Differential equation: In solving equations involving x, y, and z, taking steps with various values of h optimizes the process.
Step size h: When h=0.5 over the interval 0 to 2, solutions can be calculated by incrementing x from 1 to 1+h.
Optimizing procedures: By choosing appropriate values for h, the iterative process can be streamlined for better efficiency.
If two angles of a triangle measure 43 degrees and 48 degrees the triangle is
The third angle for the triangle is equal to 89°.
What is geometry?Geometry is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a geometer.
A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C.
Given that the two angles of a triangle measure 43 degrees and 48 degrees. the value of the third angle will be calculated as,
Third angle = 180 - 43 - 48
Third angle = 89°
The complete question is given below.
If two angles of a triangle measure 43 degrees and 48 degrees what is the third angle of the triangle?
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How do i convert 16/5 to a mixed number?
Answer: 3 and 1/5
Step-by-step explanation: To write an improper fraction as a mixed number, divide the denominator into the numerator.
[tex]\sqrt[5]{16}[/tex] = 3 with a remainder of 1
Therefore, 14/5 can be written as the mixed number 3 and 1/5.
Your iron works has been contracted to design and build a 500-ft3 square-based, open-top, rectangular steel holding tank for a paper company. The tank is to be made by welding half-inch-thick stainless steel plates together along their edges. As the production engineer, your job is to find dimensions for the base and height that will make the tank weight as little as possible. What dimensions do you tell the shop to use?
To minimize the weight of the tank, the base length should be (4/3) times the height. The height should be (3/4)^(1/4) times the fourth root of (2V/π).
Explanation:To find the dimensions that will make the tank weight as little as possible, we need to consider the volume and weight of the tank. Since the tank is square-based, the volume can be calculated by V = bh^2, where b is the length of one side of the base and h is the height.
The weight of the tank can be calculated by multiplying the volume by the density of the stainless steel. W = V * density. Since we want to minimize the weight, we want to minimize the volume.
To do this, we can differentiate the volume equation with respect to b and set it equal to zero. Solving for b, we find that b = (4/3) * h. Substituting this value into the volume equation gives: V = (4/3) * h^3.
To further minimize the volume, we can take the derivative of the volume equation with respect to h and set it equal to zero. Solving for h, we find that h = (3/4)^(1/4) * (2V/π)^(1/4).
Harita must memorize 90 measures of music for her cello solo at a concert. She plans on memorizing 18 new measures for every 3 days of practice. Which equation can be used to determine m, the number of measures Harita still needs to memorize, as a function of d, the number of days of practice since she began learning the piece?
Answer:
m=90-6 days or b
Step-by-step explanation:
i got a hundred on the quiz...
4/9 multiplied by 1/8
Which is a true statement about any two chords that are the same distance from the center of a circle?
A. They are parallel.
B. They are perpendicular.
C. They are congruent.
D. They are similar.
Answer C. If two chords are the exact same distance from the center of the circle then those two chords must be congruent.
Is 6.5 greater than 6.417
Water is pumped out of a holding tank at a rate of 6-6e^-0.13t liters/minute, where t is in minutes since the pump is started. If the holding tank contains 1000 liters of water when the pump is started, how much water does it hold one hour later?
What is the median distance jumped 7.48, 7.60, 7.15, 7.44, 7.73, 7.72
What is the median of this set of data? 66, 51, 77, 68, 60, 75, 54, 80
67````````````````````````
100 plus the product of a number and -2 equals 50 What is the number?
out of a swarm of bees one fifth part settled on a kadamba blossom; one third on a silihindra flower; three times the difference of those numbers flew to the bloom of a kutaja. one bee, which remained, hovered about in the air. tell me, charming woman, the number of bees
Ray is 2 inch taller than Lin, and Ray is 3 inch taller than Sam. What is the average height of ray, Lin and Sam? The median height of Ray, Lin and Sam?
Estimate the volume of material in a cylindrical shell with height 30 in., radius 2 in., and shell thickness 0.5 in.
The scores on a final exam were approximately normally distributed with a mean of 82 and a standard deviation of 11. If 85 students took the exam, and above a 60 is a passing grade, how many students failed the exam?
