At time t = π /6 , the position x(t) = 6 cos(t) is given by the following. x (π/6) = 6 cos (π /6 )
Gavin goes to the market and buys one rectangle shaped board. The length of the board is 16 cm and width is 10 cm. if he wants to add a 2 cm wooden border around the board, what will be the area of the rectangle board?
The area of the rectangle board, including the wooden border, is 280 cm².
The student's question pertains to finding the new area of the rectangle board after adding a 2 cm wooden border around it. Initially, the board has dimensions of 16 cm in length and 10 cm in width. To account for the new wooden border, we add 2 cm to each side of the board. This means that the new length will be 16 cm + 4 cm (2 cm for each side of the length) and the new width will be 10 cm + 4 cm (2 cm for each side of the width).
The calculation will be as follows:
New Length = 16 cm + 4 cm = 20 cm
New Width = 10 cm + 4 cm = 14 cm
Area = New Length * New Width
Area = 20 cm * 14 cm
Area = 280 cm²
Therefore, the area of the rectangle board with a 2 cm border added around it will be 280 cm².
Sonny substituted 5 for x in the proportion 16/x=48/15 and cross multiplied to get 240=240. Why is this?
A.because the cross sums of the proportion are equal
B.because the cross differences of the proportion are equal
C.because the cross products of the proportion are equal
D.because the cross quotients of the proportion are equal
the answer is c i just took the test
Answer:
i agree c
Step-by-step explanation:
because 16 times 15 = 240
and 48 times 5 =240
Aurella wants to enlarge a 4-inch by 6 inch photo so that it has a width of 15 inches. Use a ratio table to determine the new length of the photo
[ 3+ ( 18 - 4 ) / 7 ] * 8
Helene is finding the sum (9 + 10i) + (–8 + 11i). She rewrites the sum as (–8 + 11)i + (9 + 10)i. Which statement explains the property of addition that she made an error in using?
Answer:
answer is d
Step-by-step explanation:
can someone please express 105/20 as a mixed number in simplist form
There are k types of coupons. independently of the types of previously collected coupons, each new coupon collected is of type i with probability pi, ki =1 pi = 1. if n coupons are collected, find the expected number of distinct types that appear in this set. (that is, find the expected number of types of coupons that appear at least once in the set of n coupons.)
Let X be the expected number of distinct types of coupons in the collection of k coupons X = X1 + X2 + ……. + Xx.
what 3050 divided by 100
Peter is a painter, and he wonders if he would have time to catch a paint bucket dropped from his ladder before it hits the ground. He drops a bucket from the top of his 9-foot ladder. The height, h, of the bucket can be represented by the equation, h= -16t^2 + 9, where the height is measured in feet from the ground, and the time since the bucket was dropped, t, is measured in seconds. After how many seconds does the bucket hit the ground? Do you think he could catch the bucket before it hits the ground.
The paint bucket dropped from the 9-foot ladder would hit the ground in approximately 0.75 seconds, according to the equation given for free fall. Given this quick time frame, it might be difficult for Peter to catch the bucket before it hits the ground.
Explanation:The situation described involves a physical phenomenon known as free fall, under the influence of gravity. In the case of the paint bucket, when it is dropped from the top of the ladder, the height h of the bucket from the ground at any time t is given by the equation h = -16t^2 + 9. The bucket hits the ground when h = 0.
To find when the bucket hits the ground, we solve the equation -16t^2 + 9 = 0 for t. Using the quadratic formula, we find the roots to be t = -0.75s and t = 0.75s. Since time cannot be negative in this situation, we discard the negative root. Thus, the bucket hits the ground after 0.75 seconds.
As to whether Peter could catch the bucket before it hits the ground, it does depend on his reflexes and agility, but generally it may be difficult to react and move quickly enough within such a brief time frame.
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for halloween, lana received 7 4/8 pounds of candy. after a week her family had eaten 3 6/8 pounds, how many pounds does she have left?
Answer To Questions :
3 3/4
Which of the following graphs represent a function? 4072-01-02-01- a. Graph A and Graph C b. Graph A c. Graph D d. Graph B and Graph D
The graph which represent a graph of a function is:
Graph A and Graph C
Step-by-step explanation:We know that a graph of a function satisfies the vertical line test i.e. any line passing through the domain and parallel to y-axis should intersect the curve exactly once i.e. corresponding to each x-value there is exactly one y-value.
