d/dx cos^2(5x^3)
= d/dx [cos(5x^3)]^2
= 2[cos(5x^3)]
= - 2[cos(5x^3)] * sin(5x^3)
= - 2[cos(5x^3)] * sin(5x^3) * 15x^2
= - 30[cos(5x^3)] * sin(5x^3) * x^2
Explanation:
d/dx x^n = nx^(n - 1)
d/dx cos x = - sin x
Chain rule:
d/dx f(g(...w(x))) = f’(g(...w(x))) * g’(...w(x)) * ... * w’(x)
Step-by-step explanation:
f(x) = cos²(5x³)
f(x) = (cos(5x³))²
Use chain rule to find the derivative:
f'(x) = 2 cos(5x³) × -sin(5x³) × 15x²
f'(x) = -30x² sin(5x³) cos(5x³)
If desired, use double angle formula to simplify:
f'(x) = -15x² sin(10x³)
what is three half squared as a fraction
Final answer:
Three half squared is (3/2)², which equals 9/4 when you square the numerator (3² = 9) and the denominator (2² = 4) separately.
Explanation:
The expression 'three half squared' refers to the quantity (3/2) squared. To square a fraction, you square the numerator and the denominator separately. Therefore, (3/2) squared is (3 squared) over (2 squared), which is 9 over 4. Since there are no further simplifications to make, 9/4 is the final answer as a fraction.
To understand this conceptually, think about the process of squaring as finding the area of a square with side lengths of the original number. So, if the side length of a square is 3/2, the area (which represents the square of the number) will be 9/4 square units.
Final answer:
To determine what three-half squared is as a fraction, you simply square the numerator and denominator separately, arriving at the fraction 9/4.
Explanation:
Calculating Three-Half Squared as a Fraction
To find what three half squared is as a fraction, you square both the numerator and the denominator of the fraction 3/2. When you square the numerator (3), you get 9, and when you square the denominator (2), you get 4. Therefore, the answer to three half squared is 9/4, as we have calculated (3/2)² = (3²)/(2²) = 9/4.
This calculation is similar to understanding that if you start with half of a pie and you multiply this amount by itself, you are essentially getting a fraction of the original whole. In our example, by squaring half, we get a quarter, thereby following the intuitive sense of fractions.
hool.
uch
2. The length of a room is 10 feet. What is the
length of the room in inches?
Answer:
30
Step-by-step explanation:
1 foot=3 in
10*3=30 there,easy
Answer:
Should be 120 inches
Step-by-step explanation:
1 feet = 12 inches
10 feet = 12( inches) × 10 (feet)
Therefore, the formula should be:
12×10
=120 ( inches)
Hope it helps!
there were 2 yellow straws and 3 red how many red in 30
Answer:
30 yellow straws and 45 red straws
30:45
Step-by-step explanation:
Make a ratio:
2:3, 2 being the yellow straw and 3 being the red straws
They are now asking how many red if there are 30 yellow straws
2:3 = 30:x
You could either cross multiply or simply do 30 ÷ 2 = 15 then 15 × 3 = 45. Your answer is 45
Cross multiplying
2x = 90
90 ÷ 2 = 45
3(n+3) = - (1 - 5n) – 4
Answer: 7
Step-by-step explanation:
3(n+3) = - (1 - 5n) – 4
3n+9=-1+5n-4
n=7
Answer:
n=7
Step-by-step explanation:
3(n+3)=-(1-5n)-4
3n+9=-1+5n-4
3n+9=-5+5n
3n+14=5n
14=2n
7=n
I used PEMDAS and moving numbers and combing like terms
Written as a rate, 5 miles in 4 hours would be ______
miles per hour.
How did you get this and explain.
Answer:
1.25 miles/hr
Step-by-step explanation:
5miles in 4 hours, this means 5miles/ 4hrs
To find the rate per hour:
5/4 = 1.25 miles/hr
Hope this helps!
Please mark brainliest if you think I helped! Would really appreciate!
Answer:
5/4
Step-by-step explanation:
Divide the miles by the hours. It gives you the ratio.
What is 10/7=x/5?
