The surface area of a sphere of radius r is
Write the curve equation associated to those parametric equations.x(θ) = 3 cos θy(θ) = 6 sin θ
We want to rewrite the following parametric equations
[tex]\begin{gathered} \begin{cases}x={3\cos\theta} \\ y={6\sin\theta}\end{cases} \\ \frac{\pi}{2}<\theta<\frac{3\pi}{2} \end{gathered}[/tex]as one equation. Using the following property
[tex]\sin^2\theta+\cos^2\theta=1[/tex]We can eliminate the parameter theta adding the square of the coordinates
[tex]\begin{gathered} \sin^2\theta+\cos^2\theta=1 \\ 6^2(\sin^2\theta+\cos^2\theta)=6^2 \\ 6^2\sin^2\theta+6^2\cos^2\theta=6^2 \\ (6\sin\theta)^2+(6\cos\theta)^2=6^2 \\ (6\sin\theta)^2+(2\cdot3\cos\theta)^2=6^2 \\ (y)^2+(2x)^2=6^2 \\ y^2+4x^2=36 \\ \frac{x^2}{9}+\frac{y^2}{36}=1 \end{gathered}[/tex]And this is the standard equation of an ellipse
[tex]\frac{x^{2}}{9}+\frac{y^{2}}{36}=1[/tex]The constrain
[tex]\frac{\pi}{2}<\theta<\frac{3\pi}{2}\implies x<0[/tex]tells us that x can only assume negative values, therefore, the graph is only the left side of the ellipse.
Which equation is equivalent to −(5−x)=5−x? Responses −5−x=5−x − 5 − x = 5 − x −5+x=5−x − 5 + x = 5 − x 5−x=5−x 5 − x = 5 − x 5+x=5−x
The equation is equivalent to −(5−x) = 5−x is -5+x = 5-x
The given equation −(5−x) = 5−x
The distributive property states that multiplying the sum of two or more variables by a number gives the same result as when each variable is multiplied individually by the number and the products are added together.
The distributive property of addition
A(B+C) = AB + AC
The distributive property of subtraction
A(B-C) = AB - AC
The given equation is −(5−x) = 5−x
Apply distributive property in the equation
−(5−x) = 5−x
-5+x = 5-x
Hence, The equation is equivalent to −(5−x) = 5−x is -5+x = 5-x
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Find the distance between each pair of points. Round youranswer to the nearest tenth, if necessary.(7, 6), (0, 2)
Chris, this is the solution to the exercise:
• Point 1 = (7, 6)
,• Point 2, (0, 2)
Now, let's use the formula to calculate the distance between the two points, as follows:
d = √(0 - 7)² + (2 - 6)²
d = √-7² + (-4)
d = √49 + 16
d = √65
d = 8.0622
d = 8.1 (rounding to the nearest tenth)
Simplify the following exponent (x¹⁰ ÷ x²) x x³
Answer:
x^6
Step-by-step explanation:
Given X¹⁰ ÷ (x² X x³ ÷ x) : Simplify.
We know the law of exponents which states that
a^m x a^n = a^m + n
a^m / a^n = a^m - n
So the problem is x^10 / (x^2 x x^3 / x)
So we have x^10 / x ^5 / x
x ^10 / x ^5 - 1
x^10 / x^4
x ^10 -
x^6
After simplifying we get x^6
Will mark as brainlist
Which of the following best represents R= A - B ?
Please help, it’s due soon!
Answer: I would say it is C
Step-by-step explanation: If you think about it, if you have a pencil and the pencil is in A form, and you have to put it to B form, it kinda makes sence. BUT, I honestly don't know, so don't trust me...
GL LUCK THO AND GOD BLESS
Dean started with 5 metersof yarn. He used 300millimeters of yarn each dayfor 5 days. How manymeters of yarn does Deanhave left?
Given:
Dean started a yarn with 5 meters. He used 300millimeters of yarn each day for 5 days.
Required:
Find how many meters of yarn Dean has left.
Explanation:
We know that 1 meter = 1000milimeters
Dean used meters of yarn in the five days
[tex]\begin{gathered} =\frac{300\times5}{1000} \\ =\frac{3}{2}\text{ meter} \end{gathered}[/tex]The left meters are:
[tex]\begin{gathered} =5-\frac{3}{2} \\ =\frac{10-3}{2} \\ =\frac{7}{2} \\ =3.5 \end{gathered}[/tex]Final Answer:
Thus 3.5 meters of yarn left
(d) Find the domain of function R. Choose the correct domain below.
