the length of a rectangle is given by 2t+1 and its height is t^(1/2), where t is time in sec. Find the rate of change of the area with respect to time
The figure shown is formed by the arcs joining the midpoints of the four sides of a square with a side length of 15 centimeters.
The area of the shape is __
square centimeters
What is the unit rate of max wrote 10 pages of his lab report in 4 hours?
Mary and tom were buying a present for their mother on mothers day. mary spent $12 and tom spent $28 if they wanted to share the cost equally, how much money does mary owe tom?
Problem Page A car is traveling at a rate of 63 miles per hour. What is the car's rate in feet per second? How many feet will the car travel in 15 seconds? In your computations, use the fact that 1 mile is equal to 5280 feet. Do not round your answers.
Consider the level surface given by
x2−y2+z2=2. Draw a picture for the following:
1. Slice for y=2
2. Slice for x=1
3. Slice for y=0
4. Slice for x=2 ...?
Answer:
First of all, each slice represents an intersecting plane at that level.
For example, y = 2 is a plane that passes thorugh that level and cuts the volume given by [tex]x^{2} -y^{2}+z^{2}=2[/tex]
1. Slice for y = 2.We replace this value in the given volume.
[tex]x^{2} -y^{2}+z^{2}=2\\x^{2} -(2)^{2}+z^{2}=2\\x^{2}+z^{2}=2+4\\x^{2}+z^{2}=6[/tex]
So, results in a circumference with radius [tex]\sqrt{6}[/tex], because a circumference is defind as [tex]x^{2} +y^{2} =r^{2}[/tex]. (On plane XY).
2. Slice for x = 1.We repeat the process.
[tex](1)^{2} -y^{2}+z^{2}=2\\z^{2}-y^{2}=2-1\\z^{2}-y^{2}=1[/tex]
It forms a horizontal hyperbola on plane ZY.
3. Slice for y = 0.[tex]x^{2} -0^{2}+z^{2}=2\\x^{2}+z^{2}=2[/tex]
Another circle with radius of [tex]\sqrt{2}[/tex] on plane XZ.
4. Slice for x = 2.[tex](2)^{2} -y^{2}+z^{2}=2\\z^{2}-y^{2}=2-4\\z^{2}-y^{2}=-2\\\frac{z^{2}-y^{2}}{-2} =\frac{-2}{-2} \\\frac{y^{2} }{2} -\frac{z^{2} }{2} =1[/tex]
It forms a hyporbola on plane YZ.
you are studying for your final exam of the semester. up to this point,you recieved 3 exam scores of 83%,85%, and 84%. to recieve a grade of B in the class you must average exam score between 80% and 89% for all 4 exams including the final.
Find the widest range of scores that you can get on the final exam in order to recieve a grade of B for the class.Use interval notation ...?
Answer:
The widest range lies between [68,100]
Step-by-step explanation:
Given is - to receive a grade of B in the class you must average exam score between 80% and 89% for all 4 exams including the final.
So, the range of the addition of all 4 scores is -
[tex]80*4=320[/tex]
[tex]89*4=356[/tex]
Now given scores addition is = [tex]83+85+84=252[/tex]
Now, the widest range of scores that you can get on the final exam in order to receive a grade of B can be found as :
[tex]320-252= 68[/tex]
[tex]356-252= 104[/tex]
So, the range lies between [68,100]
Which shows the expression below in simplified form?
(7.4 × 10^-1) - (4.1 × 10^-4)
A. 7.3959 × 10^-1
B. 7.39959 × 10^-1
C. 7.359 × 10^-2
D. 7.3959 × 10^-2
Alan is putting weed killer on a field to get it ready for planting. The directions on the can say to use 4/5 of a quart for each acre of land. How much weed killer will Alan need for two fields, one that is 22 1/2 acres and one that is 38 1/4 acres?
28 1/8 quarts
47 4/5 quarts
60 3/4 quarts
48 3/5 quarts
100, 96, 104, 88, 120, 56, ? what comes next? here are the choices (184, 140, 77, 124, 128)
What is the value of the underlined digit in the number 1,711,799 with the lst 7 being underlined
In the context of the number 1,711,799, the first 7 underlined is in the hundred thousands position, which gives it a value of seven hundred thousand (700,000).
Explanation:In the given number 1,711,799, we're asked to find the value of the first underlined 7. Considering the location of the number, 7 is in the hundred thousands position. The value of a digit depends on its place in the number. Therefore, despite the fact that the digit is '7', because it is in the hundred thousands place, its value is seven hundred thousand (700,000).
