Answer: The answer is 9
Step-by-step explanation: 3^3/3=9
show that the graphs of the two equations and have tangent lines that are perpendicular to each other at their point of intersection.
The graphs of the two equations have a point of intersection, and the tangent lines at that point are perpendicular to each other. This can be shown by taking the derivatives of both equations and setting them equal to each other, which results in a perpendicular line equation.
To show that the graphs of the two equations have tangent lines that are perpendicular to each other at their point of intersection, we can take the derivatives of both equations, which gives us the equations of the tangent lines. We can then set the equations equal to each other and solve for the point of intersection. This will result in an equation for the perpendicular line, which is the equation of the line that passes through the point of intersection and is perpendicular to both tangent lines. We can then verify that the two tangent lines are perpendicular to each other at the point of intersection by calculating the slopes of both lines and showing that they are negative reciprocals of each other.
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The point P is on the unit circle. If the y-coordinate of P is −3/5 and PP is in quadrant IV , then X= ?
The value of X is 4/5 if point P is on the unit circle and if the coordinate of P is -3/5 and P is in iV quadrant.
We know that unit circle is the circle of radius 1 unit. We are given the y-coordinate of P, that is y = -3/5. Now if we draw a perpendicular line at x-axis, and we know the length of line joining the P and the origin is 1 unit (h = 1). We can construct a right triangle. Then by pythagorean theorem.
x² + y² = h²
x² = √(h² - y²)
x² = √(1² - (-3/5)²)
x² = √(1 - (9/25))
x² = √(16/25)
x = 4/5
Since X is in the IV quadrant, where x is positive and y is negative.
So x = +4/5
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uppose that at your university, you will pay $12,000 each year for tuition, $2,500 each year for textbooks, and $10,000 per year for room and board. Before you left for college, your boss at your high-school job offered you a job paying $25,000 per year.
The opportunity cost for four years of college is $46,000
How to determine the opportunity cost?We should know that opportunity costs represent the potential benefits that an individual, investor, or business misses out on when choosing one alternative over another.
The cost of education per year is = $12,000 + $2500 + $10000 = $24,500
The return if we decide not to go to college= $25000 - $12000 = $13000
We lose this return if we decide to go to college and we have to pay for room and board anyway.
The opportunity cost for four years of college is $24500-$13000)*4
This amounts to $11500*4 = $46,000
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Correct question:
Suppose that at your university, you will pay $12000 each year for tuition, $2500 each year for textbooks, and $10000 per year for room and board. Before you left for college, your boss at your high-school job offered you a job paying $25000 per year.
Assume that if you decided not to go to college, your parents would not let you live at home.
What is your opportunity cost for four years of college? $
What is the value of the 6 in 62.75 compared to the 6 in 6,275?
Answer:
6 in 6,275 is 100 times greater than 6 in 62.75
What is place value?
Place value is the basis of our entire number system. This is the system in which the position of a digit in a number determines its value.
as, 6 in 6,275 have a place value 6000.
and in 62.75, 6 have place value 60.
So, the difference is
6000/60
=100
Hence, 6 in 6,275 is 100 times greater than 6 in 62.75
Step-by-step explanation:
The value of the 6 in 62.75 is 60, while it is 6000 in the number 6275. This is due to the concept of place value in the decimal number system.
Explanation:In terms of place value, the value of the 6 in 62.75 is 60, because it is in the tens place. However, the value of the 6 in 6,275 is 6,000 because it is in the thousands place. This is based on the concept of place value in the decimal number system where each digit has a value depending on where it is located within the number. The further to the left a digit is, the larger its value.
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What inverse operation is used to solve the equation?
x + 2 = 5
Responses
A multiply by 2 on both sidesmultiply by 2 on both sides
B divide by 2 on both sidesdivide by 2 on both sides
C add 2 to both sidesadd 2 to both sides
D subtract 2 from both sides
Answer:
D subtract 2 from both sides
Step-by-step explanation:
x + 2 - 2 = 5- 2
==> x = 3
The solution of the equation is x = 3.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given:
An equation,
x + 2 = 5.
To solve the equation:
Subtract 2 from both sides,
x +2 -2 = 5 -2
x = 3
Therefore, the solution is x = 3.
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5 divided by 4/5???????????????????????????????????????????????????????
