Answer:
The value of x is 0.09
Step-by-step explanation:
Here, the given function is,
[tex]f(x)=\log(-20x+12\sqrt{x})[/tex]
Differentiating with respect to x,
[tex]f'(x)=\frac{1}{-20x+12\sqrt{x}}(-20+\frac{12}{2\sqrt{x}})[/tex]
[tex]=\frac{-20+\frac{6}{\sqrt{x}}}{-20x+12\sqrt{x}}[/tex]
[tex]=\frac{-10+\frac{3}{\sqrt{x}}}{-10x+6\sqrt{x}}[/tex]
[tex]=\frac{-10\sqrt{x}+3}{2\sqrt{x}(-5x+3\sqrt{x})}[/tex]
Again differentiating with respect to x,
[tex]f''(x)=-\frac{(-10\sqrt{3}+3)(-15x+3\sqrt{3})}{4x\sqrt{x}(-5x+3\sqrt{x})}[/tex]
For maxima or minima,
[tex]f'(x) = 0[/tex]
[tex]\implies \frac{-10\sqrt{3}+3}{2\sqrt{x}(-5x+3\sqrt{3})}=0[/tex]
[tex]\implies x \approx 0.09[/tex]
At x = 0.09,
f''(x) = negative,
Hence, for x = 0.09, f(x) is maximum.
What is the sum of 100.0 g and 0.01 g, expressed in scientific notation and written with the correct number of significant figures?
The sum of 100.0 g and 0.01 g, expressed in scientific notation and written with the correct number of significant figures is 1.0001 * 10².
What is sum?Sum is the output of the mathematical operation, Addition.
The sum of two numbers a and b is written as a +b.
The first number is 100.0 g
The second number is 0.01 g.
Scientific notation is the method used to write very small and large quantities.
It makes it easy to understand and interpret.
The rules followed while writing significant figures is that, the digits which are not zero is always significant, zeroes between two significant digits are significant.
The number of the form 0.0001 = 1 * 10⁻⁴,
and the number 45000000 is written as = 4.5 * 10⁷.
The sum of 100.0 g and 0.01 g has to be determined.
Let x represent the sum of the numbers, then
x = 100.00 + 0.01
x = 100.01
The sum is 1.0001 * 10²
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Find the truth value in each statement (true or false). 1.) C, E, and D are coplanar. 2.) B and E are collinear.
Which equation represents a circle with a center at (–3, –5) and a radius of 6 units?
(x – 3)2 + (y – 5)2 = 6
(x – 3)2 + (y – 5)2 = 36
(x + 3)2 + (y + 5)2 = 6
(x + 3)2 + (y + 5)2 = 36
Answer:
Option D. (x + 3)² + (y + 5)² = 36
Step-by-step explanation:
We have to find the equation of a circle given with a center at (-3, -5) and radius of 6.
Since the standard equation of a circle is
[tex](x -h)^{2}+(y-k)^{2}=r^{2}[/tex]
where (h, k) is the center and r is the radius.
Now we form an equation of a circle given with center (-3, -5) and radius = 6 units.
(x + 3)² + (y + 5)² = 6²
(x + 3)² + (y + 5)² = 36
Therefore Option D is the answer.
The domain of a function is?
A.The set of all points on the function.
B.The set of all first elements of the function.
C.The set of all second elements of the function.
Answer:
The correct option is B) the set of all first elements of the function.
Step-by-step explanation:
Consider the provided information.
Domain: Domain is the set of all values which a function can take or the domain is the set of all first elements of ordered pairs.
For example:
The domain of the polynomial function is the set of all real numbers.
Consider the another example:
A = {(green,mark), (yellow,Kyle), (blue,Elaine)}
The domain is {green,yellow,blue}
Therefore, the correct option is B) the set of all first elements of the function.
Johnathan is baking several loaves of bread to sell in his bakery. He used 9 cups of water and 12 cups of whole wheat flour. How much water was used per cup of flour?
Jose has determined he needs to have $800,000 for retirement in 30 years. His account earns 6% interest.
a.How much would you need to deposit in the account each month?
b.How much total money will you put into the account?
c.How much total interest will you earn?
a) Monthly deposit: $1,493.20. b) Total deposit: $537,552. c) Total interest earned: $262,448.
To solve these questions, we can use the formula for the future value of an annuity:
[tex]\[ FV = P \times \frac{{(1 + r)^n - 1}}{r} \][/tex]
Where:
[tex]- \( FV \)[/tex] is the future value of the annuity (the amount Jose wants to have at retirement).
[tex]- \( P \)[/tex] is the monthly deposit.
[tex]- \( r \)[/tex] is the monthly interest rate.
[tex]- \( n \)[/tex] is the total number of payments (number of years multiplied by 12, as there are 12 months in a year).