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The scientific notation 2.15 × 10-3 has what value?
Answer:
The scientific notation 2.15 × 10-3 has a value of
0.00215
Step-by-step explanation:
Step one
This problem bothers conversion from standard form otherwise known as scientific notation to decimal form
Step two
Now we are presented with the expression
2.15 × 10-³
To convert this it is equivalent to
2.15/10³= 2.15/1000
= 0.00215
On the other hand this can also be achieved without calculations by visually counting from the decimal point to the right 2 placements before inserting the first integer
This method saves alot of time expecialy when time is of essence.
Hence the scientific notation 2.15 × 10-3 has a value of
0.00215
what is the five non zero multiples of 5
The first five non-zero multiples of 5 are 5, 10, 15, 20, and 25. These are obtained by multiplying the number 5 by the integers 1 to 5. All non-zero multiples of 5 will end with the digit 5 or 0, confirming their divisibility by 5.
Identifying Non-Zero Multiples of 5
When you're looking for non-zero multiples of 5, it's important to remember that the basic property of a multiple of 5 is that it ends in either 0 or 5. However, since we're focusing on non-zero multiples, we will exclude any multiples that end in zero. A multiple of a number is obtained by multiplying that number by an integer. For the number 5, the first five non-zero multiples are 5, 10, 15, 20, and 25. Notice that these numbers are the result of multiplying 5 by the integers 1 through 5, respectively.
Understanding that the concept of multiples relates to a number being multiplied by a sequence of whole numbers or integers gives us the ability to identify patterns within these numbers. For example, all non-zero multiples of 5 will end with the digit 5 or 0, reinforcing the idea that if a number ends in 5, it is divisible by 5 without remainder. This concept is supported by empirical observation and the understanding that patterns and numbers, such as these, can offer insight into broader mathematical ideas. Furthermore, the significance of the number 5 in various mathematical circumstances, such as the number of digits in a number or the properties of multiples, is apparent throughout different contexts.
which of the following r one dimensional figures?
check all that apply.
a. ray
b. angle
c. square
d. point
e. segment
f. line
Answer: Segment, line, ray
Step-by-step explanation: too answer was confusing and point was wrong.
The answers are a. ray, e. segment and f. line
In geometry, a one-dimensional figure has only length and no other dimensions such as width or height. Let's analyze each option:
Ray - A ray is one-dimensional as it starts from a point and extends infinitely in one direction.Angle - An angle is formed by two rays meeting at a point, which makes it not one-dimensional.Square - A square is a two-dimensional figure with length and width.Point - A point has no dimensions; it is zero-dimensional.Segment - A segment is one-dimensional as it consists of two endpoints and the line connecting them.Line - A line is one-dimensional as it extends infinitely in both directions.Thus, the one-dimensional figures are the ray, segment, and line.
solve.
3/4x=18 please show work ...?
what would the answer to -|-24| be?
Which of the following equations could be used to solve for the tenth term of the following sequence?
15, 13, 11, 9, ...
A(10) = 15 + 10(-2)
A(10) = 15 + 9(-2)
A(10) = 15 + 9(2)
A(10) = 15 + 10(2)
Answer:
Option(B) is correct.
The tenth term is given by [tex]a_{10}=15+9(-2)[/tex]
Step-by-step explanation:
Given : The sequence 15, 13, 11, 9,....
We have to determine the equation that can be used to find the tenth term of the given sequence 15, 13, 11, 9,....
Consider the given sequence 15, 13, 11, 9,..
[tex]a_1= 15, a_2=13, a_3= 11[/tex]
Difference between each term is
[tex]a_2-a_1=13-15=-2\\ a_3-a_2=11-13=-2[/tex]
Since, The difference between each term is constant -2
Thus, The given sequence is an arithmetic sequence with first term 15 and common difference -2.
Thus, The general term is given by
[tex]a_n=a+(n-1)d[/tex]
where a is first term and d is common difference nd n is number of term.
Subsitute, we have,
[tex]a_{10}=15+(10-1)(-2)[/tex]
Simplify, we have,
[tex]a_{10}=15+9(-2)[/tex]
Thus, The tenth term is given by [tex]a_{10}=15+9(-2)[/tex]
The function t(n)=8n represents the number of tires t(n) that are needed for n trucks. How many tires are needed for 25 trucks? A.32 tires B.150 tires C.200 tires D.250 tires
The function t(n)=8n represents the number of tires needed for each truck. By substituting n=25 into the function, we find we need 200 tires for 25 trucks.
