The answer is : p = -4
the following are the steps to solve it::
13 - 3p = -5 (3 + 2p)
calculate the area of the right hand first by multiplying the number 5 by the number in brackets
13 - 3p = -15 - 10p
move everything that contains p to the left side
13 - 3p + 10p = - 15
count all containing p
13 + 7p = -15
move the ones that don't contain p to the right
7p = -15 - 13
count on the right side
7p = - 28
p = -4
You are running a fuel economy study. One of the cars you find is blue. It can travel 28 1/2 miles on 1 1/4 gallons of gasoline. Another car is red. It can travel 28 4/5 on 4/5 gallons of gasoline. What is the unit rate for miles per gallon for each car? Which car could travel the greater distance on 1 gallon of gasoline?
If you are running a fuel economy study. the unit rate for miles per gallon for each car is 22.8 miles and 23.04 miles and the fastest car is Red car.
How to find the unit rate?Units rate = Distance /Time
Blue car
Unit rate = 28 1/2 miles ÷ 1 1/4 gallons of gasoline
Unit rate = 28.5miles ÷ 1.25 gallons of gasoline
Unit rate = 22.8 miles
Red car
Unit rate = 28 4/5 miles ÷ 4/5 gallons of gasoline
Unit rate = 28.8miles ÷ 0.8 gallons of gasoline
Unit rate = 23.04 miles (Fastest)
Therefore the unit rate for each car is 22.8 miles and 23.04 miles and the fastest car is Red car.
Learn more about unit rate here:https://brainly.com/question/19493296
#SPJ1
Determine whether the following quadratic function has a maximum or a minimum value. Then find the maximum or minimum value and where it occur:
F(x)=-3x²+18x+3
Select the correct choice below and fill in the answer boxes to complete your choice.
(Simplify your answers.)
The function has a maximum value of ___ at x=____.
The function has a minimum value of ____ at x=____.
Answer:
maximum: 30x = 3Step-by-step explanation:
You want to find the maximum or minimum value and where it occurs for the function F(x)=-3x²+18x+3.
Vertex formThe vertex form of a quadratic is ...
f(x) = a(x -h)² +k . . . . . . . vertex at (h, k)
The graph opens downward if a < 0, and opens upward for a > 0. When the graph opens downward, the function has a maximum at the vertex. When the graph opens upward, the function has a minimum at the vertex.
ApplicationWe can put the function in vertex form as follows:
F(x) = -3(x² -6x) +3 . . . . . factor out the leading coefficient
F(x) = -3(x² -6x +9) +3 +3(9) . . . . . . subtract and add 3(9)
F(x) = -3(x -3)² +30 . . . . . . . . . simplify to vertex form
Comparing this equation to the form shown above, we see ...
a = -3 < 0 . . . . . . . . . the function has a maximum
(h, k) = (3, 30) . . . . . the maximum is 30 at x=3
__
Additional comment
The square of the binomial in parentheses is ...
(x -p)² = x² -2px +p²
That is, to "complete the square", we add the square of half the x-coefficient. Here, that coefficient is -2p=-6, so we want to add p²=9 inside parentheses. To keep the expression the same, we need to add the opposite amount outside parentheses. We are effectively adding 0 in the form of -3(9) +3(9) = 0 so the expression can be put in vertex form.
A graphing calculator can quickly show you the minimum or maximum of the function.
Suppose you want to have $300,000 for retirement in 25 years. Your account earns 5% interest.
A. How much would you need to deposit in the account each month?
B. How much interest will you earn?
A) The monthly deposit is $503.77
B) Interest per month ≈0.42
what is compound interest?
Interest that is added to a loan or deposit sum is known as compound interest. In our daily lives, it is the notion that is employed the most frequently. Compound interest is calculated for a sum using the principal and interest accrued over time. Compound interest and simple interest differ primarily in this way.
Let A be the amount in future.