Answer:
d
Step-by-step explanation:
The number of years must be non-negative.
This eliminates all of the options except for d.
Identify the parent function for the function g (x) = x+9 from its function rule. Then graph g and identify what transformation of the parent function it represents.
The parent function of g(x) = x + 9 is the function f(x) = x.
The function f(x) = x is a linear function, that is, it has degree 1 (the higher exponent of the variable x is 1).
In order to get g(x) from f(x), we can see that the function value was increased by 9 units:
[tex]g(x)=f(x)+9[/tex]Adding 9 units to the function means we have a translation of 9 units up.
Therefore the correct option is the third one.
Graphing g(x), we have:
If $8^7)^2 = 2^y, what number is y?
The value of y based on the information given about the expression (8^7)² = 2^y is 21.
How to illustrate the information?It should be noted that based on the information, the power rule will be essential. This will be illustrated thus:
(8^7)² = 2^y
It should be noted that 8 = 2 × 2 × 2 = 2³
Therefore, 8^7 = 2^(3 × 7) = 2^21
Therefore, the value of y is 21.
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(NEED ANSWER ASAP) Tom and Jessica are going to Disneyworld. Snacks are EXPENSIVE there. They each got a Mickey ice cream, and Jessica also got cotton candy. Tom only had $9, so Jessica paid for the rest, which was $4. The ice cream cost $5 each, what was the cost of the cotton candy? Write an equation to represent the word problem and solve it. (Show all of your steps)
The cost of the cotton candy that Jessica purchased is $3.
What is the cost of candy?The first step is to determine total amount spent on snacks. The total amount spent is the sum of the amount paid by Tom and Jessica.
Total amount spent = $9 + $4 = $13
Two ice creams and one cotton candy is bought. This can be represented with:
$13 = total cost of ice cream + cost of the cotton candy
$13 = (2 x$5) + c
$13 = $10 + c
c = $13 - $10
c = $3
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Simplify completely (7x²+11x-6)/(7x²-10x+3)
One way of simplifying the given expression is by factoring them, and then simplifying the common terms.
So, we need to write:
[tex]\begin{gathered} 7x^{2}+11x-6=7(x-a)(x-b) \\ \text{and} \\ 7x^{2}-10x+3=7(x-c)(x-d) \end{gathered}[/tex]The constants a and b are the zeros of the first expression, and the constants c and d are the zeros of the second expression.
So, we can find those zeros using the quadratic formula. We obtain, for the first expression:
[tex]\begin{gathered} x=\frac{-11\pm\sqrt[]{11^{2}-4(7)(-6)}}{2(7)} \\ \\ x=\frac{-11\pm\sqrt[]{289}}{14} \\ \\ x=\frac{-11\pm17}{14} \\ \\ a=\frac{-11-17}{14}=-2 \\ \\ b=\frac{-11+17}{14}=\frac{6}{14}=\frac{3}{7} \end{gathered}[/tex]And, for the second expression, we obtain:
[tex]\begin{gathered} x=\frac{-(-10)\pm\sqrt[]{(-10)^{2}-4(7)(3)}}{2(7)} \\ \\ x=\frac{10\pm\sqrt[]{16}}{14} \\ \\ x=\frac{10\pm4}{14} \\ \\ c=\frac{10-4}{14}=\frac{6}{14}=\frac{3}{7} \\ \\ d=\frac{10+4}{14}=1 \end{gathered}[/tex]Then, we can write:
[tex]\begin{gathered} 7x^2+11x-6=7(x-(-2))(x-\frac{3}{7})=7(x+2)(x-\frac{3}{7}) \\ \\ 7x^2-10x+3=7(x-\frac{3}{7})(x-1) \end{gathered}[/tex]Thus, the given function can be simplified as follows:
[tex]\frac{7x²+11x-6}{7x²-10x+3}=\frac{7(x+2)(x-\frac{3}{7})}{7(x-\frac{3}{7})(x-1)}=\frac{x+2}{x-1}[/tex]Therefore, the answer is:
[tex]\mathbf{\frac{x+2}{x-1}}[/tex]Answer this graph based Question I will provide you 50 points + make you brainliest.
Part a: The value of y is 11 for x = 2.
Part b: The graph for the function y = x² + 4x -1 is drawn.
