Mateo is constructing an equilateral triangle inscribed in a circle with center P. He draws the diameter of the circle through center P using a straight edge. Next he opens his compass to a width equivalent to the radius of the circle. What is his next step?
on a certain planet, objects weight about 7/12 of what they weigh on earth. an object weights 13 5/12 pounds on the planet. solve the equation 7/12 w= 13 5/12 for w to find the objects weight on earth in pounds.
What is the domain of y = sec(x)?
The domain of y = sec(x) is all real numbers except for values where the cosine function is zero.
Explanation:The domain of y = sec(x) is all real numbers except for values where the cosine function is equal to zero. Since the secant function is the reciprocal of cosine, it is undefined when cosine is zero.
So, the domain of y = sec(x) is all real numbers except for values of x where cos(x) = 0.
For example, if we consider the unit circle, the cosine function is equal to zero at π/2 and 3π/2. Therefore, the domain of y = sec(x) would exclude these values.
The domain of [tex]\( y = \sec(x) \)[/tex] is all real numbers except [tex]\( x = \frac{\pi}{2} + \pi \cdot n \)[/tex], [tex]\( n \)[/tex] integer.
Let's find the domain of [tex]\( y = \sec(x) \)[/tex].
The secant function, [tex]\( \sec(x) \)[/tex], is defined as the reciprocal of the cosine function, [tex]\( \cos(x) \)[/tex]. So, [tex]\( \sec(x) = \frac{1}{\cos(x)} \).[/tex]
The cosine function is defined for all real numbers, except where the denominator becomes zero, because division by zero is undefined.
So, to find the domain of [tex]\( \sec(x) \)[/tex], we need to find where [tex]\( \cos(x) \)[/tex] is not zero.
The cosine function has a range between -1 and 1. It equals zero at [tex]\( x = \frac{\pi}{2} + \pi \cdot n \)[/tex] and [tex]\( x = -\frac{\pi}{2} + \pi \cdot n \)[/tex], where [tex]\( n \)[/tex] is an integer.
So, the domain of [tex]\( \sec(x) \)[/tex] is all real numbers except where [tex]\( \cos(x) = 0 \)[/tex]. Therefore, the domain of [tex]\( \sec(x) \)[/tex] is [tex]\( x \neq \frac{\pi}{2} + \pi \cdot n \)[/tex] and [tex]\( x \neq -\frac{\pi}{2} + \pi \cdot n \)[/tex], where [tex]\( n \)[/tex] is an integer.
In interval notation, the domain of [tex]\( \sec(x) \)[/tex] is:
[tex]\[ (-\infty, -\frac{\pi}{2}) \cup (-\frac{\pi}{2}, \frac{\pi}{2}) \cup (\frac{\pi}{2}, \infty) \][/tex]
Using the given zero, find all other zeros of f(x).
-2i is a zero of f(x) = x4 - 32x2 - 144
a) 2i, 12, -12
b) 2i, 6i, -6i
c) 2i, 6, -6
d) 2i, 12i, -12i
Answer:
c) 2i, 6, -6Step-by-step explanation:
The given function is
[tex]f(x)=x^{4}-32x^{2} -144[/tex]
The given zero to this function is
[tex]x=-2i[/tex]
Remember that a function has so many roots as its grade dictates. So, in this case, the function grade is four, which means it has four solutions.
Now, the given function is an imaginary number, which happens in pairs, that means the second root must be [tex]x=2i[/tex], because a function can have complex roots as pairs, 2, 4, 6,... many solutions.
The other two solutions are 6 and -6, because if we replace them into the function, it will give zero.
[tex]f(6)=6^{4}-32(6)^{2} -144=0\\f(-6)=(-6)^{4}-32(-6)^{2} -144=0[/tex]
Therefore, the other three solutions missing are: c) 2, 6, -6.
(The image attached shows the real solutions).
Kevin is solving this problem. 737 × 205 What are the partial products Kevin will need to solve the problem? A. 3,685 and 147,400 B. 3,685 and 14,740 C. 3,685 and 1,474 D. 3,685 and 7,370 and 147,400
the answer is A
700 x 5 = 3500
30 x 5 = 150
7 x 5 = 35
3500 + 150 +35 = 3685
700 x 200 = 140,000
30 x 200 = 6000
7 x 200 = 1400
140000 + 6000 + 1400 = 147400
Carlos is putting money into a savings account. He starts with $750 in the savings account, and each week he adds $40 . Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Carlos has been adding money. Write an equation relating S to W . Then use this equation to find the total amount of money in the savings account after 11 weeks.