Monthly deposit= [tex]P= \frac{A \times \frac{r}{n}} {(1 +\frac{r}{n})^{t*n} - 1}[/tex]
n= 12, 12 months in a year
So, monthly deposit= [tex]P= \frac{300000 \times \frac{0.05}{12}} {(1 +\frac{0.05}{12})^{25*12} - 1}[/tex]
= 1250/2.4813
= $503.77
So, monthly deposit= $503.77
To find interest:
Interest per year = 5%
Interest per month = 5/12 = 0.416 ≈0.42
To learn more about compound interest from the link
https://brainly.com/question/24274034
#SPJ1
Answer: $503.77
Interest earned: $148,869
Step-by-step explanation:
Let A be the future amount.
Monthly Deposit= P=A*r/n÷ (1+r/n)^t*n-1
n=12 months in a year
P= (300,000*0.05/12)÷ [(1+0.05/12)^25*12]-1
P=1250/2.4813
P=$ 503.77
Interest earned.
$300,000-(503.77*12*25)
$300,000-151,131= $148,869
The ordering and transportation cost C for the c mponents used in manufacturing a product is c= 100(200/x^2+ x/x+30), x≥1 where C is measured in thousands of dollars and x is the order size in hundreds. Find the rate of change of C with respect to x when (a) x = 10, (b) x = 15, and (c) x = 20. What do these rates of change imply about increasing order size?
The ordering and transportation cost C for the components used in manufacturing a product is c= 100(200/x^2+ x/x+30), x≥1 where C is measured in thousands of dollars and x is the order size in hundreds.
To find the rate of change of C with respect to x when (a) x = 10, (b) x = 15, and (c) x = 20.
The rate of change of the cost with respect to x is its derivative.
The differentiation rules to apply are
Quotient Rule: [tex]\frac{d}{dx} \left[\frac{f(x)}{g(x)}\right] = \frac{g(x)f^{'}(x)-f(x)g^{'}(x)}{\left[g(x)]^{2} }[/tex]
Constant Multiple Rule: [tex]\frac{d}{dx} \left[cf(x) \right] = cf^{'}(x)[/tex]
Power Rule: [tex]\frac{d}{dx} \left[x^{n} \right] = nx^{n-1}[/tex]
Constant Rule: [tex]\frac{d}{dx} [c] = 0[/tex]
So,
[tex]c^{'}(x) = 100 (\frac{x^{2}(200)^{'}-200(x^{2})^{'}}{(x^{2})^{2} }+\frac{(x+30)(x)^{'}-x(x+30)^{'} }{(x+30)^{2} } )[/tex]
[tex]c^{'}(x) = 100 (\frac{x^{2}(0)-200(2x) }{x^{4} } + \frac{(x+30)(1)-x(1+0)}{(x+30)^{2} })[/tex]
[tex]c^{'}(x) = 100 (\frac{0-400x}{x^{4} } + \frac{x+30-x}{(x+30)^{2} })[/tex]
[tex]c^{'}(x) = 100 (\frac{-400x}{x^{4} } + \frac{30}{(x+30)^{2} })[/tex]
From the above values it appears that the rate of change of the cost increases as the size of the order increases
[tex]a) c^{'}(10) = -38.13\\ \\b) c^{'}(15) = -10.37\\ \\c) c^{'}(20) = -3.8[/tex]
Hence the above values it appears that the rate of change of the cost increases as the size of the order increases
To learn more about rate changes click here https://brainly.com/question/11627203
#SPJ9
0.438, 44%, 4/9, 9/20 out of any number what would go in between the first and second number limit to the thousandths place
The number that will go in between 0.438 and 44% in the thousandth place is 9 and the number is
0.439How to find that will go between 0.438 and 44%This is found by converting all the given number to decimal
0.438
the thousandth place has number 8
44% = 0.440
The thousandth place has number 0
4/9 = 0.44444
this is greater than the two numbers and hence cannot go in between them
9/20 = 0.45
this is greater than the two numbers and hence cannot go in between them
checking the two numbers 0.438 and 0.440 the number that can go in between them is 0.439
9 in thousandth place is 0.009
Learn more about decimal at:
https://brainly.com/question/29350765
#SPJ1
3a+3.8 is equal to. For a=1.5
Step-by-step explanation:
3a + 3.8 is equal to what when a=1.5?
substitute in 1.5 for a:
3(1.5) + 3.8
3(1.5) + 3.8
4.5 + 3.8
= 8.3
Each day, Caleb feeds his horse 2.25 lb of oats. He also feeds it hay. The weight
of the hay is 6.5 times the weight of the oats. What is the combined weight of
the oats and the hay Caleb feeds his horse in one week?