A.10x=35
B.7x=50
C.5x=70
16. Thirteen tenths written as a decimal is:
(1) 0.013 (2) 0.13 (3) 1.3 (4) 13
(5) 130
Answer:
The answer would be 3; 1.3
If we mix the alcohol solution we have with pure water at the ratio 3:2, we will obtain a solution of 18% alcohol. If we instead mix them at a ratio of 4:1, what will be the alcohol percentage of the solution?
Final answer:
To find the alcohol percentage in the 4:1 ratio, we use the information from the 3:2 ratio. For every 3 parts alcohol, there are 2 parts water. When mixed at a ratio of 4:1, the alcohol percentage is 24%.
Explanation:
To determine the alcohol percentage of the solution when mixed at a ratio of 4:1, we can use the information given in the question. When mixed at a ratio of 3:2, the solution contains 18% alcohol. This means that for every 3 parts alcohol, there are 2 parts water. We can use this information to find the alcohol percentage for the 4:1 ratio.
Let's say we have 4 mL of alcohol and 1 mL of water. The total volume is 4+1 = 5 mL. In the 3:2 ratio, the alcohol percentage is 18%. So, for 3 mL of alcohol, the total volume is 3+2 = 5 mL. Therefore, the alcohol percentage for the 4:1 ratio is (18/3) * 4 = 24%.
Please answer this correctly is the answer
7:33pm
1:33pm
4:33pm
6:57am
Answer:
the answer should be 1:38 pm, but if not, 1:33 pm is correct
Answer:
1:33 PM
Step-by-step explanation
When the plane arrives in Salt Lake City, the time in eastern time period should be 15:33 or 3:33 PM. From eastern time period to the mountains, the time should decrease by 2 hours. 3:33 - 2 hours is 1:33. 1:33 is still in the afternoon so the answer is 1:33 PM.
32 randomly picked people were asked if they rented or owned their own home, 8 said they rented. Obtain a point estimate of the proportion of home owners.
subject: Statistics
Final answer:
The point estimate for the proportion of homeowners in the given sample is 75%, calculated by dividing the number of homeowners (24) by the total number surveyed (32).
Explanation:
To obtain a point estimate of the proportion of homeowners from the given sample, we would calculate the proportion of those who did not rent, since owning and renting are the only two options provided. Out of 32 people, 8 said they rented, which means 32 - 8 = 24 owned their home. The point estimate for the proportion of homeowners is then given by the number of homeowners divided by the total number of people surveyed:
Point estimate for homeowners = (Number of homeowners) / (Total number surveyed) = 24 / 32 = 0.75 or 75%
This mean 75% of the surveyed individuals are estimated to be homeowners.
In order to prepare for your summer bash, you go to the supermarket to buy hamburgers and
chicken. Hamburgers cost $2 per pound and chicken costs $3 per pound. You have no more than
$30 to spend. You expect to purchase at least 3 pounds of hamburgers.
The complete question is:
In order to prepare for your summer bash, you go to the supermarket to buy hamburgers and chicken. Hamburgers cost $2 per pound and chicken costs $3 per pound. You have no more than $30 to spend. You expect to purchase at least 3 pounds of hamburgers.
Write a system of inequalities to represent this situation.Graph the system of inequalities on the grid.Give three possible combinations for buying hamburgers and chicken for your summer bash.Justify your answers
Answer:
A) System of inequalities:
2x + 3y ≤ 30x ≥ 3x ≥ 0y ≥ 0B) Graph: see the picture attached
C) Three possible combinations:
3 pounds of hamburgers and 8 pounds of chicken3 pounds of hamburgers and 0 pounds of chicken15 pounds of hamburgers and 0 pounds of chickenExplanation:
A) Write the system of inequalities to represent this situaction.