Equation:
Total amount of money after 11 weeks:
Final answer:
The equation relating the total amount of money S in Carlos's savings to the number of weeks W he adds money is S = 750 + 40W. By substituting W with 11, we find that after 11 weeks, Carlos will have $1,190 in his savings account.
Explanation:
The question involves creating a linear equation to represent the relationship between the total amount of money S in Carlos's savings account and the number of weeks W he has been adding money. The equation can be written as S = 750 + 40W, where 750 represents the initial amount and 40 is the amount added each week. To find the total amount of money after 11 weeks, substitute W with 11:
S = 750 + 40(11) = 750 + 440 = 1190
Therefore, after 11 weeks, the total amount of money in the savings account would be $1,190.
Find the area under the standard normal distribution curve to the left of z=-2.15 and to the right of z=1.62
Using the normal distribution table, which shows the percentage of the areas to the left a normal distribution, the area to the left z = - 2.15 and area to the right of z = 1.62 are 0.0158 and 0.0526 respectively.
1.)
The area under the normal distribution curve to the left of z = 2.15 can be expressed thus :
P(Z ≤ -2.15)
Using a normal distribution table ; the area to the left is
P(Z ≤ -2.15) = 0.0158
2.)
The area under the normal distribution curve to the right of z = 1.62 can be expressed thus :
P(Z ≥ 1.62) = 1 - P(Z ≤ 1.62)
Using a normal distribution table ; the area to the left is P(Z ≤ 1.62) = 0.94738
P(Z ≥ 1.62) = 1 - 0.94738 = 0.0526
Therefore, the area to the left z = - 2.15 and area to the right of z = 1.62 are 0.0158 and 0.0526 respectively.
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A circular fountain has a circular walkway surrounding it with a width of 7 ft. The total area taken up by the walkway is 693π ft^2. Find the diameter of the pool.
If we reject the null hypothesis, can we claim to have proved that the null hypothesis is false? why or why not?
How long will it take a bird traveling at an average speed of 12 miles per hour to travel 202 miles while flying south for winter?
Answer:
16 50 min
Step-by-step explanation:
The daily mean temperature in a particular place is 83. how many cooling-degree days were accumulated?
how to simplify expression by distribution 3(2y-7)
Omar's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Omar $4.85 per pound, and type B coffee costs $5.95 per pound. This month's blend used twice as many pounds of type B coffee as type A, for a total cost of $519.25 . How many pounds of type A coffee were used?
Suppose you have a normally distributed set of data pertaining to a standardized test. the mean score is 1000 and the standard deviation is 200. what is the z-score of 900 point score? 1.5 1 0.5 â0.5
A cone-shaped paper drinking cup is to be made to hold 36 cm3 of water. find the height and radius of the cup that will use the smallest amount of paper. (round your answers to two decimal places.)
The formula for volume of cone is:
V = π r^2 h / 3
or
π r^2 h / 3 = 36 cm^3
Simplfying in terms of r:
r^2 = 108 / π h
To find for the smallest amount of paper that can create this cone, we call for the formula for the surface area of cone:
S = π r sqrt (h^2 + r^2)
S = π sqrt(108 / π h) * sqrt(h^2 + 108 / π h)
S = π sqrt(108 / π h) * sqrt[(π h^3 + 108) / π h]
Surface area = sqrt (108) * sqrt[(π h + 108 / h^2)]
Getting the 1st derivative dS / dh then equating to 0 to get the maxima value:
dS/dh = sqrt (108) ((π – 216 / h^3) * [(π h + 108/h^2)^-1/2]
Let dS/dh = 0 so,
π – 216 / h^3 = 0
h^3 = 216 / π
h = 4.10 cm
Calculating for r:
r^2 = 108 / π (4.10)
r = 2.90 cm
Answers:
h = 4.10 cm
r = 2.90 cm
The height of the cone is [tex]\boxed{4.10}[/tex] and the radius of the cone is [tex]\boxed{2.90}.[/tex]
Further explanation:
The volume of the cone is [tex]\boxed{V = \dfrac{1}{3}\left( {\pi {r^2}h} \right)}.[/tex]
The surface area of the cone is [tex]\boxed{S=\pi \times r\times l}[/tex]
Here l is the slant height of the cone.