Answer:
102.375
Step-by-step explanation:
hope it helps :)
multiply 6.5 x 2.25, get 14.625
multiply 14.625 x 7, answer is 102.375
A 16,000-gallon pool is being filled at a rate of 50 gallons per minute. At this rate, how many minutes will it take to fill this pool 3\4 full
To fill the pool 3/4 full it will take 240 minutes
What is rate?A rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate. The word "per" can be further replaced by the symbol "/" in mathematical problems.
3/4 of the volume the pool is 3/4×16000= 12000gallons
it takes 1 minutes to fill 50gallons
therefore to fill 12000 gallons it will take 12000×1/50 =240minutes
therefore the number of minutes it will take to fill 3/4 of the pool is 240minutes
learn more about rate from
https://brainly.com/question/25793394
#SPJ1
Mrs. Smit has a yearly budget of 2.300 for the math club. she spends 36% of the budget for transportation. snacks . and rewards. 70% of the 36% was used for transportation. more money was spent on snacks iban rewards
complete the table so show possible amounts of money. in dollars Mrs . Smith could have spent this year in each category
1,858.40
2300-36%=1472
1472-70%=441.60
2300-441.6=1,858.40
Kendra earns $11.60 per hour working at the movie theater. Each week, she donates
1
10
of her earnings to Best Friends Animal Society, her favorite charity. If Kendra worked 8
1
2
hours
Answer:
Kendra will donate $9.86 to her Best Friend's Animal Society.
Step-by-step explanation:
In order to find this answer, we need to multiply $11.60 by the 8.5 hours:
11.60 x 8.5 = $98.60
Now, if she donates 1/10 every week, we can turn 1/10 into 0.10. And on a calculator set up this equation:
0.10 x 98.60 = $9.86
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
The sum of three consecutive even numbers
is 48. What are the smallest of these
numbers?
The smallest number from the sum of three consecutive even numbers is 14.
Given, The sum of three consecutive even numbers is 48.
we are asked to determine the smallest number of the numbers.
Let:
x= the 1st con.even number
x+2=the 2nd con.even number
x+4=the 3rd con.even number
Add the terms and equate it with the total, 48
x+(x+2)+(x+4) = 48
simplify
x+x+2+x+4=48
combine the like terms.
3x+6=48
3x = 48-6
3x=42
x=42/3
x=14
the three numbers are:
x = 14
x+2 = 14+2 = 16
x+4 = 14+4 = 18
smallest number of the three numbers = 14
Hence we get the smallest number as 14.
Learn more about Consecutive numbers here:
brainly.com/question/10853762
#SPJ9
Jack had received a collection of 30 baseball cards and decided he was going to start collecting. If Jack adds 2 stamps every month, how long will it take to have 50 stamps in his collection?
2. Bella opens a savings account with $100 and the bank pays 1% monthly interest rate. How much money will Bella have after 12 months, if she does not deposit or draw an amount?
If someone answers this question they have to determine which equation is linear and which is nonlinear. Then, write a function that models the linear situation and then write 1 ordered pair that is the solution to the situation.
1) The amount of time that it will take to have 50 stamps is; 10 months
2) The amount of money that bella will have after 12 months is; $112
How to solve linear equation word problems?1) We are told that Jack received a collection of 30 baseball cards. Now, he decided to start collecting after that and he adds 2 stamps every month. Thus, let m represent the number of months he collects and so we have the equation as;
2m + 30
Now, we want to find out how long it will take to get 50 stamps. Thus;
2m + 30 = 50
2m = 20
m = 10 months
2) Principal = $100
Interest rate = 1% monthly
Thus;
Interest after 12 months = 100(0.01 * 12) = $12
Thus, amount she now has after 12 months = $100 + $12 = $112
Read more about Linear Equation Word Problems at; https://brainly.com/question/20335698
#SPJ1
When the function f (x) is divided by x +8, the quotient is 3x2 -3x +1 and the remainder is -3. Find the function f(x) and write the result in standard form
The function f(x) in standard form as described in the task content is; 3x³ + 21x² - 23x + 5.
