't be expressed in the form p/q where p and q are integers.
moreover
5²=25
6²=36
so √34 is between 5 and 6.
Solve the following system of equation. Be sure to show each of your work steps.
Answers
The roots of given equation x^2 - 2x +3 are 1+4i , 1-4i
What is Quadratic Equation ?
Quadratic equation can be defined as the equation in which it is in the form of ax^2 + bx + c = 0
where c is a constant.
Given equations,
x^2 - 2x +3 = 0
so, we know that
the roots of a quadratic equation
= (- b + (√ b^2 - 4ac )) / 2a , (- b - (√ b^2 - 4ac )) / 2a
so,
here a = 1 b = -2 c = 3
by substituting the given values,
we get,
= 2+ (√ 4 - 4*1*3 ) / 2 , 2- (√ 4 - 4*1*3 ) / 2
= 2+ (√-8) / 2 , 2- (√-8) / 2
= 2+8i / 2 , 2-8i / 2
= 1 + 4i , 1- 4i
Hence, The roots of given equation x^2 - 2x +3 are 1+4i , 1-4i
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Figure out the next question
Answers
Answer:
2a + 5
Step-by-step explanation:
Use Distributive property: a(b +c) = a*b +a*c
\(\dfrac{1}{3}(9a + 8) - (a -\dfrac{7}{3})=\dfrac{1}{3}*9a + \dfrac{1}{3}*8 -a + \dfrac{7}{3}\\\\\\=3a - a +\dfrac{8}{3}+\dfrac{7}{3}\\\\\\= 2a + \dfrac{15}{3}\\\\\\= 2a + 5\)
Two ships A and B start sailing from port P at the same time .Ship A sailing at 40km/h is on a bearing of 195degrees and ship B sailing at 24km/h on a bearing of 285degrees find the distance between the two ships
Answers
Given:
Speed of sheep A = 40 km/h
Bearing = 195 degrees
Sheep of speed B = 24 km/h
Bearing = 285 degrees
Let's find the distance between the two ships.
The figure below represents this situation:
Let's find the distance between the two ships.
We can see the figure forms a right triangle.
TO find the distance between the two ships apply Pythagorean Theorem:
\(c=\sqrt[]{a^2+b^2}\)Where:
a = 24 km/h
b = 40 km/h
Thus, we have:
\(\begin{gathered} c=\sqrt[]{24^2+40^2} \\ \\ c=\sqrt[]{576+1600} \\ \\ c=46.65^{}km \end{gathered}\)The distance is 46.65 km
ANSWER:
46.65 km
In the figure, d || m. What is the value of x?
I WILL MARK BRAINLIEST!!
|
———— | ————
(2x - 20°)|
| 86°
———— | ———-
|
Answers
Answer: 53
Step-by-step explanation:
2x-20=86 [alternate interior angles theorem]2x=106 [add 20 to both sides]x = 53 [divide both sides by 2]HELP PLEASEEEEEEE!!!!!
Answers
The similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12
What are similar shapesSimilar shapes are two or more shapes that have the same shape, but different sizes. In other words, they have the same angles, but their sides are proportional to each other. When two shapes are similar, one can be obtained from the other by uniformly scaling (enlarging or reducing) the shape.
Given that the shape EFGH is a smaller shape of JKLM, and they are similar, then:
the measure of angle Z is equal to 65°
the side EF corresponds to JK and side FG corresponds to KL, so:
8/20 = 11/x
x = (11 × 20)/8 {cross multiplication}
x = 27.5
the side EF corresponds to JK and EH corresponds to JM, so:
8/20 = y/30
y = (30 × 8)/20 {cross multiplication}
y = 12
Therefore, the similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12
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Every attendant at a town's Chili Cook-off received a raffle ticket. There were 9 raffle prizes,
including 7 that were gift certificates to restaurants.
If 6 prizes were randomly raffled away in the first hour of the cook-off, what is the probability
that all of them are gift certificates to restaurants?
Answers
the probability that all 6 prizes are gift certificates to restaurants is: 0.083.
What is the probability that all of them are gift certificates to restaurants?There are a total of 9 prizes, out of which 7 are gift certificates to restaurants. If 6 prizes are randomly raffled away in the first hour, there are a total of 9 choose 6 possible outcomes, or 84 possible sets of 6 prizes.
The number of outcomes in which all 6 prizes are gift certificates to restaurants is 7 choose 6, or 7 possible sets of 6 gift certificates.
Therefore, the probability that all 6 prizes are gift certificates to restaurants is:
7/84 = 0.0833 or approximately 8.33%
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Which graph shows an image and preimage after reflecting across y = -x ? *
Option 1
Option 2
Option 3
Option 4
Answers
The graph which correct shows an image and pre-image after reflecting across the line; y = -x as required in the task content is; Option 1.