Answer:
6.94??????‽??????????????
Step-by-step explanation:
5÷4/5?????????
5×5?????????‽?/4
2.777777778/4
=69.4????????????????????
rectangle bounded by the x-axis and the semicircle x" (see figure). What length and width should the rectangle have so that its area maximum? smaller value : ___larger value: ___
The area of the rectangle will be 4.5 square units and the length and width are x=3 and y=1.5.
The equation for the line is y = -.5x + 3 (slope/intercept form).
Draw a random rectangle with the y-axis, x-axis, and the point (x,y) on the line y = -.5x + 3 as its corners.
This point's height from the x-axis (the length of the rec) will be equal to -.5x + 3 and its length from the y-axis will be x (the width of the rec).
Knowing that A = L*W equals the area of a rectangle
A(x) = (-.5x + 3) * x = -.5x^2 + 3x
In search of A'(x) = -x + 3. And we desire that A'(x) be 0.
As a result, y = -.5(3) + 3 = 1.5 and -x + 3 = 0 imply that x = 3.
So the maximum area of this rectangle is L*W = 1.5 * 3 = 4.5 square units. (We know this is a max and not a min since A’’(x) = -1 which makes the graph concave down)
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(07.01 mc) select the general solution to x squared dy over dx equals 3 plus 2y period one half ln absolute value of quantity 3 plus 2y close absolute value equals ln absolute value of x squared close absolute value plus c one half ln absolute value of quantity 3 plus 2y close absolute value equals negative 1 over x plus c
The general solution to x squared dy over dx equals 3 plus 2y is given by 1/2 ln|3 + 2y| = -1/x + c, where c is an arbitrary constant.
To calculate this, we begin by taking the derivative of both sides of the equation with respect to x. We then rearrange the equation to yield 2y + x^2 dy/dx = 3. We divide both sides by x^2 so that dy/dx is isolated on one side of the equation, yielding dy/dx = (3 - 2y) / x^2. We can then integrate both sides of the equation, with respect to x, to yield 1/2 ln|3 + 2y| = -1/x + c, where c is an arbitrary constant. This equation is the general solution to x squared dy over dx equals 3 plus 2y.
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I have a candy mix composed of Jolly Ranches, Starburst, and Twizzlers in a ratio of
7:5:3. I have 35 Jolly Ranchers. How many Starburst and Twizzlers do I have?
Answer:
25 Starburst
15 Twizzlers
========================================================
Explanation:
The ratio of Jolly Ranchers to Starburst to Twizzlers is 7:5:3
It means that you could have 7 Jolly Ranchers, 5 Starburst, and 3 Twizzlers.
In reality you actually have 35 Jolly Ranchers. So we'll multiply that "7" by 5. Do the same thing to all parts of the ratio to keep things balanced.
7*5 = 355*5 = 253*5 = 15The ratio 7:5:3 scales up to its equivalent form 35:25:15
35 Jolly Ranchers25 Starburst15 TwizzlersWhy is f not a function from R to R if
a) f (x) = 1/x?
The domain of the function is not the set of all real numbers, that is why it is not from R to R
Why is f not a function from R to R?Here we want to see why the function f is not a function from R to R, where R is the set of the real numbers.
The function here is:
f(x) = 1/x
Notice that x is on the denominator, so we can't evaluate that function on x = 0.
So there is a real number that we can't use on that function, then the domain is not R, is R minus the element {0}
That is why f(x) is not a function from R to R, because the domain is not the set of the real numbers.
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please help solve it
Note that if the family is to spend less than $60 dollars without further expenses, then they will have to spend nothing more than 6 hours. The inequality expression is given as: 36+4h < 60
What is the justification for the above result?First, the inequality expression is given as:
36+4h < 60
Where h is the number of hours they could spend.
We arrive at the above because we were given the following:
Cost of Movie = $36
Cost of parking Per Hour= $4
The maximum amount to be spent = $60
Thus, to find the number of hours the can spend without overshooting $60, we must find h. To do this, we must make h the subject of the formula by first removing 36 from both sides:
36+4h-36 < 60-36
4h < 24
h < 24/4
h < 6
What the above result show is that the number of hours that must be spent must be less than 6.
