The difference between fundamental theorem of calculus part 1 and 2 is explained below:
What is fundamental theorem of calculus?The basic theorem of calculus is a theorem that connects the ideas of differentiating and integrating functions. A constant value that relies on where one begins to compute area makes the two procedures the inverses of one another. The relationship between the integral and derivative is established by the calculus fundamental theorem. Simply put, it says that the height of the area at a point x equals the rate of change of the area under the curve up to that point. We can find definite integrals with the aid of this theorem.
The connection between the integral and the derivative is demonstrated in The Fundamental Theorem of Calculus, Part 1. Take note. A definite integral can be assessed in terms of an antiderivative of its integrand using the Fundamental Theorem of Calculus, Part 2. This formula will calculate the total area under a curve.
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-5 = t + 6 1/3 solve for t
Answer: t=-34/3 or -11 1/3
Step-by-step explanation:
isolate t
t+19/3=-5
subtract both sides with 19/3
t=-34/3 or -11 1/3
Answer:
-34/3
Step-by-step explanation:
-5=t+6 1/3
6 1/3= 19/3
-5=t+19/3
-t. -t
-5-t=19/3
+5. +5
-t=34/3
/-1. /-1
t= - 34/3
A surveyor determines that the angle of elevation to the top of a building from a point on the ground is 31.3. He then moves back 57.9 feet and determines that the angle of elevation is 23.5°. What is the height of
the building?
Round your answer to four decimal places
Answer:23 203 feet
Step-by-step explanation:
2 times 50 find the product or quotient
Answer:
product is the answer good luck on your test
what is 2⅘ equivalent to?
Answer:
2.8
Step-by-step explanation:
Answer:
2.8
Step-by-step explanation:
4/5ths is just .8 in fraction form. Add it on to your 2 and you've got your answer.
If 2 sides of a triangle are 10 and 20, what is the possible range of the 3rd side?
Answer:10<x<30
Step-by-step explanation:
According to the triangle side theorem all you need to do is this.
Difference of the two sides<x<Sum of the two sides.
That will give you the range your looking for. For the difference always remove the smaller number from the bigger number so you can always have positive integers.
Answer: 10<x<30
Step-by-step explanation: The third side of the triangle has to be greater than the difference of the other two sides and smaller than the sum of the other two sides.
Find x in this equation
Answer:
5
Step-by-step explanation:
[tex]\triangle HBK \cong \triangle NBK[/tex] by SAS. Using CPCTC, [tex]3x=x+10 \implies 2x=10 \implies x=5[/tex].
My new dog! Wanted to show him off cause he’s adorable
Answer: So Cute!
Step-by-step explanation:
Answer:
Yes. I also think he is adorable.
If you good w functions come help me out
Answer: Number one is a function
Number two is not a function
Number three is a function
Step-by-step explanation:
An easy way to determine functions in situations like these is to look and see if there are multiple outputs for the same X. If there are it is not a function. There can be multiple X values that go to the same Y value however.
quadratic equation in standard form:
17=5-6 z-z²
Answer:
i think z would be 17
Step-by-step explanation:
Question 1: Find the percent of change to the nearest tenth of a percent for Centerville
Question 2: Which town had the greatest percent of change
Question 3: What was the percent of change? (From your answer in Part B) Do Not Include 'Increase' or 'Decrease.' Round to the nearest whole percent.
Answer:
Sorry just trying to get points
find the equation of the straight line passing through the point (3, 5) which is perpendicular to the line y=3x+2
what is y
The equation of the line is y = -x/3 + 6.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction
We have the line y = 3x + 2
The slopes of perpendicular lines are negative reciprocals of each other.
The slope of the given line is m=3 the slope of the perpendicular line is -1/3.
Then the equation of the line;
y = -x/3 + b
And b is the y-intercept of the perpendicular lines passes through the point
(3,5).