Explanation:The function that represents the number of tires needed for each truck is t(n) = 8n. This means for each truck we need 8 tires, as n is the number of trucks and 8n signifies the total number of tires needed for those trucks.
If we want to find out the number of tires we would need for 25 trucks, we substitute n = 25 into the function, yielding t(25) = 8 * 25. When you perform this multiplication, the result is 200 tires.
So, for 25 trucks we would need 200 tires. Meaning "the correct answer is C. 200 tires".
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if Jane has 5 pairs of pants and 7 shirts, how many different combinations of pants and shirts are possible?
What is 2840 divided by 6 in long division
What is the answer to 86-11/11+4
What is the greatest common factor of 84 and 108?
√19 approximated to nearest tenth
2. A bowling alley charges $3.00 to rent shoes and $1.50 per game bowled.
If there is 7018 mm, what is the metric unit for 7.018?
What percent of 600 is 24?
What is the value of the function y = 2x + 3 when
x=−1
?
Solve for x. Type a numerical answer in the space provided. Do not use spaces in your answer. For example, if the answer is x = 15, type 15.
15x + 6 = 10x + 21
Which equations show that the set of whole numbers is not closed under subtraction?
Choose all answers that are correct.
A.
1 – (–2) = 3
B.
1 – 2 = –1
C.
2 – 0 = 2
D.
2 – 4 = –2
Find the x-coordinates of all points on the graph of: f(x)=6sinx-sin^2x
at which the tangent line is horizontal.
Final answer:
To find the x-coordinates where the function f(x)=6sin(x)-sin^2(x) has a horizontal tangent line, we calculate the derivative, set it equal to zero, and solve for x, using trigonometric identities and potentially numerical methods. Thus, the solutions for \( x \) in the interval [tex]\( [0, 2\pi] \) are \( x = \frac{\pi}{2} + k\pi \), where \( k \)[/tex] is an integer. These solutions represent the points where [tex]\( \cos(x) = 0 \)[/tex], causing the equation to be satisfied.
Explanation:
The question asks to find the x-coordinates of all points on the graph of the function f(x)=6sin(x)-sin2(x) at which the tangent line is horizontal. To find these coordinates, we need to look for points where the derivative of the function is equal to zero since a horizontal tangent line has a slope of zero.
We start by finding the derivative of the function:
f'(x) = d/dx[6sin(x)-sin2(x)]
f'(x) = 6cos(x)-2sin(x)cos(x)
f'(x) = 6cos(x)-sin(2x) (using the double angle identity sin(2x)=2sin(x)cos(x))
To find when the derivative is zero, we set the derivative equal to zero:
0 = 6cos(x) - sin(2x)
We then need to solve this equation for x. This involves using trigonometric identities and potentially numerical methods if the equation cannot be solved analytically. The x-coordinates will be the solutions to this equation within the domain for which we are interested, typically 0 to 2π for one full cycle of a trigonometric function.
To solve the equation [tex]\( 0 = 6\cos(x) - \sin(2x) \)[/tex], we'll first try to rewrite it in terms of a single trigonometric function using known identities.
The double angle identity for sine states that [tex]\( \sin(2x) = 2\sin(x)\cos(x) \)[/tex]. Substituting this identity into the equation, we get:
[tex]\[ 0 = 6\cos(x) - 2\sin(x)\cos(x) \]\\Now, let's factor out \( \cos(x) \):\[ 0 = \cos(x)(6 - 2\sin(x)) \][/tex]
Now, for the equation to be true, either [tex]\( \cos(x) = 0 \) or \( 6 - 2\sin(x) = 0 \)[/tex].
1. If [tex]\( \cos(x) = 0 \), then \( x = \frac{\pi}{2} + k\pi \)[/tex], where \( k \) is an integer.
2. If [tex]\( 6 - 2\sin(x) = 0 \), then \( \sin(x) = 3 \)[/tex]. However, the sine function has a range of \([-1, 1]\), so there are no solutions for \( x \) in this case.
Thus, the solutions for \( x \) in the interval [tex]\( [0, 2\pi] \) are \( x = \frac{\pi}{2} + k\pi \), where \( k \)[/tex] is an integer. These solutions represent the points where [tex]\( \cos(x) = 0 \)[/tex], causing the equation to be satisfied.