What is the function f(x) which is as described in the task content?It follows from the task content that the function, f(x) which is as described is to be determined.
Since the polynomial remainder theorem postulates that;
Polynomial = (quotient × divisor) + remainder.
According to the given task content;
The quotient is; 3x² - 3x + 1.
The divisor is; (x + 8) and the remainder is; -3.
Therefore, the required polynomial is;
f(x) = (3x² - 3x + 1)(x + 8) + (-3)
= 3x³ + 24x² -3x² -24x + x + 8 - 3
= 3x³ + 21x² - 23x + 5.
Therefore, the required function, f(x) is; 3x³ + 21x² - 23x + 5.
Read more on remainder theorem;
https://brainly.com/question/27749132
#SPJ1
C and D are sets of real numbers defined as follows. Write using interval notation.
The given sets written in interval notation are
C = (4, ∞), and = (-∞, 9]
Writing sets in interval notationFrom the question, we are to write the given sets using the interval notation
The given sets are
C = {v | v > 4}
D = {v | v ≤ 9}
For set C,
C = {v | v > 4}
The elements of the sets are 5, 6, 7, 8, 9, ...
This can be written in interval notation as (4, ∞)
For set D,
D = {v | v ≤ 9}
The elements of the sets are 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, ...
This can be written in interval notation as (-∞, 9]
Hence, the interval notation form of the sets are
C = (4, ∞)
and
D = (-∞, 9]
Learn more on Writing sets in interval notation here: https://brainly.com/question/28353123
#SPJ1
In which of the following should the random variable X not be modeled with a geometric distribution? A. According to a recent study, approximately to find someone with a master's degree of adults in the country have a master's degree. Let X represent the number of randomly selected adults in the country surveyed B. Suppose it is known that 5% of the light bulbs manufactured at a particular company are defective. Let X represent the number of randomly selected light bulbs that are inspected to find one defective light bulb. C. A particular basketball player is known to consistently make 90% of her free throws, and the outcomes of her free-throw attempts are independent. Let X represent the number of attempted free-throws to get one missed free-throw D. In a bag of 30 different colored candies, about 20% are red. One candy will be selected one at a time without replacement, and its color will be recorded. Let X represent the number of candies selected before red is selected E. It is believed that about 40's of people in the country have purchased a certain product. Let X represent the number of people randomly selected to find the first one who has purchased the product
The probability for success is not the same for each trial, then the option D cannot be modelled using a geometric distribution.
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
One of the assumptions to consider before the use of a geometric distribution can be valid is that, the probability of success must be the same for each outcome.
In the option D, selection is done without replacement, meaning that, the number total possible outcome will decrease as we make each selection and will also depend on how the colours are being chosen.
Hence, the probability of success will differ for each outcome, thus the option D is correct.
Learn more about probability, here;
brainly.com/question/19453987
#SPJ1
Tell whether the lines through the given points are parallel, perpendicular, or neither.
Line 1: (-9,3) (-5,7)
Line 2: (-11, 6) (-7, 2)
The slope of line 1 is
.
The slope of line 2 is
.
Answer:
Line 1: slope is 1
Line 2: slope is -1
Lines are perpendicular
For her party can Nina fill fewer than 10 bags with treats between 10 and 20 bags between 20 and 30 bags or more than 30 bags explain
The correct option regarding the number of bags filled by Nina, using proportions, is given as follows:
Between 20 and 30 bags.
What is a proportion?A proportion is a fraction of an amount, and this fraction is combined with the unit rates of the problem and basic arithmetic operations, especially multiplication and division, to find the desired amounts in the context of the problem.
In this problem, a proportion is applied to find the number of bags filled by Nina, which is given by the division presented as follows:
Number of bags = Number of treats / Treats per bag.
The values of these parameters are given as follows:
Number of treats: 78.Number of treats per bag: 3.Hence the numeric value of the expression is:
Number of bags = 78/3 = 26.
Which is a number between 20 and 30.
Missing InformationThe problem states that Nina had 78 treats, and each bag has 3 treats, then it asks the correct option regarding the number of bags.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Line C has a slope of -1. LINE D has a slope of -2. COMPARE the slopes of the lines.
Line C has a slope of -1. LINE D has a slope of -2.