The value of the slant height can be obtained as,
[tex]\boxed{l = \sqrt {{h^2} + {r^2}} }[/tex].
Given:
The volume of the cone shaped paper drinking cup is [tex]36{\text{ c}}{{\text{m}}^3}[/tex].
Explanation:
The volume of the cone shaped paper drinking cup [tex]36{\text{ c}}{{\text{m}}^3}[/tex].
[tex]\begin{aligned}V&=36\\\frac{1}{3}\left({\pi {r^2}h}\right) &= 36\\{r^2}&= \frac{{108}}{{\pi h}}\\\end{aligned}[/tex]
The surface area of the cone is,
[tex]\begin{aligned}S &= \pi\times\sqrt {\frac{{108}}{{\pi h}}}\times\sqrt {{h^2} + \frac{{108}}{{\pi h}}}\\&= \sqrt{108}\times\sqrt{\frac{{\pi {h^3} + 108}}{{\pi h}}}\\&=\sqrt {108}\times\sqrt {\pi h + \frac{{108}}{{{h^2}}}}\\\end{aligned}[/tex]
Differentiate above equation with respect to h.
[tex]\dfrac{{dS}}{{dh}}=\sqrt {108}\times \left( {\pi - \dfrac{{216}}{{{h^3}}}}\right)\times {\left( {\pi h + \dfrac{{108}}{{{h^2}}}}\right)^{ - \dfrac{1}{2}}}[/tex]
Substitute 0 for [tex]\dfrac{{dS}}{{dh}}[/tex].
[tex]\begin{aligned}\pi- \dfrac{{216}}{{{h^3}}}&= 0\\\dfrac{{216}}{{{h^3}}}&= \pi\\\dfrac{{216}}{{3.14}} &= {h^3}\\h &= 4.10\\\end{aligned}[/tex]
The radius of the cone can be obtained as,
[tex]\begin{aligned}{r^2}&=\frac{{108}}{{\pi \left({4.10} \right)}}\\{r^2}&= \frac{{108}}{{3.14 \times 4.10}}\\{r^2}&= 8.40\\r&= \sqrt {8.40}\\r &= 2.90\\\end{aligned}[/tex]
Hence, the height of the cone is [tex]\boxed{4.10}[/tex]and the radius of the cone is [tex]\boxed{2.90}[/tex].
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Mensuration
Keywords: cone shaped paper, drinking cup, volume, [tex]36{\text{ c}}{{\text{m}}^3}[/tex], height of cone, cup, smallest amount of paper, water.
The area of one triangle is 150 square centimeters when it's height is 20 centimeters and it's base length is 15 centimeters. What is the area of a triangle having a height of 30 centimeters and a base length of 18 centimeters.
The sum of two consecutive even integers equals 6426?
At an aquarium, 6 out of 18 deliveries are plants. Out of 15 deliveries in one week,how many are plants?
Shelley spent 17 minutes washing dishes. She spent 38 minutes cleaning her room. Explain how you can use mental math to find how long Shelley spent on the two tasks.
Car rental at Q.T. Rental is $22 per day plus an initial deposit of $36.Which expression shows how much it will cost to rent a car for d number of days?
Answer:
The expression is Price = 36 +22*d where d is each day that pass.
Step-by-step explanation:
The inicial 36 are the independant term since it's not related to how many days the car is rented. 22 is the slope since it depends on the days the car is rented.
The bookstore ordered 15 Sociology work books and 10 Economy 101 textbooks on August 1st to prepare for the fall semester. After realizing they miscounted, the bookstore order 1 more Sociology workbook and three more Economy 101 textbooks on August 15th. If August 1st the order was for $4300 and the August 15th order was $800 , find the cost of one Sociology workbook and one Economy 101 textbook?
The cost of one Sociology workbook is $140, and the cost of one Economy 101 textbook is $220, determined by solving two simultaneous equations based on the initial and additional orders placed by the bookstore.