Part c: Range; (-∞,-3.75]∪[-0.25,∞)
Part d: The function is y = -5 - (x + 2)².
Part e: The approximate value of √3 is 1.732.
What is defined as the term function?A function is an expression, rule, or law in mathematics that defines a relationship between one dependent variable (a independent variable) and also one more variable (the dependent variable). Functions are common in mathematics and are required for the formulation of actual relationships with in sciences.For the given function;
y = x² + 4x -1, the values of y for the corresponding x is given in tables shown.
Part a: value of y when x = 2.
Put x = 2 in the function;
y = x² + 4x -1
y = 2² + 4×2 -1
y = 11
The value of y is 11 for x = 2.
Part b: The graph for the function y = x² + 4x -1 is drawn using the scale of 10 small divisions as 1 unit along x and y axis.
Part c: Range of value of x for which y ≥ -2.
Locate the point of x from the graph for which the value of y y ≥ -2.
Range; (-∞,-3.75]∪[-0.25,∞)
Part d: The function in the form of y = k - (x - h)², where k and h are the vertex.
The vertex from the graph is found as (-2, -5) (h, k)
Putt in the equation;
y = k - (x - h)²
y = -5 - (x - (-2))²
y = -5 - (x + 2)²
Part e: 2 - √3 is the root of the equation 0 = x² + 4x -1.
It 2 - √3 is the root of the equation, then by putting this value at x the equation becomes zero.
The approximate value of √3 is 1.732 which is found by long division method.
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8.1÷0.9+0.4^(3)÷0.8×30
Answer:
11.4
Step-by-step explanation:
Answer:
11.4
p.s you try it may help
Bobby can work at most 20 hours next week, but she needs to earn at least $150. Herdog-walking job pays her $6 per hour and her iob as a car wash attendant pays her $10 perhour. If d is the number of hours she walks dogs this week and w is the number of hours sheworks at the car wash, write a system of inequalities that represents Bobby's situation.
Solution:
Let d represent the number of hours Bobby walks dogs,
and w be the number of hours she works at the car wash.
Given that she can work at most 20 hours next week, this implies that the total number of hours she works is expressed as
[tex]d+w\leq20[/tex]If her dog-walking job pays her $6 per hour, this implies that for d number of hours, she will earn
[tex]\begin{gathered} \frac{\$6}{1\text{ hour}}\times d\text{ hours} \\ =\$\text{ 6d} \end{gathered}[/tex]and her iob as a car wash attendant pays her $10 per hour, similarly for w number of hours, she will earn
[tex]\begin{gathered} \frac{\$10}{1\text{ hour}}\times w\text{ hours} \\ =\$10w \end{gathered}[/tex]Given that she needs to earn at least $150, this implies that her total earnings will be expressed as
[tex]6d+10w\ge150[/tex]Hence, the system of inequalities that represents Bobby's situation is:
[tex]\begin{gathered} d+w\leq20 \\ 6d+10w\ge150 \end{gathered}[/tex]PLEASE AWNSER NOW Sandy uses three and one half pounds of clay to make 7 small vases. Use a proportion to find how many pounds of clay she will use to make 21 small vases.
7 and one fourth pounds
8 and one half pounds
10 and one half pounds
14 and one fourth pounds
Answer:
The answer is 10 and one half pounds
Explanation:
3.5/7 = 2
21/2 = 10.5
10 and one half pounds use to make 21 small vases.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Sandy uses clay= 3 1/2 pounds for 7 vase
So, for 1 vase amount of clay used
= 7/2 x 1/7
= 1/2 pounds
Now, for 21 small vases amount of clay used
=21 x 1/2
= 21/2
= 10 1/2 pounds.
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S = 1/3 x pi x r^2 + pi x r^2 x h
The solved equation for h is h= S/ pi x r^2-1/3.
The problem we are dealing with here is related to the literal equation, where a literal equation is an equation that comprises basically letters. Formulas are an illustration of strict equations. Each variable within the condition "truly" speaks to an important part of the full relationship expressed by the equation. To illuminate a literal equation implies modifying the equation so a different variable stands alone on one side of the equals sign. We got to be told which variable we need to solve.
For the given equation,S= 1/3 x pi x r^2 + pi x r^2 x h
for th the equation will be
=>S= pi x r^2(1/3 +h)
=>S/ pi x r^2= 1/3+h
=>h= S/ pi x r^2-1/3
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S = 1/3 x pi x r^2 + pi x r^2 x h , solve for h
You invest $275 to start a sandwich stand and decide to charge 515 per sandwich set of a linear model that determines your profit or loss based on the number of sandwiches
The linear model that determines your profit or loss based on the number of sandwiches is 15y-275, where y is the number of sandwiches sold.
