g(θ) = 20θ − 5 tan θ
To find out critical points we take first derivative and set it =0
g(θ) = 20θ − 5 tan θ
g'(θ) = 20 − 5 sec^2(θ)
Now we set derivative =0
20 − 5 sec^2(θ)=0
Subtract 20 from both sides
− 5 sec^2(θ)=0 -20
Divide both sides by 5
sec^2(θ)= 4
Take square root on both sides
sec(θ)= -2 and sec(θ)= +2
sec can be written as 1/cos
so sec(θ)= -2 can be written as cos(θ)= -1/2
Using unit circle the value of θ is [tex]\frac{2\pi}{3} and\frac{4\pi}{3}[/tex]
sec(θ)= 2 can be written as cos(θ)=1/2
Using unit circle the value of θ is [tex]\frac{\pi}{3}and\frac{5\pi}{3}[/tex]
For general solution we add 2npi
So critical points are
[tex]\frac{2\pi}{3} + 2n\pi,\frac{4\pi}{3} + 2n\pi , \frac{\pi}{3} + 2n\pi, \frac{5\pi}{3} + 2n\pi[/tex]
The critical points of a function are where its derivative is zero or undefined. The critical points for the function g(θ) = 20θ − 5 tan θ can be found by taking its derivative, setting it to zero, and solving for θ. Additional critical points may occur when the derivative does not exist.
Explanation:In mathematics, the critical points of a function are those where its derivative is zero or undefined. We can find the critical points for the function g(θ) = 20θ − 5 tan θ by taking its derivative and setting it equal to zero.
To find these points, we differentiate the function g(θ) to obtain g'(θ) = 20 - 5/(cos^2 θ). Setting this equal to zero and solving for θ will provide the critical points. In this case, the function is undefined whenever cos θ=0 , providing additional potential critical points. Thus, with trigonometric functions like the tangent function in this question, the critical points occur when the derivative is zero or the derivative does not exist.
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15 divided into 6396 show the steps on how to solve I know the answer is 42 just don’t know the step to put in order
Therefore, 6396/15 = 426.5
A fair coin has been tossed 6 times and come up heads each time. What is the probability that the next toss will also be heads? A) 1 /12
B) 1/ 2 C) 1 3 D) 1/6
Answer:B
Step-by-step explanation:
Answer:
1/2
Step-by-step explanation:
How do you write 75% as a fraction.
There is not much that can be done to figure out how to write .75 as a fraction, except to literally use what the decimal portion of your number, the .75, means. Since there are 2 digits in 75, the very last digit is the "100th" decimal place. So we can just say that .75 is the same as 7/100.
a store having a sell where everything 30 percent. off find the discount and the sale price if a comustor buys an item for 365$
The item is $365 and is 30% off.
What we need to do first is find 30% of $365. We can do this by multiplying
$365 x 0.3 = $109.5
The discount is $109.5
but what we need to pay is $365 - $109.5 = $255.5
The Sale price is $225. 5
GOOD LUCK :)
Arianna runs up 4 flights of stairs and then runs down 4 flights of stairs. Does this situation represent additive inverses?Explain.
Yes due to the fact that additive inverse is the oppsite. so she runs up +4 and runs down -4.
An international company has 25,900 employees in one country if this represents 21.7% of the company’s employees how many employees does it have in total?
Round your answer to the nearest whole number
Corey earned $50 painting his neighbors garage and then he spent $15 of it on a new hat.What percent of his earnings did corey spend?
15 is 30% percent of 50, so Corey spent 30% of his earnings.
Final answer:
Corey spent 30% of his earnings on the new hat, calculated by dividing the amount spent by the total earnings and then multiplying by 100.
Explanation:
To calculate the percentage of earnings Corey spent on the hat, we should find out what portion of his total earnings ($50) was spent ($15).
We can use the formula for percentage: Percentage Spent = (Amount Spent / Total Earnings) × 100.