Hence, from the figure attached to the answer we see that the Graph which is a function is:
Graph A and Graph C
Graph A represents a function.
Explanation:A function is a relation in which each input has only one output. In other words, for every x-value, there can only be one y-value. To determine if a graph represents a function, we can use the vertical line test. If a vertical line intersects the graph at more than one point, then the graph does not represent a function. Looking at the given graphs, Graph B and Graph D do not pass the vertical line test, as there are vertical lines that intersect these graphs at multiple points. Therefore, the correct answer is Graph A.
A cube has a volume of 125 cubic inches. What is the length of each edge? Enter your answer in the box.
Answer: 5 cm
Step-by-step explanation:
Given : The volume of a cube = 125 cubic inches.
The formula for the volume of a cube is :
[tex]V=s^3[/tex], where s is the side-length .
Substitute V= 125 in the above formula ,
[tex]125=s^3[/tex]
Taking cube root on both the sides , we get
[tex]\sqrt[3]{125}=s\\\\\Rightarrow\ s= \sqrt[3]{5^3}=5[/tex]
Hence, the side length of cube= [tex]5\ cm[/tex]
Each edge will be 5 inches.
Volume of the cube = 125 cubic inches
It should be noted that a cube's volume is gotten by multiplying the side thrice. In this case, let's say the value of each side is a. Therefore, based on the information given above:
a × a × a = 125
a³ = 125
a = 3✓125
a = 5
Therefore each edge is 5 inches.
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Zach read a book for 10 minutes every weekend in the first month, 20 minutes in the second month, 40 minutes in the third month, and 80 minutes in the fourth month. Victoria read a book for 35 minutes every weekend in the first month, 50 minutes in the second month, 65 minutes in the third month, and 80 minutes in the fourth month. Which statement best describes the methods used by Zach and Victoria to increase the time they spent reading a book? Zach's method is linear because the number of minutes increased by an equal factor every month. Victoria's method is linear because the number of minutes increased by an equal number every month. Both Victoria's and Zach's methods are exponential because the number of minutes increased by an equal factor every month. Both Victoria's and Zach's methods are exponential because the number of minutes increased by an equal number every month.
(NEVER MIND GUYS IM GOING WITH A)
What is the slope of the line tangent to the curve 3y^2-2x^2=6-2xy at the point (3 2)?
Solve the following equation exactly on the interval 0 ≤ θ ≤ 2π ? cos 2θ + sin θ = 0
What percent of 450 is 60? Round to the nearest hundredth of a percent.
hich numbers are to solve this problem? A bicycle shop sold 60 road bikes, 50 racing bikes, and 75 mountain bikes each month for 15 months. How many more mountain bikes than road bikes did the shop sell in the 15 months?
One integer is 5 more than another. Their product is 234. Find the integers?
Final answer:
The integers in question are 13 and 18, which fulfill both conditions of one integer being 5 more than the other and their product being 234.
Explanation:
We are looking for two integers where one is 5 more than the other and their product equals 234. Let's designate the smaller integer as x. Then the larger integer can be represented as x + 5. The equation describing their product is:
x * (x + 5) = 234
Expanding this, we get:
x2 + 5x - 234 = 0
Solving this quadratic equation, we can find the values of x that satisfy the equation. The factors of 234 that have a difference of 5 are 13 and 18. So, the two integers we are looking for are 13 and 18.
Nick bought a pair of glasses for $200. He later saw the same glasses advertised for 20% less than what he originally paid. What price were the glasses being advertised for?
Create a factorable polynomial with a GCF of 2. Rewrite that polynomial in two other equivalent forms. Explain how each form was created.
The quotient Of 30 and the sum of -4 and -6
Silver is a white metal and is an excellent conductor of heat and electricity. The density of silver is 10.49 g/cm3. Silver does not react with water but it does react with nitric acid. Silver tarnishes when exposed to air or light. What is a physical property of silver?
Answer:
The density of silver is 10.49 g/cm3.