Given:
[tex]- \( FV = \$800,000 \)[/tex]
[tex]- \( r = 0.06/12 = 0.005 \) (monthly interest rate)[/tex]
[tex]- \( n = 30 \times 12 = 360 \)[/tex]
a) To find [tex]\( P \)[/tex]:
[tex]\[ P = \frac{{FV \times r}}{{(1 + r)^n - 1}} \][/tex]
Substitute the values:
[tex]\[ P = \frac{{800000 \times 0.005}}{{(1 + 0.005)^{360} - 1}} \][/tex]
Calculate [tex]\( P \):[/tex]
[tex]\[ P ≈ \frac{{4000}}{{(1.005)^{360} - 1}} ≈ \$1,493.20 \][/tex]
So, Jose needs to deposit approximately $1,493.20 each month.
b) Total money put into the account:
[tex]\[ Total\,Money = P \times n \][/tex]
Substitute the values:
[tex]\[ Total\,Money = \$1,493.20 \times 360 ≈ \$537,552 \][/tex]
Jose will put approximately $537,552 into the account over the 30 years.
c) Total interest earned:
[tex]\[ Total\,Interest = FV - Total\,Money \][/tex]
Substitute the values:
[tex]\[ Total\,Interest = \$800,000 - \$537,552 = \$262,448 \][/tex]
Jose will earn approximately $262,448 in total interest over the 30 years.
2x+5y=20,-3x-10y=37 elimination
Steve’s car manual says his car does 42 mpg. A gallon is 4.55 litres. A litre of diesel costs £1.38. Steve drives from Leeds to Edinburgh a distance of 215 miles. How much would it cost for diesel
To calculate the cost of diesel for Steve's trip from Leeds to Edinburgh, divide the distance by the car's mpg to find the number of gallons needed. Then, multiply the gallons by the cost of diesel per gallon to get the total cost.
Explanation:To determine the cost of diesel for Steve's trip, we need to calculate the number of gallons he will need and then multiply by the cost per gallon. Steve's car does 42 miles per gallon (mpg), and he is driving a distance of 215 miles. Therefore, he will need 215/42 = 5.12 gallons of diesel. Since a gallon is 4.55 liters, Steve will need 5.12 * 4.55 = 23.36 liters of diesel. The cost of diesel per liter is £1.38, so the total cost for diesel will be 23.36 * £1.38 = £32.19.
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Which problem can be solved using this equation?
2
5
b = 4
A) Kyle's class is making banners for a fund raiser. They have 4 yards of material. How many banners can they make?
B) Kyle's class is making banners for a fund raiser. Each banner takes
2
5
yard of material. How many banners can they make?
C) Kyle's class is making banners for a fund raiser. Each banner takes
2
5
yard of material. They have 4 yards of material. How many yards will be left?
D) Kyle's class is making banners for a fund raiser. Each banner takes
2
5
yard of material. They have 4 yards of material. How many banners can they make?
Answer
The answer is
D) Kyle's class is making banners for a fund raiser. Each banner takes
2
5
yard of material. They have 4 yards of material. How many banners can they make?
Step-by-step explanation:
Let b = number of banners
(
2
5
yd)b = 4 (total material available)
2
5
b = 4
a ferris wheel rotates around in 30 seconds. the maximum height above theground is 55 feet and the minumum height above the ground is 5 feet. what function would model the height as a funtion of T in seconds
Answer:
The required function is [tex]h(T)=30\sin (\frac{\pi T}{15})+25[/tex].
Step-by-step explanation:
The general sine function is
[tex]y=A\sin (Bx+C)+D[/tex] .... (1)
Where, A is amplitude, [tex]\frac{2\pi}{B}[/tex] is period, C is phase shift and D is midline.
It is given that the maximum height above the ground is 55 feet and the minimum height above the ground is 5 feet.
The amplitude of the function is
[tex]A=\frac{Maximum+Minimum}{2}=\frac{55+5}{2}=30[/tex]
The Midline of the function is
[tex]D=\frac{Maximum-Minimum}{2}=\frac{55-5}{2}=25[/tex]
A ferris wheel rotates around in 30 seconds. So, the period of the function is 30.
[tex]\frac{2\pi}{B}=30\Rightarrow B=\frac{2\pi}{30}=\frac{\pi}{15}[/tex]
[tex]2\pi=30B[/tex]
Substitute A=30, [tex]B=\frac{\pi}{15}[/tex], C=0 and D=25 in equation (1), to find the required function.
[tex]y=30\sin (\frac{\pi}{15}x+0)+25[/tex]
The required variable is T. Replace the variable x by T. So the height function is
[tex]h(T)=30\sin (\frac{\pi}{15}T+0)+25[/tex]
Therefore the required function is [tex]h(T)=30\sin (\frac{\pi T}{15})+25[/tex].