1. Variables:
x: number of pound of hamburgersy: number of pound of chicken2. Costs:
x pounds of hamburgers at $2 per pound: 2xy: pounds of chicken at $3 per pound: 3ytotal cost: 2x + 3y3. First constraint:
You have no more than $ 30 to spend: means that the cost of what you buy can be at most (less than or equal to) $ 30.2x + 3y ≤ 304. Second constraint:
You expect to purchase at least 3 pounds of hamburgers: means that the number of pounds of hamburgers may be greater than or equal to 3.x ≥ 35. Additional constraints:
Both, x and y cannot be negative: x, y ≥ 06. System of equations:
2x + 3y ≤ 30x ≥ 3x ≥ 0y ≥ 0B) Graph
You have to graph all the constraints in a x-y coordinate system.
1. To graph 2x + 3y ≤ 30 graph the line 2x + 3y = 30
Choose the y-intercept and x-intercept.x = 0 ⇒ 3y = 30 ⇒ y = 10 ⇒ point (0, 10)y = 0 ⇒ 2x =30 ⇒ x = 15 ⇒ point (15, 0)With two points you can draw the lineClear y: y ≤ 10 - 2x/3. Since, the symbol is ≤ you shade the region below the line, and the line is included, so you draw it as as solid line.2. To graph x ≥ 3 just draw the vertical line x = 3 and shade the region to the right of it. The points of the line are included (solid line).
3. The constraints x ≥ 0 and y ≥ 0 mean that the region is restricted to the first quadrant (including the positive axis).
4. The feasible solutions are the set of points inside the common regions (intersection).
With all that information the graph is the one attached. The feasible solutions is the region defined by the triangle with vertices (3,8), (3,0), and (15,0).
C) Give 3 possible combinations.
You can pick any three points inside the region, as long as the coordinates are integer numbers. For instance the 3 vertices are solutions:
(3, 8) ⇒ 3 pounds of hamburgers and 8 pounds of chicken(3,0) ⇒ 3 pounds of hamburgers and 0 pounds of chicken(15,0) ⇒ 15 pounds of hamburgers and 0 pounds of chickenYou could also prove that (5,4), 5 pounds of hamburgers and 4 pounds of chicken meet, the inequalities.
This is how you prove it:
5 ≥ 05 ≥ 34 ≥ 02(5) + 3(4) = 10 + 12 = 22 ≤ 30And you can do the same for any pairs to verify whether they are solution or not.
solve each equation by factoring
m^2-5m=0
Answer:
m = 0 or 5
Step-by-step explanation:
m² − 5m = 0
Factor out m:
m (m − 5) = 0
Set each term to 0:
m = 0
m − 5 = 0
Solve for m:
m = 0
m = 5
You have $.80 in your backpackin dimes and quarters. Let x represent the number of dimes and y
represent the number of quarters.
a. Write an equation in standard form that represents the situation.
Answer:
$0.10x + $0.25y = $0.80
The equation in standard form that represents the situation is 10x + 25y = 80.
Explanation:To represent the situation in terms of the number of dimes and quarters, we can use the equation 0.10x + 0.25y = 0.80. This equation states that the value of the dimes (0.10x) plus the value of the quarters (0.25y) equals $0.80. Rearranging the equation to standard form, we have:
0.10x + 0.25y = 0.80
10x + 25y = 80
So, the equation in standard form that represents the situation is 10x + 25y = 80.
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please help wit number 3!! leave work below thanks!
Answer:
She did not drive consistently because if 65 = 1 hour, the two-hour mark would be 130, not 120 and the second-hour mark would be 185, not 195. You have to have the same mileage added to each hour to make it consistent.
How to substitute for -5x+3y=51 and y=10x-8
Answer:
x=3, y=22. (3, 22).
Step-by-step explanation:
-5x+3y=51
y=10x-8
----------------
-5x+3(10x-8)=51
-5x+30x-24=51
25x-24=51
25x=51+24
25x=75
x=75/25
x=3
y=10(3)-8
y=30-8
y=22
The value of x is 3 and y is 22.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
-5x+3y=51 ..........(1)
y=10x-8 .............(2)
Put the value of y from equation (2) in equation (1) we get
-5x+ 3(10x - 8)= 51
-5x + 30x - 24 = 51
25x = 51+ 24
25x = 75
x= 3
and, y= 10(3)- 8= 30 -8 = 22
Hence, the value of x is 3 and y is 22.