So, let's plug in the numbers:
Percentage Spent = ($15 / $50) × 100
= 0.3 × 100 = 30%.
Therefore, Corey spent 30% of his earnings on the new hat.
Hi can you guys help me? In 1,2,3 and 4?
Given the function, complete the table of values then graph the ordered pairs.
1. 3, -1, -5, -9
2. -5, -3, -1, 1
3. -2, 0, 2, 4
4. 6, 5, 4, 3
Hope this helps!
To complete the table of values and graph the ordered pairs for the function f(x) = 2x + 1, we substitute the x-values (1, 2, 3, 4) into the function to get the y-values (3, 5, 7, 9). The ordered pairs (1, 3), (2, 5), (3, 7) and (4, 9) are then plotted on the graph and connected with a line.
Explanation:Given a function, you can complete the table of values by substituting the given x-values into the function to find the corresponding y-values. Following this, you can plot the ordered pairs on the graph. Let's assume the function is f(x) = 2x + 1. For x = 1, 2, 3, 4, you get the ordered pairs (1, 3), (2, 5), (3, 7) and (4, 9) respectively. Draw the corresponding points on a graph and connect them with a straight line if it's a linear function.
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x2y - 2xy - 24y = y(x2 - 2x - 24) What is the completely factored form of x2y – 2xy – 24y? (xy + 4)(x – 6) xy(x + 4)(x – 6) y(x + 4)(x – 6) y(x + 4)(xy – 6)
The required factorized form of the given expression is y(x - 6)(x + 4), where y is the greatest common factor (GCF).
What is the Factorization?
Factorization, also known as factoring, is the breakdown of one element into a product of other objects, or factors, which when multiplied together generate the original.
We have been given that the expression below as
x²y - 2xy - 24y
We have to determine the factor of the expression 50x + 100
First, we have to find the Greatest Common Factor (GCF).
GCF = y
y Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
y(x² - 2x - 24)
Simplify each term in parentheses.
y(x² - 2x - 4x - 24)
y(x - 6)(x + 4)
Therefore, the required factorized form of the given expression is y(x² - y(x - 6)(x + 4)
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The completely factored form of x²y - 2xy - 24y is y(x + 4)(x - 6).
Explanation:The completely factored form of x²y - 2xy - 24y is y(x + 4)(x - 6).
To factor the given expression, we can factor out the common term 'y' from all three terms: y(x² - 2x - 24). Then, we factor the quadratic expression inside the parentheses: (x + 4)(x - 6). Combining these factors, we get y(x + 4)(x - 6), which is the completely factored form of the given expression.
pls help me pls i beg u pls help me
I believe the answer is b
Answer:
i think its B but im not 100%
Step-by-step explanation:
A local hamburger shop sold a combined total of 444 hamburgers and cheeseburgers on Saturday. There were 54 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Saturday?
To find the number of hamburgers sold on Saturday, we can set up an equation and solve for the variable.
Explanation:Let's represent the number of hamburgers sold as 'x'. We are given that the combined total of hamburgers and cheeseburgers sold is 444, and there were 54 fewer cheeseburgers sold than hamburgers. So, the number of cheeseburgers sold can be represented as 'x - 54'.
The sum of the hamburgers and cheeseburgers sold is 444, so we can write the equation: x + (x - 54) = 444.
Simplifying the equation, we get: 2x - 54 = 444.
Adding 54 to both sides of the equation, we get: 2x = 498.
Dividing both sides of the equation by 2, we get: x = 249.
Therefore, 249 hamburgers were sold on Saturday.
convert 9% into a decimal
0.09
Here is how yah do it
The easiest approach is to multiply a number in decimal format by 100. Move the decimal: Another way to convert from decimal to percentage format is to move the decimal two places to the right.
If im correct mark brainliest
Answer: 0.09
Step-by-step explanation: We can change a percent to a decimal by simply moving the decimal point two places to the left. In this example, we would simply move the decimal point two places to the left and we would fill in the missing position with a zero. Now, we can write 9% as 0.9 or 0.09. A common mistake that many people will make is writing 0.9 but you have to move the decimal two places to the left.
why do -3 2/7 and 3 2/7 have the same absolute value?