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Could you help me find the inverse of the function F(n)=n+1
Answer: [tex]F^{-1} (n)=n-1[/tex]
Step-by-step explanation:
[tex]F(n)=n+1[/tex]
[tex]F(n)-1=n[/tex] Subtract 1 from both sides
Done!
We can rewrite as: [tex]F^{-1} (n)=n-1[/tex]
A 15 meter long cylinder with a diameter of 7 meters has a square prism with a base length of 3 meters hole going all the way through the center of it as shown in the diagram (not to scale).
Find the volume of the composite shape rounding to the nearest cubic meter.
Hint: while working the problem carry figures at least three decimal places, then round to the nearest cubic meter only once at the very end.
The square prism's volume is 135 meter
Explain about the volume of the composite shape?Either the total number of smaller prisms that make up the composite shape, or its volume. the distinction between a larger prism and a smaller prism that was taken out of it.
A composite shape is a shape that was produced from two or more fundamental shapes. Composite shapes are also referred to as compound and complex shapes frequently.
Any shape that is constructed from two or more geometric shapes is referred to as a composite or compound shape. The triangle and square in the following shape are joined together. The square and the rectangle that make up the blue shape. There are two triangles making up the green shape.
Detailed explanation:
The parameters listed are;
L = 15 meters is the cylinder's length.
D = 7 meters is the cylinder's diameter.
B = 3 meters is the square prism's base length.
Consequently, we have;
The square prism's volume is
= B² x L
= 3² x 15
= 9 x 15
= 135 meter
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a blank is a relation in which each member
A function is a relation in which each member in the domain is paired with exactly one element in the range.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.
Given:
A phrase: A blank is a relation in which each member in the domain is paired with exactly one element in the range?
We have to find the blank word.
From the function definition,
A relation between a collection of inputs and outputs is known as a function.
A function is a connection between inputs in which each input is connected to precisely one output.
Each function has a range, co-domain, and domain.
Therefore, blank word is a function.
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The complete question:
A blank is a relation in which each member in the domain is paired with exactly one element in the range?
Select the two statements about risk and return that are true or potentially true.
As the risk of an investment increases, so does the potential for a higher return.
As the risk of an investment decreases, the return potential increases.
O Diversification increases the risk of a group of investments.
O Holding stocks of companies of different sizes and from different sectors reduces investment risk in
a portfolio.
O Investors should choose only investments that move up in price at the same time.
The two statements about risk and return that are true or potentially true are:
As the risk of an investment increases, so does the potential for a higher return.Holding stocks of companies of different sizes and from different sectors reduces investment risk in a portfolio.What is risk and return?
The risk connected to a particular investment and its returns are known as risk and return in financial management. High-risk investments typically produce higher financial returns, and low-risk investments typically produce lower returns. In other words, a given investment's risk and return are directly correlated.
As the risk of an investment increases, so does the potential for a higher return because there is a direct correlation between risk and return.
Also, holding stocks of companies of different sizes and from different sectors reduces investment risk in a portfolio because on diversifying the portfolio, risk also gets divided thus, giving a satisfactory return to the investor.
Hence, the above two statements are true.
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Answer: As the risk of an investment increases, so does the potential for a higher return. and Holding stocks of companies of different sizes and from different sectors reduces investment risk in a portfolio.
Step-by-step explanation: Increased price fluctuation, upward or downward, increases risk and the possibility of a high return or a huge loss. When the risk, or price fluctuation, is low, so is the return potential. Diversification helps decrease the risk of a group of investments because the value of individual investments will increase or decrease at different time periods and help to lessen value fluctuation in the overall portfolio.
A college library has four copies of a certain book; the copies are numbered 1, 2, 3, and 4. Two of these are selected at random. The first selected book is placed on 2- hour reserve, and the second book can be checked out overnight. a. Construct a tree diagram to display the 12 outcomes in the sample space. b. Let A denote the event that at least one of the books selected is an even-numbered copy. What outcomes are in A? c. Suppose that copies 1 and 2 are first printings, whereas copies 3 and 4 are second printings. Let B denote the event that exactly one of the copies selected is a first printing. What outcomes are contained in B?
The event A is that at least one of the books selected is an even-numbered copy. The event B is that exactly one of the copies selected is a first printing.