When adding decimals, use a zero as a placeholder so that both decimals have the same number of digits after their decimal points?
Using a zero as a placeholder so that both decimals ahve the same number of digits after their decimal point is a good strategy while adding decimals because it helps you line the decimals up in the correct way to get the correct sum.
how do you do this?
fg-9h=10j solve for g
It should be noted that when g is made the subject of the formula in fg - 9h = 10j, g will be g = (10j - 9h) / f.
How to illustrate the information?It should be noted that an equation is used to show the relationship that exist between the variables that are illustrated.
Based on the information, it should be noted that we want to make g the subject of the formula. This will be illustrated as:
fg - 9h = 10j
Add 9 h to both sides
fg - 9h + 9h = 10j - 9h.
fg = 10j - 9h.
Divide through by f
fg / f = (10j - 9h) / f
g = (10j - 9h) / f
In this case, it should be noted that when g is made the subject of the formula in fg - 9h = 10j, g will be g = (10j - 9h) / f.
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To solve for g in the equation fg - 9h = 10j, add 9h to both sides and then divide by f, resulting in g = (9h + 10j)/f.
To solve the equation fg - 9h = 10j for g, you need to isolate g on one side of the equation. This can be achieved by performing the following steps:
Add 9h to both sides to get fg = 9h + 10j.Divide both sides by f to get g = (9h + 10j)/f.By following these steps, g is isolated and the equation is solved for g. Remember to apply the order of operations correctly when substituting any given values for f, h, and j.
kelly subscribes to a service called mysongs for downloading music she pays a $7 fee each month to download an unlimited number of songs at $0.20 each month last month kelly's bill was $23.80
subtract the $7 fee from the total first:
23.80-7 = 16.80 was spent on songs
divide by cost of each song
16.80 / 0.20 = 84 songs were downloaded
Cole had 3/4 hour of free time before dinner. He spent 2/3 of the time playing guitar. How long did he spend playing guitar? Please help me! I have seen some previous people asking questions but I am not sure if they are correct.
HELP! Tell me if my answer is wrong or not.
Debra started a babysitting business. She purchased toys, snacks, and other supplies. She charged an hourly rate for each child. The expression −145+6y
represents the profit Debra has earned from her babysitting business.
Which expression represents the total amount Debra earns from babysitting?
a) y
b) 6y
c) −145
d) 6
My answer was C, but I think I'm wrong
Answer:
6y i literally just did the test
Step-by-step explanation:
a drop on a wooden roller coaster is -98 1/2 feet. a drop on a steel roller coaster is 100 3/4 feet lower that the drop on the wooden roller coast. what is the drop on the steel roller coaster?
Answer:
The drop is -198 3/4
Step-by-step explanation:
There are 120 students on a field trip to orlando. the ratio of boys to girls is 2:1 how many boys were on the trip
John took 45 minutes to bicycle to his grandmother's house, a total of four kilometers. what was his speed in km/hr?
Will give Brainliest
Use a calculator to find an approximate solution to the equation. Round any intermediate work and steps to three decimal places. Show all of your steps in solving the equation
6ln (x + 2.8) = 9.6
The word ____ tells you that the relationship describes an equation?
Reza paid $4,500 as a down payment on a car. She then made equal monthly paments of $250. Reza paid a total of $10,500 for her car. How many months did she make payments on the car and which fuction can be used to find the answer?
Reza made monthly payments for 24 months to pay off her car after making a $4,500 down payment. The total cost of the car was $10,500, and she paid the remaining amount in installments of $250 per month.
Explanation:Reza's car payments can be calculated using a simple algebraic function. She made an initial down payment of $4,500 and paid off the remaining balance with equal monthly payments of $250. The total cost of the car was $10,500. To find out how many months Reza made payments on the car, you can use the following function:
Total Cost = Down Payment + (Monthly Payment × Number of Months)
First, we subtract the down payment from the total cost:
$10,500 - $4,500 = $6,000
This is the amount Reza paid in monthly installments. Now we divide this amount by the monthly payment amount to find the number of months:
$6,000 / $250 = 24 months.
Therefore, Reza made payments for 24 months.
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What is the smallest degree of rotation that will map a regular 15-gon onto itself?
Enter your answer in the box.
The correct answer is:
24°.
Explanation:
To find the degrees of rotational symmetry, you divide 360° by the order of symmetry.
For a regular 15-gon, the order of symmetry is 15 (there are 15 vertices that the polygon can be turned to and be mapped onto itself).
This means the degrees of symmetry would be
360/15 = 24°.
Answer:
24
Step-by-step explanation:
A football game lasted 3.15 hours. how many seconds did the game last? if necessary, round your answer to the nearest tenth of a second
Answer:
The football game last for 11340 seconds.