A weather research airplane began descending from an altitude of 36000 feet above its base at a rate of 125 feet per minute how long did it take for the plan to land at its base
El área de un triángulo es de 36 pies cuadrados y la base mide 9 pies. ¿Cuál es la altura del triángulo en pulgadas?
The height of the triangle will be 8 ft.
What is Parallelogram? What is triangle?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given is the area of a triangle is 36 square feet and the base is 9 feet. .
We can write the area of a triangle as -
A (Δ) = (1/2) x b x h
36 = 4.5 x h
h = 36/4.5
h = 8 ft
Therefore, the height of the triangle will be 8 ft.
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[Question in english -
The area of a triangle is 36 square feet and the base is 9 feet. What is the height of the triangle in inches?]
Shrina is selling cookie dogh for her soccer team. She sold 2 tubs of oatmeal raisin and 2 tubs of peanut butter. How much money did she make
Oatmeal - $6
Peanut butter - $5
$6 x 2 = $12
$5 x 2 = $10
$12 + $10 = $22
So Shrina made $22 selling cookie dough.
Hope this Helps!!
To accurately calculate the total amount of money Shrina made from selling the cookie dough, we need to know the price per tub for each type of cookie dough, which are oatmeal raisin and peanut butter.
This information is crucial to compute the answer. Hence, without the prices of the oatmeal raisin and peanut butter tubs, it is impossible to determine how much money Shrina made.
Generally, the calculation would look like this:
The total money earned from selling oatmeal raisin tubs would be the quantity of oatmeal raisin tubs sold multiplied by its price per tub. The same calculation would apply to the peanut butter tubs.
Assuming `oatmeal_raisin_price` and `peanut_butter_price` to be the price per tub of oatmeal raisin and peanut butter respectively, and the quantity sold be represented by `oatmeal_raisin_qty` and `peanut_butter_qty`, the total money made, `money_made` would be:
money_made = (oatmeal_raisin_price * oatmeal_raisin_qty) + (peanut_butter_price * peanut_butter_qty)
The above formula would give us the total amount Shrina made from selling the cookie dough. But without the price of each tub, we can't proceed with the calculation.
pls help. i am new and i want to know if thise app works
aw yeah hon it works :) welcome. -20
A quadratic equation of the form 0=ax^2+bx+c has a discriminant value of -16. How many real number solutions does the equation have?
None
If the discriminant b² - 4ac < 0
There are no real solutions
The equation has no real solutions because the discriminant is -16.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
We are given the quadratic equation by;
ax² + bx + c = 0
By using the quadratic formula,
x = [-b ± √b² - 4ac]/2a
The discriminant of a quadratic equation explains the nature of the roots of that quadratic equation.
If the discriminant is negative, then the equation has no real roots.
If the discriminant us positive, then the equation has two real roots.
If the discriminant is zero, then the equation has a repeated root.
Since the discriminant is -16, then the equation has no real roots.
b² - 4ac < 0. There are no real solutions
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24/22 = x/77
What is x?
Answer:
The answer is x=84
Step-by-step explanation:
Step 1 X/77
Equation at the end of step 1 24/22 - x/77= 0
Step 2 Simplify 12/11
Equation at the end of step 2 12/11 - x/77 =0
Find lest common multiple left denomaintor is 11 and Right is 77
Now its 12*7-(x)/77= 84-x/77
84-x/77 *77= 0 * 77
subtract 84 from both sides -x=84 multiply both sides of the equation by (-1): x =84
So your answer is 84
24 : 22 = x : 77
x = 24 * 77 : 22
x = 84
-------------------------
24 : 22 = 1,090909090909091
84 : 77 = 1,090909090909091
the answer is good
Create four equations using 9, 54 and 6 fact families
These would be 2 of the 4 equations, because 6 times 9 equals 54 and 9 times 6 equals 54, but are written in a different way. Thus meaning they are 2 of the 4 equations.