A tree diagram to display the 12 outcomes in the sample space would look like this:
1st Selection | 2nd Selection
----------------------------
1 | 2
1 | 3
1 | 4
2 | 1
2 | 3
2 | 4
3 | 1
3 | 2
3 | 4
4 | 1
4 | 2
4 | 3
The event A is that at least one of the books selected is an even-numbered copy. This would include outcomes 1-2, 1-4, 2-1, 2-3, 2-4, 4-1, 4-2, and 4-3.
The event B is that exactly one of the copies selected is a first printing. This would include outcomes 1-3, 1-4, 3-1, 3-2, 3-4, 4-1, 4-2, and 4-3.
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the range (in miles) of a broadcast signal from a radio tower is bounded by a circle given by the equation
The cars receive the broadcast signal for length of about 36 miles.
What is meant by equations?The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.
A condition on a variable (or variables) is a pair of expressions in the variable (or variables) that have the same value. The solution or root of the equation is the quantity at which the variable's value satisfies the equation. If you swap the LHS and RHS, an equation still makes sense.
Equations can be categorized as either identities or conditional equations. For each value of the variables, an identity holds true. Only specific values of the variables make a conditional equation true. An equals symbol ("="), separating two expressions, is used to represent an equation.
Simultaneous equations are obtained:
[tex]$$x^2+y^2=1620 \\y=-\frac{1}{3} x+30\end{array}\right.$$[/tex]
[tex]$x^2+\left(-\frac{1}{3} x+30\right)^2=1620$[/tex]
simplifying the above equation, we get
[tex]$x^2-18 x-648=0$[/tex]
(x - 36)(x + 18) = 0
x = -18 and x = 36
Therefore, the cars receive the broadcast signal for length of about 36 miles
The complete question is:
The range (in miles) of a broadcast signal from a radio tower is bounded by a circle given by the equation [tex]$x^2+y^2=1620$[/tex]. A straight highway can be modeled by the equation [tex]$y=-\frac{1}{3} x+30$[/tex]. For what length of the highway are cars able to receive the broadcast signal? Round your answer to the nearest tenth.
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5a>5.45 solve for a.
Answer is in attached photo.
Step-by-step explanation:
SolutionSolution is in the attached photo, do note that this question tests on the concept of Inequality.
[tex]5a > 5.45[/tex]
Divide both sides by 5:
[tex]\dfrac{5a}{5} > \dfrac{5.45}{5}[/tex]
Answer:
[tex]a > 1.09[/tex]
what is the slope through the line of (9, 10) and (7, 2)
Answer:4
Step-by-step explanation:
Write an informal negation for each of the following statements. Be careful to avoid negations that are ambiguous.
a. All dogs are friendly.
b. All people are happy.
c. Some suspicions were substantiated.
d. Some estimates are accurate.
The informal negation for each of the following statements:
1) No dog is ferocious.
2) Noboby is sad.
4) No suspicions were unsubstantiated.
5) No estimate is incorrect.
What is informal negation?It is sometimes necessary in mathematics to determine the inverse of a given mathematical statement. This is commonly known as "negating" a statement. Keep in mind that if a statement is true, then its negation is false (and if a statement is false, then its negation is true). A conditional statement's negation is logically equivalent to a conjunction of the antecedent and the negation of the consequent. The logical negation symbol or is one of the statement connectives or operators that can be used to combine two or more statements to form new compound statements. It simply flips the truth value of any statement it appears in front of.
Here,
Each of the following statements has an informal negation:
1) No dog is ferocious.
2) Noboby is sad.
4) No suspicions were unsubstantiated.
5) No estimate is incorrect.
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Find the determinant of the coefficient matrix 3x+4y=0 -2x+3y=17
The determinant of the coefficient matrix 3x+4y=0 and -2x+3y=17 is 17.
What is matrix?A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the numbers.
Given:
A system of equations,
3x+4y=0
-2x+3y=17.
To find the determinant,
we will find the matrix from Cramer's rule,
A =
[tex]\left[\begin{array}{cc}3&4\\-2&3\end{array}\right][/tex]
So, determinant of matrix A
ΔA = 3 x 3 -(4 x -2)
ΔA = 9 + 8
ΔA = 17.
Therefore, the determinant is 17.
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Classify the following triangle according to its sides and its angle measures.