A. 13
B. 1
C. 2
D. 12
Answer:
2 students failed in the final exam.
Step-by-step explanation:
The scores on a final exam were approximately normally distributed.
We know that,
[tex]Z=\dfrac{X-\mu}{\sigma}[/tex]
X = raw score = 60
μ = mean = 82
σ = standard deviation = 11
Putting the values,
[tex]Z=\dfrac{60-82}{11}=-2[/tex]
From Normal distribution table, we get
[tex]P(-2)=0.0227=2.27\%[/tex]
Hence, 2.27% of 85 students failed the final exam.
So the number of students who failed the exam is,
[tex]=85\times 0.0227=1.9295\approx 2[/tex]
Bruce wants to make 50 ml of an alcohol solution with a 12% concentration. He has a 10% alcohol solution and a 15% alcohol solution. The equation 0.10x + 0.15(50 – x) = 0.12(50) can be used to find the amount of 10% alcohol solution Bruce should use. How much of the 10% alcohol solution should Bruce use? mL How much of the 15% alcohol solution should Bruce use?
Answer:
0.10x + 0.15(50 – x) = 0.12(50)
Step-by-step explanation:
round 624 to the nearest hundred
Write unit rate for 1.98 for 6
What conversion factor can be used to convert the number of blocks to the weight of the blocks, in pounds?
The correct answer is:
The conversion factor would be the number of blocks multiplied by the weight of 1 block.
Explanation:
Consider the following example:
Suppose 1 block weighs 3 pounds. If there are 15 blocks, to find the total weight of the blocks, we multiply 3 by 15: 3(15) = 45. This means the total weight would be 45 pounds.
For any given number of blocks and any given weight of 1 block, to find the total weight of the blocks we would multiply the number of blocks by the weight of 1 block.
Expression as a decimal number 6x0.1 6x0.01 1x0.001
Final answer:
To express the given multiplications as decimal numbers: 6 times 0.1 equals 0.6, 6 times 0.01 equals 0.06, and 1 times 0.001 equals 0.001. Moving the decimal point due to multiplication by powers of 10 is the underlying concept.
Explanation:
The student's question involves expressing multiplications involving decimals in decimal form. To convert each term:
6 x 0.1 is moving the decimal point one place to the left in the number 6, which results in 0.6.6 x 0.01 is moving the decimal point two places to the left in the number 6, giving 0.06.1 x 0.001 is moving the decimal point three places to the left in the number 1, resulting in 0.001.When numbers are multiplied by powers of 10, the decimal point is shifted to the right for positive exponents and to the left for negative exponents. Scientific notation is often used for this purpose.
Here are examples demonstrating the use of scientific notation:
0.006 can be expressed as 6 x 10-3 (moving the decimal point three places to the left).0.0000045 becomes 4.5 x 10-6 (the decimal point moves six places to the left).Negative exponents indicate the decimal point moves to the left, whereas positive exponents indicate it moves to the right. For instance, 2.4 x 10-2 is equivalent to 0.024 as the decimal has moved two places to the left.
The product of two rational numbers is _________rational.
sometimes
always
never
What is 3.99999..... converted into a fraction?
in a carnival drawing,a green ticket wins $1,a yellow ticket wins $5,and a blue ticket wins $10. There are 100 green tickets, 25 yellow tickets and 5 blue tickets. in simplest form, what are the odds in favor of winning $5 or more?
Which of the following has the most inertia, four kilograms of iron or four kilograms of cork? ...?
Answer:
Both will have same inertia.
Step-by-step explanation:
The inertia of a body is defined as its property to oppose the state of rest or uniform motion. In this question, we have to write out of four kilograms of iron and four kilograms of cork which will have maximum inertia. Inertia of a body is also equal to measure of its mass.
In this case, the masses of both iron and cork are same i.e. 4 kg. So, it is clear that the inertia of both iron and cork are same due to their same masses.
1. A circle has a center at (3,5). The point (3,8) is on the circle. What is the circumference of the to the nearest tenth of a unit?