What is a linear model?A continuous response variable is described as a function of one or more predictor variables in a linear model. They can assist you in comprehending and forecasting the behaviour of complex systems, as well as analyzing experimental, financial, and biological data. Linear regression is a statistical technique for developing a linear model.
It is given that the investment amount is $275.
The charge per sandwich is $15
So, generated revenue= 15 y
where y is the number of sold sandwiches.
Profit/ Loss= Revenue- total investment= 15y-275
So, the linear model determining the profit or loss is 15y-275, where y is the number of sandwiches.
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What is the slope of a line perpendicular to the line whose equation is x+4y=16. .
Answer:
The slope is [tex]-\frac{1}{4}[/tex].
Step-by-step explanation:
This is the slope formula equation.
[tex]y=mx+b[/tex]
[tex]x+4y=16[/tex]
First, you divide the entire equation by 4 to get rid of the 4 in 4y.
[tex]\frac{x}{4} +y=4[/tex]
Then, you subtract [tex]\frac{x}{4}[/tex] on both sides.
[tex]y=-\frac{x}{4} +4[/tex]
In front of the x should be and invisible 1. So this should be your slope.
[tex]m=-\frac{1}{4}[/tex]
Your phone plan charges you an initial fee, and then a certain amount depending on the amount of data you use. They send you periodic updates of your usage andyour current bill cost. After using 3 GB of data you owe $30. After 5 GB of data, you owe $40. What is the initial fee prior to the data usage charge?A.$15B.$5C.$2.50D.$10
If for 3 Gb we get a bill for $30 and for 5 Gb we get a bill of $40. It implies that every Gb costs $5, therefor the equation we have use 3 Gb is
[tex]30=3\cdot5+b[/tex]where b is the initial fee. Solving this for b we get that
[tex]b=30-15=15[/tex]so the initial fee is $15
Write the correct inequality for the following statement and then solve for the given number of
guests.
You are in charge of planning your mother's surprise party. You have
found a hall that rents for $225 and a caterer that will charge you $15 per
guest. Write an inequality to calculate your total cost (T) based on the
number of guests (g).
If you have a total budget of $1000 how many guests can you
invite?
The inequality that can be used to calculate total cost (T) based on the number of guests (g) is 225 + 15g ≤ 1000.
If you have a total budget of $1000, 51.67 guests can be invited.
How to write inequality equation?Cost of hall rent = $225Caterer's charge per guest = $15Total cost = TNumber of guests = gTotal cost = Cost of hall rent + Caterer's charge per guest(Number of guests)
225 + 15g ≤ T
If you have a total budget of $1000
225 + 15g ≤ T
225 + 15g ≤ 1000
substract 225 from both sides15g ≤ 1000 - 225
15g ≤ 775
divide both sides by 15g ≤ 775 / 15
g ≤ 51.66666666666666
Approximately,
g ≤ 51.67
So therefore, the inequality to represent the situation is 15g ≤ 1000 - 225 and about 51.67 guests can be invited if you have a budget of $1000
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1. Round to the nearest thousand. Use the number line to model your thinking.
9,340=
After rounding off the number we get ; 9,300
What does rounding off to thousand mean?When a number is rounded to the closest thousand, it is changed to an approximated value that is simpler to recall and utilize. The closest value to the supplied integer is this value, which is a multiple of 1000. For instance, 342984 becomes 343000 if it is rounded to the closest thousand.
So as in this question the number given is 9340
Since we have to round it off to thousands
and the number next to 9 is 3
Thus we can say that after rounding off the number will be
9,300.
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Factoring binomials math
we have the expression
[tex]x^3-125[/tex]we have that
x=5 is a zero of the given equation
so
Divide x^3-125 by (x-5)
x^3-125 : (x-5)
x^2+5x+25
-x^3+5x^2
---------------
5x^2-125
-5x^2+25x
------------------
25x-125
-25x+125
----------------
0
therefore
x^3-125=(x-5)(x^2+5x+25)
the answer is the fourth optionSee question below. I am not sure how to set this up.
Answer and Explanation:
Let x represent the number of hours Sandy needs to work.