To Compare the slopes of the lines.
Let us consider the following problem:
In the xy-plane, the point (-1,-2) is on the line j, and the point (-2,-1) is on the line k. Each of the lines has a Negative slope.
We should compare slopes of both the lines to each other, because we may have such kind of two lines
y=x+1 and y=x−1
so we see that their slopes are equal, but we may have also
y=2∗x or slope 2
and
y=1/2∗x or slope 1/2,
Hence, the answer is i think that there is not enough information to compare slopes of the lines.
To learn more about slopes click here https://brainly.com/question/3493733
#SPJ9
Find the equation of the line through point (1,2) and parallel to 3x+4y=12
Answer:
y=-3/4x + 11/4
Step-by-step explanation:
First thing is to minus 3x from 3x and 12.
You will get 4y=-3x+12.
Divide all the sides by 4.
You will get y=-3/4+3.
Now input 1(x), and 2(y) into the slope-intercept form equation.
2=-3/4(1)+b
2=-3/4+b
+3/4 +3/4
2 3/4=b
You can simplify it into 11/4
So, the equation will be y=-3/4x + 11/4
I hope I got this right.
Which of the following sentences is true?
O 6.473 is less than 6.453.
O24.358 is less than 24.357.
O 19.861 is greater than 19.851.
O 19.322 is greater than 19.522.
Answer:
3
Step-by-step explanation:
19.861>19.851
look at hundreds column
Differentiate the function with respect to x. Shot steps
Differentiation of function [tex]y=e^{4x^{4} } (2x^{3} -1)[/tex] is [tex]\frac{dy}{dx} =6x^{2}e^{4x^{4} } +e^{4x^{4} } (2x^{3}-1)(16x^{3} )[/tex]
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
Given,
[tex]y=e^{4x^{4} } (2x^{3} -1)[/tex]
We need to apply product rule of differentiation
dy/dx=xy'+yx'
In the given equation
x=[tex]e^{4x^{4} }[/tex]
y=[tex](2x^{3} -1)[/tex]
[tex]\frac{dy}{dx} =e^{4x^{4} } .6x^{2} +(2x^{3}-1)e^{4x^{4} } (16x^{3} )[/tex]
[tex]\frac{dy}{dx} =6x^{2}e^{4x^{4} } +e^{4x^{4} } (2x^{3}-1)(16x^{3} )[/tex]
Hence, differentiation of function [tex]y=e^{4x^{4} } (2x^{3} -1)[/tex] is [tex]\frac{dy}{dx} =6x^{2}e^{4x^{4} } +e^{4x^{4} } (2x^{3}-1)(16x^{3} )[/tex]
To learn more on Differentiation click:
https://brainly.com/question/24898810
#SPJ1
8y-2x=-40 put the following equation in slope intercept form simplyifing all fractions
Answer:
[tex]y = \frac{1}{4} x\\[/tex] [tex]- 5[/tex]
Step-by-step explanation:
Take a look at the attachment...
Hope this helps! :)
The figure below is rotated 180° counterclockwise. What are the coordinates of the image of point W after this transformation?
The coordinates of the image of point W after a rotation of 180° counterclockwise are W'(-2,-5).
What is graph transformation?The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation.
The coordinates of the given point W are W(2,5).
The coordinate rule for a 180°counterclockwise rotation is:
(x,y)→(-x,-y)
Substitute (x,y) = (2,5) into the above coordinate rule:
(2,5) → (-2,-5)
Hence, the coordinates of the image of point W after a rotation of 180° counterclockwise are W'(-2,-5).
To learn more about graph transformation, click here:
https://brainly.com/question/10059147
#SPJ1
Angles A and B are supplementary. Determine the measure of angle A if the measure of angle B is 121.3°.
238.7°
31.3°
53.7°
58.7°
The required measure of angle m ∠A is 58.7° which is the correct answer would be an option (D).
What are supplementary angles?The supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles.
Angles A and B are supplementary.
We have been given that m angle ∠B= 121.3°,
To determine the measure of angle A if the measure of angle B is 121.3°.