54/6 = 954/9 = 6These 2 would be the final to, because 54 divided by 6 is 9, and 54 divided by 9 is 6. Thus meaning they are the final 2 equations.
I hope this helps!
If you placed $1000 in a savings account with an interest rate of 4.5%/ month verses an account with 3.75%/ month, how much more interest could you earn in that month?
A- $1.25 more
B- $12.50 more
C- $7.50 more
D- $75.00 more
ANSWER:
C - $7.50
REASONING:
If I placed $1,000 in a savings account with an interest rate of 4.5% per month, I would earn $45 in one month.
$1000x.045=$45
If I placed $1,000 in a savings account with an interest rate of 3.75% per month, I would earn $37.50 in one month.
$1000x.0375=$37.50
I would earn an additional $7.50 in one month by placing the money in the savings account with the 4.5% interest rate.
$45-$37.50=$7.50
mrs payne needs 35 notepads she can buy them in packs of 10 notepads or as single pads what are all the different ways mrs payne can buy the notepade? find a pattern to solve choose two of the ways from the chart explain how thesetwo ways show the some number of notepads
Mrs. Payne can buy the notepads in 5 different ways: 0 packs, 1 pack, 2 packs, 3 packs, or 35 single pads. The number of notepads in each option is either a multiple of 10 or 35.
Explanation:To find all the different ways Mrs. Payne can buy the notepads, we need to consider two scenarios: buying in packs of 10 and buying as single pads. Let's start with buying in packs of 10. The number of packs Mrs. Payne can buy ranges from 0 to 3, since if she buys 4 packs she would have 40 notepads which is more than she needs. So the different ways she can buy notepads in packs of 10 are 0 packs, 1 pack, 2 packs, and 3 packs.
Next, let's consider buying single pads. If Mrs. Payne buys 35 single pads, she would exactly reach her requirement. So another way she can buy the notepads is by purchasing 35 single pads. In total, there are 5 different ways she can buy the notepads: 0 packs (0 notepads), 1 pack (10 notepads), 2 packs (20 notepads), 3 packs (30 notepads), or 35 single pads.
From the chart, we can observe that each option involves a multiple of 10 notepads except for the last option. This indicates that the number of notepads can be obtained by multiplying a whole number by 10, or in the case of 35 single pads, the count is not a multiple of 10.
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Which values have exactly 2 significant figures? Check all that apply.
A. 302 yards
B. 980 gallons
C. 1,200 feet
D. 84 liters
E. 6,040 meters
ANSWER
Options B, C and D have exactly 2 significant figures.
EXPLANATION
To see whether the numbers have exactly 2 significant figures, round all to 2 significant figures. The ones that remains the same have exactly 2 significant figures.
[tex]302\approx 300[/tex]yards to 2.s.f
[tex]980\approx 980[/tex]gallons to 2.s.f
[tex]1200\approx 1200[/tex]feet to 2.s.f
[tex]84\approx 84[/tex]litters to 2.s.f\
[tex]6,040\approx 6,000[/tex]meters to 2.s.f
a pole 24 feet high has a shadow 8 feet long.a nearby pole is 72 feet high. how long is it's shadow?
Final answer:
The 72 feet high pole has a shadow that is 24 feet long, as determined by using proportional relationships between the heights and shadows of two similar triangular shapes formed by the poles and their shadows.
Explanation:
Given the first pole that is 24 feet high has a shadow that is 8 feet long, we can determine the ratio of the height to the shadow length. Since similar triangles have proportional sides, we can apply the same ratio to the second pole that is 72 feet high to find the length of its shadow.
Setting up the proportion, we have:
24 feet (height of first pole) / 8 feet (shadow of first pole) = 72 feet (height of second pole) / x (shadow of second pole).
To solve for x, we cross multiply to get
24 * x = 72 * 8.