Explanation:To solve for the cost of one Sociology workbook and one Economy 101 textbook, let's label the cost of one Sociology workbook as S and the cost of one Economy 101 textbook as E. Initially, the bookstore ordered 15 Sociology workbooks and 10 Economy 101 textbooks, spending a total of $4300. This gives us the equation: 15S + 10E = 4300. Later, the store ordered an additional 1 Sociology workbook and 3 Economy 101 textbooks for $800, leading to the equation: 1S + 3E = 800.
To solve these equations simultaneously, we can multiply the second equation by 15 to get 15S + 45E = 12000 and subtract the first equation from it: (15S + 45E) - (15S + 10E) = 12000 - 4300, simplifying to 35E = 7700. Dividing both sides by 35 gives us E = 220. Substituting E = 220 back into the first equation 15S + 10(220) = 4300 gives us 15S + 2200 = 4300, thus 15S = 2100 and S = 140.
Therefore, the cost of one Sociology workbook is $140 and the cost of one Economy 101 textbook is $220.
61702 67102 same or different?
If the minimum value of the function y = cos θ + d is –5, the value of d is...
The value of d, when the function is at its minimum is -4.
What is a Function?A function is a law that relates two variables namely, a dependent and an independent variable.
A function always has a defined range and domain, domain is all the value a function can have as an input and range is all the value that a function can have.
The function is of various types, logarithmic, exponential, quadratic, radical etc.
The function is y = cos [tex]\rm \theta[/tex] + d
The minimum value of the function, y = cos [tex]\rm \theta[/tex] + d is -5.
The minimum value is the lowest value of the function.
The minimum value of cos [tex]\rm \theta[/tex] is at 180 degree equals to -1
Substituting the value in the equation.
-5 = - 1 + d
d = -5 +1
d = -4
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when I make macaroni and cheese for my brother and me, I use 2 2/3 tablespoons of butter. how much butter will I n need to make my macaroni and cheese dish for Thanksgiving dinner if 15 people are attending?
The Grand Prix Formula 1 race this weekend is in Singapore. The race consists of 61 laps around a 5.067 km long track. At 225 miles per hour, how long will it take to go around once?
In a survey of 3450 registered voters who reside in California, 1789 were found to be republican. Construct a confidence estimate for the true percentage of republicans among registered voters in California. Use a confidence level of 95%.
Assume that a procedure yields a binomial distribution with a trial repeated n times. use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. round to three decimal places. n = 14, x = 6 , p = 0.5
Write five numbers that round to 360 When rounded to the nearest 10.
Given the following triangle, if a = 12 and ∠B = 48°, find b to the nearest whole number.
Answer:
The value of b nearest whole number is, 13.
Step-by-step explanation:
We know an [tex]\angle B=48^{\circ}[/tex] and the side adjacent to it i.e, a=12.\
In a right triangle BCA ,
the tangent(tan) of an angle is the length of the opposite side divided by the length of the adjacent side.
i.e, [tex]\tan B=\frac{opposite}{Adjacent}=\frac{b}{a}[/tex]
Substitute the value of a=12 and [tex]\angle B=48^{\circ}[/tex] to solve for b in above expression:
[tex]\tan 48^{\circ}=\frac{b}{12}[/tex]
we have the value of [tex]\tan 48^{\circ}=1.110613[/tex]
then, [tex]1.20012724=\frac{b}{12}[/tex]
On simplify we get,
[tex]b=1.110613 \times 12=13.327356[/tex]
Therefore, the value of b nearest whole is, 13
A car uses 25L of petrol to travel 280km. What is the rate of petrol usage in kilometres per litre?
The rate of petrol per liter is 11.2 liter
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
In 25l car travels = 280km
For finding rate of petrol per liter we have to divide as
Rate of petrol = 280/25
Rate of petrol = 11.2 liter
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The rate of petrol usage for the car is 11.2 kilometers per litre, calculated by dividing the distance travelled, 280km, by the amount of petrol used, 25L.
The question asks to find the rate of petrol usage in kilometers per litre for a car that uses 25L of petrol to travel 280km. To calculate the fuel efficiency, you divide the distance travelled by the amount of petrol used.
Step-by-step calculation:
Distance travelled = 280 km
Amount of petrol used = 25L
Fuel efficiency (km/L) = Distance travelled / Amount of petrol used
Fuel efficiency = 280 km / 25L = 11.2 km/L
Therefore, the car's fuel efficiency is 11.2 kilometers per litre.