Step-by-step explanation:
Physical properties are those that can be observed without any change in the identity of the element in question. In this case, the physical property that is mentioned is density. Other examples include color and hardness. On the other hand, chemical properties describe how a substance can change into a different substance. This would include characteristics such as flammability and corrosion resistance.
Let f be the function defined by f(x) = x + lnx. What is the value of c for which the instantaneous rate of change of f at x = c is the same as the average rate of change of f over [1, 4]?
write the following decimal as a fraction or mixed number in lowest terms 0.85
how do the 8 differ in 38108
A city's population is represented by the function P=25,000(1.0095)t , where t is time in years.
How could the function be rewritten to identify the daily growth rate of the population?
What is the approximate daily growth rate?
The daily population growth function is P=25,000((1.0095)1/365.25)t, and the daily growth rate is approximately 1.000026 or an increase of about 0.0026% per day.
Explanation:The city population growth function given, P=25,000(1.0095)t, is an exponential function. To identify the daily growth rate, we need to rewrite this function in terms of days. As there are approximately 365.25 days in a year, we substitute this into the formula for t. Hence, the daily population growth function becomes P=25,000(1.0095)t/365.25.
To find the approximate daily growth rate, we solve for the base of the exponent. Using the fact that (ab)c = abc, we can rewrite the function as P=25,000((1.0095)1/365.25)t.
Thus, the daily growth rate of the population is approximately the value of (1.0095)1/365.25, which calculates to about 1.000026, or an increase of about 0.0026% per day.
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Find the area of the surface obtained by rotating the curve y x2 0 ≤ x ≤ 2 about the y axis
ds=√1+(dydx)2dx=√1+14(x4−2+1x4)dx
=√14(x4+2+1x4)dx=√122(x2+1x2)2dx
=12(x2+1x2)dx
factor 2x^3+3x^3-18x-27
After combining like terms, the polynomial simplifies to 5x^3 - 18x - 27. It cannot be factored using basic techniques due to the lack of common factors and its incompatibility with simple factoring patterns.
Explanation:To factor the polynomial 2x^3 + 3x^3 - 18x - 27, we first combine like terms and then look for common factors or patterns that we can use to factor the polynomial.
Combining Like Terms
Combining the cubic terms, we get 5x^3. Therefore, the polynomial simplifies to 5x^3 - 18x - 27.
Factoring
We look for a greatest common factor (GCF) among the terms. In this case, there are no common factors other than 1.
Since there is no obvious way to factor by grouping, and the polynomial does not fit the patterns for difference of cubes or sum of cubes, we'd have to consider other methods such as Rational Root Theorem or synthetic division to find if the polynomial has rational roots and can be factored further. However, those methods are more complex and require trial and error or a systematic approach that typically isn't covered until more advanced algebra classes or college algebra.
Conclusion
Without additional methods, we conclude that the polynomial 5x^3 - 18x - 27 cannot be factored over the rationals using basic factoring techniques commonly taught in high school algebra.
To factor the expression 2x^3 + 3x^3 - 18x - 27, we can group the terms with common factors and factor out those common factors.
Explanation:To factor the expression 2x^3 + 3x^3 - 18x - 27, we can group the terms with common factors. The first two terms, 2x^3 and 3x^3, have a common factor of x^3. The last two terms, -18x and -27, have a common factor of -9. Factoring out these common factors, we get:
2x^3 + 3x^3 - 18x - 27 = x^3(2 + 3) - 9(2 + 3) = x^3(5) - 9(5) = 5x^3 - 45
So, the factored form of the expression is 5x^3 - 45.
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The graph below shows the velocity f(t) of a runner during a certain time interval:
graph of line segment going through ordered pairs 0, 4 and 4, 8. Graph of another line segment going through ordered pairs 4, 8 and 8, 0. Label on the x axis is time in seconds and label on the y axis is velocity in meters per second
Which of the following describes the intercepts on the graph?
A. The initial velocity of the runner was 4 m/s, and the runner stopped after 8 seconds.
B. The initial velocity of the runner was 8 m/s, and the runner stopped after 4 seconds.
C. The initial acceleration of the runner was 4 m/s2, and the runner stopped after 8 seconds.
D. The initial acceleration of the runner was 8 m/s2, and the runner stopped after 4 seconds.