As per the property supplementary angles,
m∠A + m ∠B = 180°
m∠A + 121.3 ° = 180°
m ∠A = 180° - 121.3°
m ∠A = 58.7°
Therefore, the required measure of angle m ∠A is 58.7°
Learn more about supplementary angles here:
brainly.com/question/3027144
#SPJ1
A total of 96 pints of blood were collected at the blood drive. How many quarts were collected?
Answer: 48 qt
Step-by-step explanation:
The conversion factor between pints and quarts is two which means there are 2 pints in every quart. divide the number of pints by two to find the number of quarts.
96/2 = 48
EX: 24 pints = 12 quarts
24/2 =12
EX 8 quarts = 16 pints
The same rule works in reverse but instead of dividing you multiply.
8x2 = 16
Oleg is training for a triathlon. One day he jogged for 2 hours at x miles per hour . Then he bicycled for 2 hours at y miles per hour. Finally. He swam a distance. The total number of miles did not exceed 30.
The inequality to express the information when Oleg is training for a triathlon is 2x + 2y ≤ 30
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal.
Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
In this case, Oleg jogged for 2 hours at x miles per hour and then he bicycled for 2 hours at y miles per hour.
The inequality will be:
2(x) + 2(y) ≤ 30
2x + 2y ≤ 30
Learn more about inequalities on:
brainly.com/question/25275758
#SPJ1
Complete question
Oleg is training for a triathlon. One day he jogged for 2 hours at x miles per hour . Then he bicycled for 2 hours at y miles per hour. Finally. He swam a distance. The total number of miles did not exceed 30. Express this as an inequality
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
The value [tex]x=66[/tex] and [tex]2x=132[/tex] that make line m parallel to line n.
What is corresponding angle?According to the definition of corresponding angles, when two parallel lines cross a third one, the angles that are in the same relative position at each intersection are referred to as being corresponding angles to one another.Geometry and the definition of the appropriate angles allow us to state the following:Parallel lines m and n are shown. we have two parallel lines as a result.Lines m and n cross at line 3. As a result, when parallel lines intersect, we can see that angles m and n occupy the same relative position in the intersection region: the upper right side angles.As a result, it appears that our definition of equivalent angles is reasonable. Angles m and n are therefore said to be equivalent angles.Therefore,
∠132°=∠2x°
[tex]\frac{132}{2} =66[/tex]
hence, x=66°
To learn more about corresponding angle, refer to
https://brainly.com/question/28769265
#SPJ1
Taylor's sister is 7 years less than twice Taylor's age,a. The sum of Taylor's age and her sister's age is 41. Which equation represents this relationship
1) a + (7 - 2a) = 41
2) a + (2a-7)=41
3) 2a-7=41
4) a = 2a - 7
Explain why the other 3 choices are incorrect.
By simplifying a system of equations we will see that the correct option is the second one:
(2a - 7) + a = 41
Which equation represents this relationship?
Let's define the variables:
a = Taylor's Age.s = Sister's Age.We have the statements:
"Taylor's sister is 7 years less than twice Taylor's age"
s = 2*a - 7
"The sum of Taylor's age and her sister's age is 41"
s + a = 41
So we have a system of equations:
s = 2a - 7
s + a = 41
Replacing the first equation in the second one we get:
(2a - 7) + a = 41
So the correct option is the second one, that is the equation that represents this relationship.
Learn more about systems of equations:
https://brainly.com/question/13729904
#SPJ1
5. It is recommended that a pregnant woman should increase her calcium
intake by 1.2 g per day. A normal pregnancy last 40 weeks. How much
extra calcium would a woman receive if she follows this advice?
The required extra calcium that women receive is 336 g during pregnancy.
Given that,
It is recommended that a pregnant woman should increase her calcium intake by 1.2 g per day. A normal pregnancy last 40 weeks.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
According to the question,
Amount of calcium intake,
= 1.2 × 40 × 7
= 336g
Thus, the required extra calcium that women receive is 336 g during pregnancy.