A. 9.4 units
B. 18.8 units
C. 28.3 units
D. 56.5 units
2. A triangle has a perimeter of exactly 24 units. Which of the following could be the vertices of the triangle?
A. (-1 ,3 ), (2,-1), (-1,-1)
B. (6,0), (6,7), (0,7)
C. (-1,-1), (-6,-13), (-9,-9)
D.(-3,-4) (-3,4), (3,4)
3. A circle has an area of approximately 78.5 square units. If the center of the circle is at (2,4). Which of the following points is on the circle?
A. (-6,4)
B. (2,-1)
C.(-4,-4)
D. (2,-9)
4. The end point of a diameter of a circle are A (2,1) and B (5,5). Find the area of the circle in terms of pi.
A. 25/4 pi square units
B. 10 pi square units
C 25 pi square units
D. 5 pi units
Answer:
1. B
2. D
3. B
4. A
Step-by-step explanation:
Which expression is equaivalent to mn+z
nm+n
z+mz
mz+n
z+nm
Answer:
D. z+nm
Step-by-step explanation:
Equaivalent to mn+z: Just switch the letters around and you get z+nm
8.find the result when 40 is INCREASED by 85%
10.find the result when 350 is DECREASED by 10%
28.find the result when 24 is INCREASED by 75%
30.find the result when 30 is DECREASED by 85%
Which of the following tables shows the correct steps to transform x^2 + 10x + 24 = 0 into the form (x - p)^2 = q? [p and q are integers]
Answer: D
Step-by-step explanation:
The correct transformation of the equation is achieved by completing the square to obtain the form (x + 5)^2 = 1, which gives the values of p = -5 and q = 1.
The transformation of the quadratic equation x^2 + 10x + 24 = 0 into the form (x - p)^2 = q involves completing the square. To complete the square, one must find a number that, when added to x^2 + 10x, completes a perfect square trinomial. This number is calculated by taking half of the x-coefficient (b/2), squaring it, and adding it to both sides of the equation. In this case, (10/2)^2 = 25. We then have x^2 + 10x + 25 on the left and 25 - 24 on the right, which simplifies to (x + 5)^2 = 1. The values of p and q are thus -5 and 1, respectively.
Three largest earthquakes ever recorded took place in chile, russia, and alaska. they measured 9 1/10, 9.5, & 9 1/5 on the richter scale. the largest earthquake was in chile. the earthquake in russia was smaller than the one alaska. what did the three earthquakes measure on the richter scale
Final answer:
The largest earthquakes recorded in Chile, Russia, and Alaska measured 9.5, 9.1, and 9.2 on the Richter scale respectively, with Chile's earthquake being the largest and Russia's the smallest.
Explanation:
The three largest earthquakes ever recorded took place in Chile, Russia, and Alaska. Based on the information provided, the earthquake in Chile was the largest, measuring 9.5 on the Richter scale. The earthquake in Alaska, being larger than the one in Russia but not as large as the one in Chile, would measure 9 1/5, or 9.2, on the Richter scale. Lastly, the earthquake in Russia was the smallest of the three, measuring 9 1/10, or 9.1, on the Richter scale.
These seismic events, marked by their enormity on the Richter scale, underscore the geological dynamics in different regions of the world. The specific magnitudes assigned to each earthquake provide a quantitative measure of their intensity, offering valuable insights for understanding and preparing for such natural phenomena.
For any positive number b not equal to 1 and any number or variable n, evaluate the following expression.
logb(b^n) =
with logb being the base
Answer:
[tex]log_{b} b^{n}[/tex] = n.
Step-by-step explanation:
Given : [tex]log_{b} b^{n}[/tex] , b is any positive number not equal to 1 and n is any number.
To find : Evaluate the expression [tex]log_{b} b^{n}[/tex].
Formula used : [tex]log_{b} x^{y}[/tex]. = y ∙ [tex]log_{b}[/tex](x) and
[tex]log_{b}(b) = 1.
Solution : We have [tex]log_{b} b^{n}[/tex].
By logarithm rule : [tex]log_{b} x^{y}[/tex]. = y ∙ [tex]log_{b}[/tex](x).
Then [tex]log_{b} b^{n}[/tex] = n∙ [tex]log_{b}[/tex](b).
By logarithm rule : [tex]log_{b}(b) = 1.
Now, n∙ [tex]log_{b}[/tex](b) = n.
Therefore, [tex]log_{b} b^{n}[/tex] = n.