Substituting the (3, 5) to the required line;
5 = -3/3 + b
b = 6
Now the line is y=-x/3 + 6
Therefore, the equation of the line is y = -x/3 + 6.
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Is 70/100 equal to 7/10?
Answer:
Yes
Step-by-step explanation:
A simple way to know is by simplifying them.
70/100 divided by 10 is 7/10
First divide 70 by 10: you get 7
Then divide 100 by ten: you get 10
Question 1 of 10
What is the value of x?
35⁰
70⁰
⇒Sum of interior angles of a triangle is 180°
⇒ The above statement means that
[tex]70+35+x=180[/tex]
⇒Solving for x :
[tex]105+x=180\\x=180-105\\x=75[/tex]
∴ x=75°
Option D is the answer.
Write an equation of a line with the given slope and y-intercept.
m = 1, b = 4
Answer: " y = x + 4 ".
Step-by-step explanation:
We shall write the equation of a line written in slope-intercept format;
that is, " y = mx + b " ;
in which y is isolated as a single variable on the 'left-hand' side of the question, and with no "coefficient"—
{except for the implied coefficient of 1 }; and:
m refers to the slope of the line—and is the coeffcient of x ;
and b refers to the y-intercept—or more specifically, the value of the y-coordinate when "x = 0" [i.e. the value of the y-coordinate where the line crosses the x-axis].
So: We can plug the given values: m = 1 ; and b = 4 ; into the equation:
" y = mx + b " ; as follows:
→ y = 1x + 4 ; Note: By convention, we often omit the 1 as the coefficient of x —since the 'stand-alone' variable, x ; has an implied coefficent of x ; and we can write the equation:
→ y = x + 4 ; which is our answer.|
______
Hope this is helpful to you! Best wishes!
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Given the following table of values of the polynomial f(x), what is the minimum number of zeros of f(x) that are guaranteed to exist by the Intermediate Value Theorem?
The number of zeros of f(x) that are guaranteed to exist by the Intermediate Value Theorem is given as follows:
0.
What is the Intermediate Value Theorem?The intermediate value theorem defines that if a continuous function passes in two points, it will pass through all the points between these two values.
The zeros of a function are all the values of x for which the function assumes a value of zero.
Hence, if for a value of x = a the function is positive, and then for a value of x = b > a the function is negative, or vice versa, a zero is guaranteed to exist in the interval between a and b.
In this problem, the function does not assume any negative values, hence a zero is not guaranteed to exist in the function, and the number is of zero.
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Subtract the expressions.
Pls help asap
(8.21n − 5.3) − (7 + 11.8n)
−3.59n − 12.3
−35.90n − 4.8
13.51n − 4.8
20.01n + (−12.3)
Answer:
I will gladly help (see explanation)
Step-by-step explanation:
1. 8.21n−5.3−(7+11.8n)
Distribute the Negative Sign:
=8.21n−5.3+−1(7+11.8n)
=8.21n+−5.3+(−1)(7)+−1(11.8n)
=8.21n+−5.3+−7+−11.8n
Combine Like Terms:
=8.21n+−5.3+−7+−11.8n
=(8.21n+−11.8n)+(−5.3+−7)
=−3.59n+−12.3
(Hope his helped, Good Luck! )
Answer:
-3.59 - 12.3
Step-by-step explanation:
Algebraic ExpressionsAlgebraic Expressions are similar to numerical expressions but instead of just numbers, alphabet variables are being used as well.
Note: BODMAS rule applies to Algebraic Expressions as well.
Eg. 7x + 4 + 5y + 4x = 11x + 5y + 4
SolutionGiven from the question:
(8.21n - 5.3) - (7 + 11.8n)
= 8.21n - 5.3 - 7 - 11.8n
= 8.21n - 11.8n - 5.3 - 7
= -3.59n - 12.3
Therefore, the answer is -3.59 - 12.3.
HELP ASAP PLS AND USE THE ANSWERS GIVEN!