Learn more about Equation here:
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hey how to do this and what the answer
Answer:
5x + y - 4 = 0
Step-by-step explanation:
When we are given two points and are asked to find the equation of the line we use the two - point form.
Two - point form: [tex]$ \frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1} $[/tex].
where: [tex]$ (x_1,y_1) $[/tex] and [tex]$ (x_2,y_2) $[/tex] are the two points on the line.
Given the two points are: (5,21) and (-5,-29).
Substituting in the two point form:
⇒ [tex]$ \frac{y - 21}{-29 - 21} = \frac{x - 5}{-5 -5} $[/tex]
[tex]$ \implies \frac{y - 21}{-50} = \frac{x - 5}{-10} $[/tex]
[tex]$ \implies y - 21 = 5x - 25 $[/tex]
⇒ 5x + y - 4 = 0
Tomas was flying from Neww York to visit his brother in paris. From takeoff of landing,it was exactly 12 hours. The map he had showed that he had traveled approximately 6,000 miles. About how fast was the plane traveling
Answer:
500 miles per hour
Step-by-step explanation:
6000 miles/12 hours = 500 miles per hour
Shirley and her family ate out last night.the bill was $95 including tax. If the tax was 8.25%, what is the total price?
Answer:
$87.76
Step-by-step explanation:
108.25/100 = 95/x
95×100=9500
9500÷108.25=87.76
To find the total price including tax after a meal at a restaurant, convert the tax rate to a decimal, then multiply it by the total cost and add the result to the original total cost.
Explanation:First, find the amount of sales tax. To do this, convert the percent to a decimal by dividing by 100: 8.25% = 0.0825.
Then multiply the total cost by the decimal tax rate to get the tax amount. In this case, $95 * 0.0825 = $7.8375.
Next, add the tax amount to the original total cost to find the total price: $95 (original cost) + $7.8375 (tax) = $102.8375.
Therefore, the total price, including tax, for Shirley and her family's meal last night was $102.84.
8. There are 4,800 plastic spoons in a case.
There are 6 boxes of spoons in each case.
How many spoons are in each box?
Answer:
Each box has 800 spoons.
Step-by-step explanation:
4800/6=800
The least common multiple of two whole numbers is 60. The ratio of the greater number to the lesser number is 6:5. WhAt are the two numbers
Answer:
The two numbers are 12 , 10
Step-by-step explanation:
Given as :
The least common multiple of two numbers = LCM = 60
The ratio of the greater number to lesser number = 6 : 5
let the greater number = 6 x
And The smaller number = 5 x
∵ The LCM of numbers = 60
So, 6 × 5 × x = 60
Or, 30 × x = 60
∴ x = [tex]\frac{60}{30}[/tex]
I.e x = 2
So The greater number = 6 x = 6 × 2 = 12
And The smaller number = 5 x = 5 × 2 = 10
Hence The two numbers are 12 , 10 Answer
Eggs were $2.05 per dozen on January 1 and $2.00 per dozen on February 1. What percent did the price increase during January?
Answer:
2.5%
Step-by-step explanation:
The price increased from 2 to 2.05. So the increase was:
2.05 - 2 = 0.05 dollars
Now, to find percentage increase, we use the formula below:
[tex]\frac{New-Old}{Old}*100[/tex]
Where
New is the latest price (here it is the increased price of 2.05)
Old is the previous price (here it is the less price of 2.00)
Now, we substitute and find:
[tex]\frac{2.05-2.00}{2.00}*100=2.5[/tex]
So the price increase was 2.5%
mckenna had $32 when she got to the carnival . after riding 6 rides , she had $20 left . write an eqaution and solve to find the price for each ride
Answer:
$2 per ride
Step-by-step explanation:
$32-$20=$12
McKenna rode 6 rides so $12 divided by 6 rides is $2 for every ride
Final answer:
The equation to find the price for each ride McKenna paid at the carnival is $32 - 6P = $20. Solving for P gives us P = $2, so each ride costs $2.