Step-by-step explanation:
Football Game last for 3.15 hours
We have to convert this time into seconds.
First we convert it into minutes then into seconds.
We know that 1 hour = 60 minutes
⇒ 3.15 hour = 3.15 × 60 = 189 minutes
We also know that 1 minute = 60 seconds
⇒ 189 minutes = 189 × 60 = 11340 seconds
Therefore, The football game last for 11340 seconds.
After 8 years, what is the total amount of a compound interest investment of$25,000 at 3% interest compounded quarterly?
Your question: After 8 years, what is the total amount of a compound interest investment of $25,000 at 3% interest compounded quarterly?
Answer: $31,752.78
Good luck mate. Remember to look through notes and so-forth.
the answer is this :3
Rose bought 7/20 kilogram of ginger candy and 0.4kilogram of cinnamon candy. Which did she buy more if
Final answer:
After converting 7/20 to a decimal, we find that Rose bought 0.35 kilogram of ginger candy, which is less than the 0.4 kilogram of cinnamon candy; therefore, Rose bought more cinnamon candy.
Explanation:
Rose bought 7/20 kilogram of ginger candy and 0.4 kilogram of cinnamon candy. To determine which she bought more of, we need to compare these amounts. The fraction 7/20 can be converted into a decimal to make the comparison easier. To convert a fraction to a decimal, you divide the numerator by the denominator.
So, 7 ÷ 20 = 0.35. This means that Rose bought 0.35 kilogram of ginger candy, which is less than the 0.4 kilogram of cinnamon candy. Therefore, Rose bought more cinnamon candy than ginger candy.
is a liter bigger or smaller than a milliliter
1 liter = 1000 milliliter
so a liter is bigger
A test has a mean of 80 and standard deviation of 4. what score would be 1 deviation from the mean
Test has a mean of 80 and standard deviation of 4 than after one deviation from the mean, most of the score will fall in the interval ([tex]\mu - \sigma\;,\; \mu + \sigma[/tex]) which is (76 , 84).
Given :
Mean, [tex]\mu = 80[/tex]
Standard Deviation, [tex]\sigma = 4[/tex]
After one deviation from the mean, most of the score will fall in the interval ([tex]\mu - \sigma\;,\; \mu + \sigma[/tex]). Where [tex]\mu[/tex] is the mean which is arithmetic average of all values and [tex]\sigma[/tex] is the standard deviation which is the square root of its variance.
Now, the value of [tex]\mu - \sigma = 80-4 = 76[/tex].
And the value of [tex]\mu + \sigma = 80+4=84[/tex].
After one deviation from the mean, most of the score will fall in the interval ([tex]\mu - \sigma\;,\; \mu + \sigma[/tex]) which is (76 , 84).
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The price of an item has been reduced by 55%. The original price was $75. What is the price of the item now?
Final answer:
To calculate the new price of an item after a 55% reduction from an original price of $75, you multiply $75 by 55% to get the reduction amount of $41.25. Subtracting this from the original price gives a new price of $33.75.
Explanation:
The student is asking how to calculate the new price of an item after a percentage decrease, specifically a 55% reduction from the original price. To find the new price, we can apply the percentage decrease to the original price and then subtract that amount from the original price.
Original price = $75
Percentage decrease = 55%
First, calculate the amount of the reduction:
Reduction amount = (Original price) × (Percentage decrease)
Reduction amount = $75 × 0.55
Reduction amount = $41.25
Now, subtract the reduction amount from the original price to get the new price:
New price = Original price - Reduction amount
New price = $75 - $41.25
New price = $33.75
So the new price of the item after a 55% reduction is $33.75.
Write the first ten positive perfect-square integers
A perfect square is a figure that can be conveyed as the product of two identical integers.
The first ten positive perfect squares are the following:
1 = 1 x 1
4 = 2 x 2
9 = 3 x 3
16 = 4 x 4
25 = 5 x 5
36 = 6 x 6
49 = 7 x 7
64 = 8 x 8
81 = 9 x 9
100 = 10 x 10
14. During a paint sale, a hardware store sold 33 gallons of flat paint and 57 gallons of high-gloss paint. What's the ratio of gallons of high-gloss sold to the total gallons sold? A. 33 : 90 B. 57 : 90 C. 57 : 33 D. 33 : 57
The ratio of gallons of high-gloss sold to the total gallons sold is,
D. 33 : 57
What are ratio and proportion?In its most basic form, a ratio is a comparison between two comparable quantities.
There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.
If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.
Given, The hardware store sold 33 gallons of flat paint and 57 gallons of high-gloss paint.
Therefore, The ratio of flat paint : high-gloss paint = 33 : 57.
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