Simplify the expression.
negative 15 plus the quantity negative 3 and seven tenths plus 9 and 15 hundredths end quantity divided by 5 all times 3 squared minus 4 and 7 tenths
−13.16
−9.89
0.49
20.11
The value of the given Fraction expression is -6.93.
What is Fraction?
A fraction is a mathematical expression that represents the division of a whole number or quantity into parts. It is written as two separate numbers, a numerator and a denominator, separated by a slash. The numerator represents the number of parts being considered, and the denominator represents the total number of parts. Additionally, fractions can also represent parts of a whole number. For example, the fraction 1/2 represents one part of a whole number that has been divided into two equal parts. Fractions can also be combined to create a sum of parts.
So, we have
-15 - 3.7 + 9.15/5 * 3^2 - 4.7
Evaluate the quotient and the exponent
So, we have
-15 - 3.7 + 1.83 * 9 - 4.7
Evaluate the product
-15 - 3.7 + 16.47 - 4.7
Evaluate the sum and the difference
-6.93
Hence, the value of the given fraction expression is -6.93 (none of the options is correct)
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A school is arranging a field trip to the zoo. The school spends 778.88 dollars on passes for 28 students and 4 teachers. The school also spends 241.64 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
The total money spent on a pass and lunch for each student is $850.14.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division.
here,
As mentioned in the question, Passes for 28 pupils and 4 teachers cost the school $778.88 and the school also spends $241.64 on lunch for kids only.
Total number of person = 28 + 4
= 32
Cost per pass = 778.88 / 32
= $24.34
Total passes of students = 25 × 24.34 = 608.5
Total spend on lunch of student = 241.64
Total spend on lunch = 241.64 + 608.5 = $850.14
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five apple pies were shared equals by 12 people. How much pie did each pie
Answer:2.4
Step-by-step explanation:20 - 8.99 = 2.4
What is the value of K?
Answer:
0
Step-by-step explanation:
ik my math
The value of k in the solution [tex]x=\frac{5\pm i\sqrt{k}}{8}[/tex] of the quadratic equation 4x² - 5x = -6, is 71.
Given a quadratic equation:
4x² - 5x = -6
It is required to find the solution of the quadratic equation first.
It is known that the solution of the quadratic equation of the form ax²+bx+c can be written as [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex].
Here, the equation can be written as:
4x² - 5x + 6 = 0
Here, a = 4, b = -5 and c = 6.
Substitute.
[tex]x=\frac{-(-5)\pm \sqrt{(-5)^2-4(4)(6)}}{2(4)}[/tex]
[tex]x=\frac{5\pm \sqrt{25-96}}{8}[/tex]
[tex]x=\frac{5\pm \sqrt{-71}}{8}[/tex]
Now, [tex]\sqrt{-71} =\sqrt{-1} \sqrt{71}[/tex].
But, [tex]\sqrt{-1} =i[/tex]
So, the solution is:
[tex]x=\frac{5\pm i\sqrt{71}}{8}[/tex]
Hence, the value of k is 71.
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Criteria: I can explain what happens to lines and angles in a dilation.
Triangle DEF is a scaled copy of Triangle ABC}, answer the following question equations that could be used to solve for x.
7 ÷ x = 1.5 is the equation used to solve for x.
Given,
Triangle DEF is a scaled copy of triangle ABC.
We have to find the equation to solve for x.
Scaled Copy;-
A scaled copy is a representation of a figure in which each length from the original representation has been multiplied by the same amount. Triangle ABC, for instance, is a scaled version of triangle DEF. Triangle DEF's side lengths were calculated by multiplying each side length from triangle ABC by 1.5.
Here,
Length of side AB = 6
Length of side DE = 4
Let y be the value used for scaling.