Explanation:
To find the price for each ride that McKenna paid at the carnival, we need to set up an equation based on the information given. McKenna started with $32 and ended with $20 after riding 6 rides. The amount spent on rides is the difference between the starting amount and the remaining amount.
The equation will be:
Initial amount - (Price per ride × Number of rides) = Remaining amount
$32 - (Price per ride × 6) = $20
Let's denote the price for each ride as P. So the equation becomes:
$32 - 6P = $20
To solve for P, we rearrange the equation:
6P = $32 - $20
6P = $12
P = $12 / 6
P = $2
Hence, the price for each ride is $2.
what is.3x^2 +x+2-4x^2(3x-4) equal to
Answer:
-12x^3+17x^2+x+2
Step-by-step explanation:
3x^2+x+2-4x^2(3x-4)
3x^2+x+2-12x^3+14x^2
3x^2+14x^2-12x^3+x+2
17x^2-12x^3+x+2
-12x^3+17x^2+x+2
Find the value of c that completes the square.
a2 + 12a + c
Answer:
c = 36
Step-by-step explanation:
Given
a² + 12a + c
To complete the square
add ( half the coefficient of the a- term )² to a² + 12a
a² + 2(6)a + 6²
= (a + 6)² + 36
Hence the value of c = 36
it’s literal equations and i really need help
Answer:
Part 1) [tex]x=\frac{g}{c}[/tex]
Part 2) [tex]a=\frac{1}{3b}[/tex]
Part 3) [tex]a=\frac{n+p}{m}[/tex]
Part 4) [tex]x=g-y+c[/tex]
Part 5) [tex]x=\frac{z}{m-1}[/tex]
Part 6) [tex]a=\frac{g+b}{c}[/tex]
Part 7) [tex]b=\frac{A}{h}[/tex]
Part 8) [tex]W=\frac{P}{2}-L[/tex]
Part 9) [tex]d=2Q-c[/tex]
Part 10) [tex]a=\frac{Q}{3+5c}[/tex]
Part 11) [tex]N=\frac{A)}{P-IR}[/tex]
Part 12) [tex]b=P-a-c[/tex]
Step-by-step explanation:
Part 1) we have
[tex]g=xc[/tex]
solve for x
That means---> Isolate the variable x
Divide by c both sides
[tex]\frac{g}{c}=\frac{xc}{c}[/tex]
simplify
[tex]x=\frac{g}{c}[/tex]
Part 2) we have
[tex]12ab=4[/tex]
solve for a
That means---> Isolate the variable a
Divide by 12b both sides
[tex]\frac{12ab}{12b}=\frac{4}{12b}[/tex]
simplify
[tex]a=\frac{1}{3b}[/tex]
Part 3) we have
[tex]am=n+p[/tex]
solve for a
That means---> Isolate the variable a
Divide by m both sides
[tex]\frac{am}{m}=\frac{n+p}{m}[/tex]
simplify
[tex]a=\frac{n+p}{m}[/tex]
Part 4) we have
[tex]g=x-c+y[/tex]
solve for x
That means---> Isolate the variable x
Subtract y both sides
[tex]g-y=x-c+y-y[/tex]
[tex]g-y=x-c[/tex]
Adds c both sides
[tex]g-y+c=x-c+c[/tex]
[tex]g-y+c=x[/tex]
rewrite
[tex]x=g-y+c[/tex]
Part 5) we have
[tex]xm=x+z[/tex]
solve for x
That means---> Isolate the variable x
Subtract x both sides
[tex]xm-x=x+z-x[/tex]
[tex]xm-x=z[/tex]
Factor x left side
[tex]x(m-1)=z[/tex]
Divide by (m-1) both sides
[tex]\frac{x(m-1)}{m-1}=\frac{z}{m-1}[/tex]
[tex]x=\frac{z}{m-1}[/tex]
Part 6) we have
[tex]g=ca-b[/tex]
solve for a
That means---> Isolate the variable a
Adds b both sides
[tex]g+b=ca-b+b[/tex]
[tex]g+b=ca[/tex]
Divide by c both sides
[tex]\frac{g+b}{c}=\frac{ca}{c}[/tex]
[tex]a=\frac{g+b}{c}[/tex]