Learn more about arithmetic here:
https://brainly.com/question/11424589
#SPJ1
differentiate [tex] \sqrt{ \frac{(x - 3)( {x}^{2} + 4) }{ {3x}^{2} + 4x + 5 } } [/tex]with respect to x
Step-by-step explanation:
Let [tex]{ \green{ \tt{y = \sqrt{ \frac{(x - 3)( {x}^{2} + 4)}{3 {x}^{2} + 4x + 5}}}}} [/tex]
Take log on both sides
[tex]{ \purple{ \sf{ log_{e}y = log_{e} [\frac{(x - 3)( {x}^{2} + 4}{3 {x}^{2} + 4x + 5}]^{ \frac{1}{2}}}} } { \to}{ \tt{ {eq}^{n} (1)}}[/tex]
This above expression is in the form of
[tex]{ \boxed{ \red {\sf{ {x}^{n} = nx}}}}[/tex]
[tex]{ \boxed{ \red{ \sf{ log( \frac{m}{n} ) = log \: m \: - log \: n}}}}[/tex]
Let's apply these two formulas to eqⁿ (1) then,
[tex]{ \purple{ \sf{ log_{e}y = \frac{1}{2}[log(x - 3) + log( {x}^{2} + 4) - log( {3x}^{2} + 4x + 5) ]}}}[/tex]
differentiate with respect to x.
[tex]{ \blue{ \sf{ \frac{1}{y} \frac{dy}{dx} = \frac{1}{2}[ \frac{1}{x - 3} (1 - 0) + \frac{1}{ {x}^{2} + 4 } (2x - 0) - \frac{1}{3 {x}^{2} - 4x + 5} (6x + 4 + 0)]}}}[/tex]
[tex]{ \blue{ \sf{ \frac{dy}{dx} = y[ \frac{1}{2(x - 3)} + \frac{x}{ {x}^{2} + 4} - \frac{3x + 2}{ {3x}^{2} + 4x + 5 } ]}}}[/tex]
where [tex]{ \boxed{ \purple{ \sf{y = \sqrt{ \frac{(x - 3)( {x}^{2} + 4) }{3 {x}^{2} + 4x + 5}}}}} } [/tex]
Answer:
[tex]let \: \: y = \sqrt{ \frac{(x - 3)( {x}^{2} + 4) }{ {3x}^{2} + 4x + 5 } } \\ \\ y =( {{\frac{(x - 3)( {x}^{2} + 4) }{ {3x}^{2} + 4x + 5 } }})^{ \frac{1}{2} } \\ \\ taking \: \: logarathim \ \: both \: \: sides \: \: \\ \: we \: \:get ⇒ \: ln(y) = {\frac{1}{2} ln(\frac{(x - 3)( {x}^{2} + 4) }{ {3x}^{2} + 4x + 5 } }) \\ \\ ⇒2 ln(y) = ln(x - 3) + ln( {x}^{2} + 4) - ln(3 {x}^{2} ) + ln(4x) + ln(5) \\ differeciate \: \: both \: \: the \: \: sides \: \: we \: \: get \: \: \\ ⇒ 2 \times \frac{1}{y} (\frac{dy}{dx} ) = \frac{1}{x - 3} + \frac{1}{ {x}^{2} + 4} .2x - \frac{1}{3 {x}^{2} } .6x + \frac{1}{4x} .4 + 0 \\ \\ ⇒ \frac{2}{y} \times \frac{dy}{dx} = \frac{1}{x - 3} + \frac{2x}{ {x}^{2} + 4} - \frac{2}{x} + \frac{1}{x} \\ \\ ⇒ \frac{dy}{dx} = \frac{y}{2} . (\frac{1}{x - 3} + \frac{2x}{ {x }^{2} + 4} - \frac{1}{x} ) \\ \\ put \: \: the \: \: value \: \: of \: \: y \: \: we \: \: get \: \\ ⇒ \frac{dy}{dx} = \frac{\sqrt{ \frac{(x - 3)( {x}^{2} + 4) }{ {3x}^{2} + 4x + 5 } } \\ }{2} \times (\frac{1}{x - 3} + \frac{2x}{ {x }^{2} + 4} - \frac{1}{x} )[/tex]
Step-by-step explanation:
used formula
[tex] { ln(m) }^{n} = n \: ln \: m \\ \\ ln(mn) = ln(m) + ln(n) \\ \\ ln( \frac{m}{n} ) = ln(m) - ln(n) \\ \\ \frac{d}{dx} ( ln(x) ) = \frac{1}{x} [/tex]