Then,
6 = 4y
y = 6/4 = 1.5
So,
Length of side BC ÷ x = 1.5
7 ÷ x = 1.5
7 = 1.5x
x = 7/1.5
x = 4.67
That is,
The equation used for getting the value of x is 7 ÷ x = 1.5
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PLEASEE HURRY
Frank is wanting to create a scale model of the Eiffel Tower. The real Eiffel Tower is 984 feet tall and 328 feet wide at its base. If Frank's model is 12 inches tall, how wide (in inches) must his scale model be?
Answer:
4 Inches.
Step-by-step explanation:
To find the width of Frank's scale model, we need to first determine the scale of the model. This can be done by dividing the height of the real Eiffel Tower by the height of Frank's model. Since the real Eiffel Tower is 984 feet tall and Frank's model is 12 inches tall, the scale of the model is 984 / 12 = 82 feet per inch.
Next, we can use this scale to determine the width of the model. Since the real Eiffel Tower is 328 feet wide at its base, and the scale of the model is 82 feet per inch, the width of the model must be 328 / 82 = 4 inches.
Therefore, the width of Frank's scale model of the Eiffel Tower must be 4 inches.
hi everyone, I'm studying for a math test. I just have one specific question: are all equations in the format y=mx+b linear equations? Or do I still need to graph it and check if it is a straight line first??
Yes, all equations in the format y=mx+b are linear equations. In this format, "m" represents the slope of the line and "b" represents the y-intercept, which is the point where the line intersects the y-axis. This means that all equations in this format will produce a straight line when graphed.
However, it is always good practice to graph the equation to confirm that it is a straight line. This will also allow you to see the slope and y-intercept of the line, and check if they match the values of "m" and "b" in the equation.
5. At Automotive Shop, 50 cars were inspected. 23 of the cars needed new brakes, 34 needed new exhaust systems, and 6 cars needed neither repair. How many cars needed both repairs? How many cars needed new brakes, but not a new exhaust system.
13 cars needed both repairs and 10 cars needed new brakes, but not a new exhaust system.
In the given question, at Automotive Shop, 50 cars were inspected. 23 of the cars needed new brakes, 34 needed new exhaust systems, and 6 cars needed neither repair.
(a) We have to find the how many cars needed both repairs.
Total inspected cars = 50
The cars needed new brakes = 23
The cars needed new exhaust systems = 34
The cars needed neither repair = 6
So the cars that needed repair = 50-6 = 44
Total cars that needed new brakes and new exhaust systems = 23+34 = 57
So, the cars that needed both repairs = 57-44
The cars that needed both repairs = 13
Hence, 13 cars needed both repairs.
(b) Now we have to find how many cars needed new brakes, but not a new exhaust system.
The cars needed new exhaust systems = 34
The cars that needed repair = 44
So, the cars needed new brakes, but not a new exhaust system = 44-34
The cars needed new brakes, but not a new exhaust system = 10
Hence, 10 cars needed new brakes, but not a new exhaust system.
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Which of the following equations has a maximum at (9,7)?
A.
y = -x2 − 14x − 58
B.
y = -x2 − 18x − 88
C.
y = -x2 + 14x − 40
D.
y = -x2 + 18x − 74
The equation which will have the maximum value at (9,7) is [tex]y = -x^{2} + 18x-74[/tex]
What is an equation ?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 4x + 6 = 15 consists of the two equations 4x + 6 and 15, which are separated by the 'equal' sign.
How do you find the maximum value of an equation ?The graph's transition from increasing to decreasing must be identified in order to determine the maximum. We look at the second derivative and see when the value changes from positive to negative to determine the rate at which the graph goes from increasing to decreasing.
According to the given information
[tex]y = -x^{2} + 18x-74[/tex]
The equation which will have the maximum value at (9,7) is [tex]y = -x^{2} + 18x-74[/tex]
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Convert 97°C to degrees Fahrenheit.
If necessary, round your answer to the nearest tenth of a degree.
Here are the formulas.