Part 7) we have
[tex]A=bh[/tex]
solve for b
That means---> Isolate the variable b
Divide by h both sides
[tex]\frac{A}{h}=\frac{bh}{h}[/tex]
simplify
[tex]b=\frac{A}{h}[/tex]
Part 8) we have
[tex]P=2L+2W[/tex]
solve for W
That means---> Isolate the variable W
Subtract 2L both sides
[tex]P-2L=2L+2W-2L[/tex]
simplify
[tex]P-2L=2W[/tex]
Divide by 2 both sides
[tex]\frac{P-2L}{2}=\frac{2W}{2}[/tex]
simplify
[tex]W=\frac{P-2L}{2}[/tex]
[tex]W=\frac{P}{2}-L[/tex]
Part 9) we have
[tex]Q=\frac{c+d}{2}[/tex]
solve for d
That means---> Isolate the variable d
Multiply by 2 both sides
[tex]2Q=(2)\frac{c+d}{2}[/tex]
simplify
[tex]2Q=c+d[/tex]
subtract c both sides
[tex]2Q-c=c+d-c[/tex]
[tex]2Q-c=d[/tex]
rewrite
[tex]d=2Q-c[/tex]
Part 10) we have
[tex]Q=3a+5ac[/tex]
solve for a
That means---> Isolate the variable a
Factor the variable a in the right side
[tex]Q=a(3+5c)[/tex]
Divide by (3+5c) both sides
[tex]\frac{Q}{3+5c}=\frac{a(3+5c)}{3+5c}[/tex]
simplify
[tex]a=\frac{Q}{3+5c}[/tex]
Part 11) we have
[tex]I=\frac{PN}{RN+A}[/tex]
solve for N
That means---> Isolate the variable N
Multiply in cross
[tex]I(RN+A)=PN[/tex]
Apply distributive property left side
[tex]IRN+AI=PN[/tex]
subtract PN both sides
[tex]IRN+AI-PN=PN-PN[/tex]
[tex]IRN+AI-PN=0[/tex]
subtract AI both sides
[tex]IRN+AI-PN-AI=-AI[/tex]
[tex]IRN-PN=-AI[/tex]
Factor N left side
[tex]N(IR-P)=-AI[/tex]
Divide by (IR-P) both sides
[tex]\frac{N(IR-P)}{IR-P}=-\frac{A}{IR-P}[/tex]
simplify
[tex]N=-\frac{A}{IR-P}[/tex]
[tex]N=\frac{A}{P-IR}[/tex]
Part 12) we have
[tex]P=a+b+c[/tex]
solve for b
That means---> Isolate the variable b
subtract (a+c) both sides
[tex]P-(a+c)=a+b+c-(a+c)[/tex]
simplify
[tex]P-(a+c)=b[/tex]
rewrite
[tex]b=P-a-c[/tex]
bob bedroom room weights 62 kilograms how many grams does bob bed weight
Answer:
62,000 grams as there are 1000 grams in a kilogram
if p^3 is 0.027, what is p's value
Answer:
0.3
Step-by-step explanation:
To find p we require the cube root of 0.027, that is
p³ = 0.027, then
p = [tex]\sqrt[3]{0.027}[/tex] = [tex]\sqrt[3]{\frac{27}{1000} }[/tex] = [tex]\frac{3}{10}[/tex] = 0.3
What is the slope of the line that contains these points?
Each increase of 1 in x decreases y by 7, i.e. increases y by -7. That's a slope of
Answer: -7
Answer:
[tex] -7[/tex]
Step-by-step explanation:
Use the rise over run equation
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
Find the annual rate of interest. Principal = 4600 rupees Period = 5 years Total amount = 6440 rupees Annual rate of interest = %
Answer:
Annual rate of interest is 8%.
How do u find the circumference of a circle and the radius of a circle?
Answer: radius=8, circumference=16π
Step-by-step explanation:
diameter is 16 centimeters
the radius of a circle is half its diameter
so, radius = 16/2 = 8
circumference of a circle = 2πr
so, circumference = 2π(8cm) = (16π) cm