2 cm
83⁰
53
2.5 cm
3 cm
44
This triangle is classified as an acute triangle since all three angles measure less than 90° (83⁰, 44⁰). It is also classified as an isosceles triangle since two of the sides (2 cm and 2.5 cm) are equal in length.
What are acute and isosceles triangle?An acute triangle is a triangle in which all three angles measure less than 90 degrees. It is the opposite of an obtuse triangle, which has one angle measuring more than 90 degrees.
An acute triangle can also be referred to as a “sharp” triangle. The sum of all three angles in an acute triangle will always equal 180 degrees. An acute triangle can be either isosceles or scalene.
An isosceles triangle is a triangle with two sides of equal length and two equal angles opposite the two sides. The two angles are often referred to as the base angles, while the third angle is called the vertex angle. The two sides of an isosceles triangle are also often referred to as the legs, while the longest side is referred to as the base.
Isosceles triangles are studied in geometry, and the properties of such triangles can be used to solve many mathematical problems.
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. The following list of monthly expenses for a first-year student at a post-secondary
institution are presented. The student has a monthly income of $1,450. Is the student
following the recommended rule of allocating 50% of monthly income to needs, 30% to
wants and 20% to savings or debt?
Income: $1,450
Based on the information provided, it can be concluded the student is not following the rule of allocating 50% to needs, 30% to wants, and 20% to savings.
What percentage is the student allocating for each category?Needs: 300 +10 + 50 +150 + 100 + 100= $710
Now, let's calculate the percentage this represents:
710 x 100 / 1450 = 48%
Wants: 9.99 + 9.95 +9.99 + 19.99 + 25 + 500 + 65= $639.92
Now, let's calculate the percentage this represents:
639 x 100/ 1450 = 44%
Savings: 48 + 44 = 92 which means he can save 8%
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Use the following statements to write a compound statement for each conjunction or disjunction. Then find its truth value.
p: 60 seconds = 1 minute
q: Congruent supplementary angles each have a measure of 90.
r: –12 + 11 < –1
answer choices
O Congruent supplementary angles each have a measure of 90 and –12 + 11 < –1; true.
O Congruent supplementary angles each have a measure of 90 and –12 + 11 < –1; false.
O Congruent supplementary angles each have a measure of 90 or –12 + 11 < –1; true.
O Congruent supplementary angles each have a measure of 90 or –12 + 11 < –1; false.
The answer is O Congruent supplementary angles each have a measure of 90 or –12 + 11 < –1; true.
This can be proven by using the following formula:
p: 60 seconds = 1 minute
q: Congruent supplementary angles each have a measure of 90.
r: –12 + 11 < –1
For p, we can use the formula to calculate the number of minutes:
60 seconds * 1 minute = 60 minutes.
Therefore, 60 seconds = 1 minute.
For q, we can use the formula to calculate the measure of each angle:
2x = 90
Therefore, each angle has a measure of 45°.
For r, we can use the formula to calculate the result of the operation:
–12 + 11 = –1
Therefore, –12 + 11 < –1 is true.
In conclusion, the compound statement “Congruent supplementary angles each have a measure of 90 or –12 + 11 < –1” is true.
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Julia had a bag filled with gumballs. There were 1 lemon-lime, 2 watermelon, and 3 grape gumballs. What is the correct sample space for the gumballs in her bag?
A. Sample space = 1, 2, 3
B. Sample space = 1, 2, 3, 4, 5, 6
C. Sample space = lemon-lime, watermelon, grape
D. Sample space = lemon-lime, watermelon, watermelon, grape, grape, grape
The correct sample space for the gumballs in Julia's bag is {lemon-lime, watermelon, watermelon, grape, grape, grape} which makes option D correct.
How to evaluate for the sample sapceThe sample space for the gumballs in Julia's bag would be all the possible outcomes of selecting one gumball from the bag without replacement.
Since there are 1 lemon-lime, 2 watermelon, and 3 grape gumballs in the bag, the sample space would be expressed as:
sample space = {lemon-lime, watermelon, watermelon, grape, grape, grape}.
Therefore,we have 6 total outcomes in the sample space for the gumballs in Julia's bag.
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toss a coin three times, and let x be the number of heads. find the probability mass function of x.