Which answer choice represents an image and pre-image after a reflection across y = -x?It follows from the task content that the answer choice which correctly represents an image ajd pre-image after reflecting across the line; y = -x.
First it is noteworthy to know that the line; y = -x is one which passes through the origin and has a negative slope of; -1.
On this note, by observation; when the line y = -x is drawn; the graph which represents the image and pre-image after reflecting across the line; y = -x is; Option 1.
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please help me with these problems
Answers
Answer:
√x⁸y² of question 3
= x⁸/² y²/²
=x⁴y
Answer:
\( \sqrt{2} (6 + \sqrt{12} ) = 6 \sqrt{2} + 2 \sqrt{6} \)
\( \sqrt{ {x}^{8} {y}^{2} } = {x}^{4} y\)
\( \sqrt{8} \sqrt{18} = 12\)
I hope I helped you^_^
A meteorologist reports that the ratio of snowfall in January to total snowfall during
the average winter is 2 to 5. If 34 inches have fallen in January of the current year,
find the predicted total snowfall for the entire winter.
Answers
The predicted total snowfall for the entire winter is 85 inches.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, The ratio of snowfall in January to total snowfall during the average winter is 2 to 5.
Assuming x inches have faller in the entire winter.
∴ 2 : 5 : : 34 : x.
2/5 = 34/x.
2x = 170.
x = 85.
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please can someone answer all these
Answers
Answer:
what is it what math
Step-by-step explanation:
um what kind of math is this high school primary school
2. Use Structure The donations by a restaurant
to a certain charity, y, will be two-fifths of its
profits, x, plus $50. How can you determine the
equation in slope-intercept form that shows the
relationship between x and y without graphing
the line?
Answers
The equation in slope-intercept form that shows the relationship between x and y is written as: y = ⅖x + 50.
How to Determine the Equation of a Line in Slope-intercept Form?Without graphing a line, we can determine the equation of a scenario that shows the relationship between two quantities, x and y, by expressing it in slope-intercept form which is given as y = mx + b.
We would need to determine the following:
The unit rate or slope = mThe starting value or initial value or y-intercept = b.Once you determine the above values, simply plug in their values into y = mx + b.
Therefore:
y = donations made by the restaurant
x = profits of the restaurant
Unit rate / slope (m) = ⅖
Initial value / y-intercept (b) = 50
To write the equation in slope-intercept form, substitute m = ⅖ and b = 50 into y = mx + b:
y = ⅖x + 50.
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Farmer Dubble wanted to sell some corazs and yoys at the market. She expected to sell at least 6 corazs. She expected to sell at least 6 units. Write a system of statements, in standard form, modeling the relationships between amount of corazs (x) and amount of yoys (y).
Answers
The system of statements, in standard form, modeling the relationships between amount of corazs (x) and amount of yoys (y) are:
x ≥ 6y ≥ 6. What system of statements models the relationships between the amount?A statement system is made up of a set of statements, each of which has a truth-value of true or false assigned to it.
To write the system of statements, in standard form. Let x be the number of corazs that Farmer Dubble sells and y be the number of yoys that she sells.
Based on the given information, we can write the following system of statements in standard form:
x ≥ 6 (Farmer Dubble expected to sell at least 6 corazs)y ≥ 6 (Farmer Dubble expected to sell at least 6 yoys)These inequalities ensure that the amount of corazs and yoys sold will be greater than or equal to 6 units.
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How many solutions exist for the equation cos 2theta - sin2 theta =0 on the interval [0,360]?
Answers
The solution that exist is 35.26438 or 215.3.
What is Trigonometry?Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
Given:
We have cos 2x - sin²x = 0
Rewrite the expression
cos² x - 2sin²x = 0
Factor the expression:
(cos x + √2 sin x) (cos x - √2 sin x) = 0
So, cos x + √2 sin x = 0 or cos x - √2 sin x =0
after solving them we get 35.26438 or 215.3
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solve 4 + 1.8x = 8 (1 + 0.1x)
Answers
Answer: x=4
Distribute
4+1.8x=8+0.8x
Move terms
4+1.8x-0.8x=8
Collect liketerms
x=8-4
x=4
Answer: x = 4
Step-by-step explanation:
Given:
4 + 1.8x = 8 (1 + 0.1x)
Distribute:
4 + 1.8x = 8 + 0.8x
Subtract 0.8x and 4 from both sides of the equation:
1x = 4
Divide both sides of the equation by 1:
x = 4