Dividing both sides by 24, we get x = 24 feet.
Hence, the shadow of the 72 feet high pole is 24 feet long.
Identify the constant of proportionality in the equation. 5y = 35x A) 1 B) 5 C) 7 D) 35
Answer:
It's 7
Step-by-step explanation:
5y=35 the easiest way is 35/5=7 7x5=35
The value of constant of proportionality in the equation. 5y = 35x is,
⇒ 7
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The equation is,
⇒ 5y = 35x
Now, We can find value of constant of proportionality in the equation as,
⇒ 5y = 35x
Divide by 5;
⇒ y = 7x
Thus, The value of constant of proportionality in the equation. 5y = 35x is,
⇒ 7
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Given: 2/3x-7=4/3x-9 prove: x=3 set up a 2 column proof and complete each
I have attached a picture which clearly explains.
A stereo system cost $275. It was on sale for 15% off. The sales person receives a 2% commission how much of a commission. do they receive?
If the salesperson receives a 2% commision on the sale price (which I am assuming) first you want to calculate the sale price.
Total price - 15% * total price
so
275 - (.15*275)
233.75 is the sale price.
Then take two percent of that
233.75 * .02 = $4.675
They make $4.68 (If rounded to the nearest cent.)
To find the commission received by the sales person, calculate the discounted price of the stereo system and then multiply it by the commission rate.
Explanation:To find the commission received by the sales person, we first need to calculate the total cost of the stereo system after the discount. The discount is 15% of $275, which is calculated as:
$275 × 0.15 = $41.25
So the discounted price of the stereo system is $275 - $41.25 = $233.75.
Now, we can calculate the commission received by the sales person. The commission is 2% of the total cost, which is:
$233.75 × 0.02 = $4.675
The sales person will receive a commission of $4.675.
An airplane is flying 2250 feet in the air. A submarine submerged 1300 feet below sea level. What is the difference in elevation between the airplane and the submarine?
2250+1300= 3550 and that is your answer
3/8 ×4/5 = in simplest form
Final answer:
To find 3/8 multiplied by 4/5, multiply the numerators together and the denominators together and then simplify the resulting fraction. The solution in simplest form is 3/10.
Explanation:
To multiply two fractions, you multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together. For the multiplication of 3/8 × 4/5, we multiply the numerators 3 and 4 to get 12, and the denominators 8 and 5 to get 40.
The result of this multiplication is 12/40. However, this fraction can be simplified. We notice that both the numerator and the denominator are divisible by 4. Thus, we divide both by 4 to get the simplest form: 12 ÷ 4 is 3, and 40 ÷ 4 is 10, resulting in the fraction 3/10.
So, 3/8 × 4/5 in its simplest form is 3/10.
A display has 6 packs of marbles with a total mass of 629g. The packaging of each pack has a mass of 2/3 g and each marble has a mass of 4 1/2 g.
Which equation can we use to determine m, the number of marbles per pack?
A 6*4 1/2 m+ 2/3=629
B 6 m(4 1/2+ 2/3)=629
C 6 m+4 1/2+ 2/3=629
D 6(4 1/2 m + 2/3)=629
PLZ HELP 25 POINTS
Answer:
D
Step-by-step explanation:
answer was done on khan academy
The equation that can we use to determine m, the number of marbles per pack is 6(4 1/2 m + 2/3)=629.
The correct answer choice is option D.
Which equation can we use to determine m, the number of marbles per pack?Number of packs = 6
Total mass of 6 packs = 629g
Mass of each pack = 2/3 g
Mass of each marble = 4½g
Number of marbles per pack = m
Total mass of 6 packs = Number of packs(Mass of each pack) + Number of packs(Mass of each marble × Number of marbles per pack)
629 = 6(2/3) + 6(4½m)
629 = 6(2/3 + 4½m)
Hence, 6(4 1/2 m + 2/3)=629 is the equation to determine the number of marbles per pack?
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