The probability mass function of x is P(0)= 1/8, P(1)= 3/8, P(2)= 3/8, P(3)= 1/8.
Here number of trials = 3
In tossing a coin for once, the outcomes of the trial are either head or tail.
The trials are independent.
probability of getting head(success)=p=1/2
probability of getting tail(failure)=1-p=1-(1/2)=1/2
Number of success=X
Since there are two mutually exclusive outcomes of independent trials, the probability mass function of Binomial = (nx)px(1−p)n−x(nx)px(1 − p)n−x {in this case n=3}
The probability distribution of X is -
= X=0, P(X=0)=1/8
= X=1, P(X=1)=3/8
= X=2, P(X=2)=3/8
= X=3, P(X=3)=1/8
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Assume that for dry rice and beane - 1 basin 20 cups 40 basins - 1 sack a A sack contains 100 kg of rice. Estimate the number of kilograms of rice in 1 basin Estimate the number of grams of rice in Toup. b A trader buys a sack of rice for N6 000 for beans. Four women biry a sack of beans between them. They share the beans equally to bear) N150 How many basins does each woman get? How much does each woman save by buying the beans in this way?
A single basin of dry rice and beans 20 cups One bag of 40 basins 100 kilogrammes of rice is included in a sack.
Do you save money buying whole bean coffee?In the majority of circumstances, whole coffee beans won't be less expensive than ground coffee. Unfortunately, that is not the case if you think that by grinding your own coffee at home you can save some money.There are three factors that contribute to pre-ground coffee's cost advantage over whole bean coffee. If you decide to go the whole-bean way, you'll also need to buy a grinder, which will run you anywhere from $10 to $1000 up front. tea leaves: If kept in a cold, dark, dry location, a bag of whole coffee beans can be kept for up to twelve months if it is unopened, and for one week if it is opened. Coffee ground: store a sealed bag of coffee ground for three to five months in the pantry.To learn more about buying refer to :
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find each measure m < 5
The measure of all the angles are estimated.
∠1 = 104 ; ∠4 = 45 ; ∠3 = 65 ; ∠2 = 79.Explain the term linear pair?When two lines cross at one point, a linear pair with angles is created. If the angles follow the intersection of both the two lines in a straight line, they are classified as linear. A linear pair's total angles are indeed equal to 180°.For the stated question:
For ∠1
∠1 = 68 + 36 (sum of opposite interior angle equals exterior angle).
∠1 = 104
For ∠4.
∠4 = 180 - 70 - 65 (linear pair)
∠4 = 45
For ∠3.
∠3 = 65 (vertically opposite angle)
For ∠2.
∠2 = 180 - 65 - 36 (sum of angles of triangle are 180)
∠2 = 79
Thus, the measure of all the angles are estimated.
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What is 26,430,000 in expanded form
Answer: 20,000,000 + 6,000,000 + 400,000 + 30,000
Step-by-step explanation:
Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places.
16o sin(x) dx, n = 4
the value of integration [tex]\int\limits^{64}_0 {sinx} \, dx =5[/tex] by the midpoint rule of approximate.
we want to approximate the integral
[tex]\int\limits^{64}_0 {sinx} \, dx \\using n=4[/tex]
the midpoint rule is given by.
[tex]\int^b_af(x)dx=\triangle x(f(\frac{x_{0} +x_1)}{2})+f(\frac{x_1+x_2}{2} )+....+f(\frac{x_{n-1}+x_n}{2}))[/tex]
where Δx=(b-a)/n
we know that a=0,b=64 and n=4
Δx=64/4=16
we need to divide the interval [0,64] into four subinterval of length Δx=16: 0,16,32,48,64.
now, we just evaluate the function at these endpoints.
[tex]f(\frac{x_1+x_0}{2} ) =f(\frac{0+64}{2} )\\f(8)=sin8=0.9894\\\\f(\frac{x_1+x_2}{2}) =f(\frac{16+32}{2} )\\\\f(24)=sin24=-0.9056\\\\similarly\\\\f(40)=sin(40)=0.7451\\\\f(56)=sin56=-0.5216[/tex]
finally, just sum up above values and multiply by Δx=16.
[tex]\int\limits^{64}_0 {sinx} \, dx=4.9168= 5[/tex]
learn more about midpoint rule.
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