We can go ahead and set up the required inequality as shown below;
[tex]150<10x+20<200[/tex]Let's go-ahead and determine x by splitting the compound inequality above as shown below;
[tex]\begin{gathered} 150<10x+20 \\ 150-20<10x \\ 130<10x \\ x>\frac{130}{10} \\ x>13 \end{gathered}[/tex][tex]\begin{gathered} 10x+20<200 \\ 10x<180 \\ x<\frac{180}{10} \\ x<18 \end{gathered}[/tex][tex]13We can see from the above that Sandy needs to work between 13 and 18 hours to be able to meet her goal.Hiro picks up four digits card, he says: I can make a multiple of 10 with these cards. I can also make a number that rounds to 5300 and a number where the digit 8 is worth 800?
If g(x) = -4x + 5, what is the value of (g o g) (3)?
A -7
B 48
C -23
D 33
Answer:
A. -7
Step-by-step explanation:
g(x) = -4x+5
We know that g(x)= (3) so just substitute 3 for x.
g(3)= -4(3)+5
g(3)= -12+5
g(3)=-7 answer.
Far from home: A survey asked first-year college students, “How many miles is this college from your permanent home?” Students had to choose from the following options: 5 or fewer, 6 to 10, 11 to 50, 51 to 100, 101 to 500, or more than 500. The side-by-side bar chart shows the percentage of students at public and private 4-year colleges who chose each option.
The average distance between students in public is smaller than that in private.
While the data for the public appears to closely follow a bimodal distribution, the data for the private appears to be negatively skewed, meaning that the tail is lopsided to the left. However, it might be nearly symmetrical. While the modal class for the public is 11–50, it is 101–500 for private.
While the mean for public data is close to 50, it is close to 100 for private data.
Therefore, it is clear from the graphs that students' average distances from Public are closer than those from Private.
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64,32,16,8 what is the next three terms of it? (no negatives)
Notice that each new term is half the previous one. For example, 32 is half 64, 16 is half 32, and so on.
Having said that, the constant ratio is 1/2. Using this ratio we can find the next three terms.
[tex]\begin{gathered} 8\cdot\frac{1}{2}=4 \\ 4\cdot\frac{1}{2}=2 \\ 2\cdot\frac{1}{2}=1 \end{gathered}[/tex]Therefore, the next three terms are 4, 2, and 1.Describe the graph of the quadratic function f (x) = -3x^2+ 6x + 5 by stating whether it opens upward or downward and stating how it is stretched or compressed when compared to the parent quadratic functionA. The parabola opens downward. It is compressed shorter by a factor of 3.B. The parabola opens upward. It is stretched taller by a factor of 3.C. The parabola opens downward. It is stretched taller by a factor of 3.D. The parabola opens upward. It is compressed shorter by a factor of 3.
Answer:
B. The parabola opens upward. It is stretched taller by a factor of 3.
Step-by-step explanation:
You want to know how the quadratic opens, and how it is stretched or compressed, given its equation is f(x) = -3x^2 +6x +5.
Leading coefficientThe "leading coefficient" is the coefficient of the highest-degree term. That term is -3x^2, and its coefficient is -3.
The minus sign tells you the parabola opens downward.
The magnitude of 3 tells you the parabola is stretched vertically (taller) by a factor of 3.
What is the factored form of the polynomial?x^2 + 2x - 24
Let's try to factorize this polynomial
[tex]x^2+2x-24=(x+)(x-)[/tex]in the blank spaces we have to put numbers that multiplied are 24, and substracted are +2. So we have 6 and 4
[tex]x^2+2x-24=(x+6)(x-4)[/tex]So the factored form of the polynomial is (x+6)(x-4)
i need help asap!!! im bad at graphing
Points are (1, -3)
What is equation?In algebra, an equation is a declaration of equivalence that includes one or more variables or unknowable quantities. In mathematics, an equation is a relationship between two expressions that is expressed as an equality on each side of the equal to sign. An equation would be 3y = 16, for instance.
Given Data
Slope = -[tex]\frac{1}{2}[/tex]
Points (-1, -5)
The line's general equation is y=ax+b.
Since we are aware that the slope is -[tex]\frac{1}{2}[/tex], an is equal to -[tex]\frac{1}{2}[/tex].
We also understand that if x = -1, then y = -5.
Let's connect it:
-5=1*(-1)+b
-5=-1+b
b= -4
So, y=x -4 is the line's equation.
Let x = 1
y = 1 - 4
y = -3
(1, -3)
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