C=(F-32)
9
F ==C+32
5
97 °C
= F
Answer: 97 degrees Celsius is 206.6 degrees Fahrenheit.
write an equation in point-slope form for the line that passes through (2,-5) and is perpendicular to the graph of y=3x+1
An equation in point-slope form for the line that passes through (2,-5) and is perpendicular to the graph of y=3x+1 is y = -1/3x-17/3.
What is a slope-intercept form?When the line to be examined slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). B stands in for the y value of the y-intercept point in the formula. In order to make it simple to identify the slope and y-intercept of a line, its equation can be written in the slope-intercept form. The y-intercept, or point where the line crosses the y-axis, is referred to as the slope.
Perpendicular line slopes are reciprocals with a negative sign. In the slope-intercept form, y = mx + b, where m is the slope, the supplied line, y = 3x+1, is already in the slope-intercept form.
The line in the example has a slope of 3.
The negative reciprocal of three, or -1/3, is the slope of the perpendicular.
Y = -1/3x + b is the equation for the line that we are looking for.
We must track down b. We solve for b by using the x and y coordinates of the provided location as x and y in the equation above.
y = -1/3x + b
5 = (1/3)(2) + b
5 = (2/3) + b
b = -5-(2/3)
b= -17/3
B is now substituted for in the equation
y = -1/3x-17/3 as we know that b =-17/3.
Therefore, an equation in point-slope form for the line that passes through (2,-5) and is perpendicular to the graph of y=3x+1 is y = -1/3x-17/3.
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A psychologist is studying the self image as measured by the self image score for a personality
The minimum sample size needed for the desired margin of error of the confidence interval is given as follows:
44.
How to obtain the sample size needed?The sample size needed is obtained using the z-distribution, as the standard deviation for the population is known.
The equation that gives the margin of error for a z-distribution confidence interval is:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which the parameters are given as follows:
z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.The known measures in this problem are given as follows:
[tex]M = 20, \sigma = 80, z = 1.645[/tex]
Then the desired sample size is obtained as follows:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]20 = 1.645\frac{80}{\sqrt{n}}[/tex]
[tex]20\sqrt{n} = 1.645 \times 80[/tex]
Simplifying by 4, we have that:
[tex]\sqrt{n} = 1.645 \times 4[/tex]
[tex](\sqrt{n})^2 = (1.645 \times 4)^2[/tex]
n = 43.3.
Rounding up, as a sample size of 43 would have a margin of error slightly above 20, the sample size needed is of 44.
Missing InformationThe problem is given by the image shown at the end of the answer.
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Sandy wants to graph the equation y=2x^2+4x-6. What set of key points can she use to graph the equation?
The key points of option (B) are the x-axis: (1, 0), y-axis: (-3, 0), and Vertex: (-1, -8) she can use to graph the given equation.
What are graphs?Write the equation in the form y = MX + b to determine the slope m and the y-intercept.
This will allow you to graph the equation using the slope and y-intercept (0, b). The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
So, we have the equation:
y=2x^2+4x-6
Now, plot this equation in the graph as follows:
(Refer to the image attached below)
x-axis: (1, 0)
y-axis: (-3, 0)
Vertex: (-1, -8)
Therefore, the key points of option (B) which are the x-axis: (1, 0), y-axis: (-3, 0), and Vertex: (-1, -8) she can use to graph the given equation.
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describe the end behavior of the function y=-x^2+4
The end behaviour of the function [tex]y = -x^{2} + 4[/tex] is
f(x) → −∞, as x → −∞
f(x) → −∞, as x → +∞
The degree of the function is even, and the leading coefficient is negative.
End behaviour of a function:
A polynomial function's final behaviour is how its graph behaves as x gets closer to positive or negative infinity.
The graph's final behaviour is determined by a polynomial function's degree and leading coefficient.
For very big or very small values, the leading coefficient is more important than the other function coefficients. Therefore, it is sufficient to forecast the function's final behaviour based on the sign of the leading coefficient.
To predict the end-behaviour of a polynomial function, first check whether the function is odd-degree or even-degree function and whether the leading coefficient is positive or negative.
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