The period T in seconds of a simple pendulum of length L in feet is given by T=2π√L/32. Determine the length in feet of a simple pendulum whose period is 8.72 seconds. Round your answer to the nearest foot.
1972 feet.
387 feet.
62 feet.
256 feet.
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A catapult is malfunctioning and not throwing objects in the intended manner. The builders have modeled the path of the objects thrown by using the following parametric equations. rewrite the parametric equations by eliminating the parameter.
x(t)=2t-1
y(t)= square root of t; t> or equal to 0
Answer:
The equation is [tex]y ^ 2 = \frac{x + 1}{2}[/tex]
Step-by-step explanation:
The parameter that we have is t. We want to eliminate this parameter in both equations, therefore in the first equation we solve for t and in the second equation we solve for the variable t.
We have:
[tex]x = 2t-1\\\\x + 1 = 2t\\\\t = \frac{x + 1}{2}[/tex]
Now we solve the other equation for t.
[tex]y= \sqrt{t}[/tex]
[tex]y ^ 2 = t[/tex] because [tex]t> 0[/tex]
As [tex]t = y ^ 2[/tex] and also [tex]t = \frac{x + 1}{2}[/tex]
Then:
[tex]y ^ 2 = \frac{x + 1}{2}[/tex]
The correct answer is:
D. [tex]x=2y^{2} -1, y\geq 0[/tex]
The diameter of a bowling ball is 12.57 centimeters. What is this value rounded to the nearest tenth of a centimeter?
Plato explains that we know geometry by _________.
Plato explains that we know geometry by our gain knowledge through recollection. Our soul is what recollects this place hence we came where there exist unchanging truths. Delivered the theory of Forms, according to which the world people know by means of the senses is just an imitation of the eternal, pure, eternal, and fixed world of the Forms.
the diagonals of a rhombus are 12 centimeters and 16 centimeters. what is the length of one side of the rhombus?
Solve the quadratic equation. 8x2 + 16x + 8 = 0 A) 1 B) -1 C) 1 and 8 D) 1 and -1
-2x+3 > x +24
Show steps how you got your solution
What is the value of x? Round the answer to the nearest tenth. The diagram is not drawn to scale.
We have been given that the chords AB and CD are equal.
Now, we know that two equal chords subtends equal angle at the center of the circle.
The chord CD subtends and angle CPD at the center and the chord AB subtends an angle APB at the center.
Hence, from above mentioned theorem, we can say that
[tex]\angle CPD = \angle APB[/tex]
Now, we have been given that
[tex]\angle CPD =50 ^{\circ} [/tex]
[tex]\angle APB =x ^{\circ} [/tex]
Hence, we have
[tex]x=50^{\circ}[/tex]
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Haley read three less than twice as many books as her brother did last summer. haley read five books.which equation could you use to find how many books her brother read (b)?
Answer:
2b - 3 = 5
Step-by-step explanation:
If her brother read b number of books last summer, twice the number of books her brother read
= 2b
three less than twice as many books as her brother read
= 2b - 3
If haley read five books and it is same as three less than twice as many books as her brother last summer, then
2b - 3 = 5
someone help me please
suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor, it rebounds to 85% of its previous height. how high will the ball rebound after its third bounce? round to the nearest tenth
Alan is giving a basic math test in his class. One of the questions in the test is about finding two factors of the number 221. Which are the two factors of the given number? The two factors of the number 221 are ___ and ____.
How to find the volume of a equilateral triangular prism?
Find the value of the combination 9 c 4
Enter your answer in the box.
Kenny is making creamy rice pudding his recipe requires 4 cups of milk he has a quart of milk in his fridge dose he have enough milk explain
Help Geometry!!
AC is tangent to circle O at A. If , m<BY= 24 , what is m<YAC?
a) 48
b) 156
c) 78
d) 132
please help- Your supposed to find x, y, and z and round to the nearest tenth
The Venn diagram represents the results of a survey that asked participants whether they would want a bird or a fish as a pet.
Enter your answers in the boxes to complete the two-way table based on the given data.
Answer with Step-by-step explanation:
As we can see the venn diagram:
number of bird+fish=6
number of bird+not fish=8
number of fish+not bird=19
and number of not fish and not bird=22
Hence, we get the following table
Fish Not Fish Total
Bird 6 8 14
Not Bird 19 22 41
Total 25 30 55
Fish Not Fish Total
Bird 6 18 14
Not Bird 19 22 41
Total 25 30 55
To solve this system of equations by elimination, what operation could be used to eliminate the y-variable and find the value of x? 2x − 4y = 6 −3x + 3y = 12 A) add 3 times the second equation to 4 times the first equation B) add 4 times the second equation to 3 times the first equation C) subtract 3 times the second equation from 4 times the first equation D) subtract 4 times the second equation from 3 times the first equation
Answer:
Option B is correct.
add 4 times the second equation to 3 times the first equation
Step-by-step explanation:
Given the system of equation:
[tex]2x - 4y = 6[/tex] ......[1]
[tex]-3x + 3y =12[/tex] .....[2]
Multiply equation [1] by 3 we get;
[tex]3(2x-4y) = 3 \cdot 6[/tex]
Using distributive property; [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]
6x - 12y = 18 .......[3]
Multiply equation [2] by 4 we get;
[tex]4(-3x+3y) = 4 \cdot 12[/tex]
Using distributive property we get;
-12x + 12y = 48 ......[4]
Add equation [3] and [4] to eliminate y and solve for x;
(6x -12y) + ( -12x +12y ) = 18 + 48
6x - 12y -12x + 12y = 66
Combine like terms;
6x - 12x = 66
or
-6x = 66
Simplify:
x = -11
Therefore, the operation which could be used to eliminate the y-variable and find the value of x is;
add 4 times the second equation to 3 times the first equation.
Answer:
Option B
Step-by-step explanation:
Given is a system of two equations as
[tex]2x − 4y = 6 \\−3x + 3y = 12[/tex]
To solve them using elimination:
Elimination method is the method of making coefficients of one variable numerically equal
IN the given system we have -4 as coefficient for y in I equation and 3 for y in II equation.
To make them numerically equal with opposite signs we can multiply I equation by 3 and II by 4
WE get
[tex]6x-12y =18\\-12x+12y=48[/tex]
Now if we add these two we are able to eliminate y from the system
Adding gives
[tex]-6x=66\\x=-11[/tex]
So option B is right
Find the height of the cylinder.
options;
4.8 in.
2.4 in.
14.4
7.2 in.
The height of cylinder is,
⇒ h = 2.4 inches
We have to given that,
In a cylinder,
Volume = 271.4 inches³
And, Radius = 6 inch
Since, We know that,
Volume of cylinder is,
⇒ V = πr²h
Where, V is volume , r is radius and h is height.
Substitute all the values, we get;
⇒ 271.4 = 3.14 × 6² × h
⇒ 271.4 = 3.14 × 36 × h
⇒ 271.4 = 113.04 × h
⇒ h = 2.4 inches
Thus, The height of cylinder is,
⇒ h = 2.4 inches
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How do you use properties of exponents and logarithms to rewrite functions in equivalent forms and solve equations?
Final answer:
To use properties of exponents and logarithms effectively, one must apply specific rules such as the logarithm of a product being the sum of the logarithms and the logarithm of a number raised to an exponent being the product of the exponent and the logarithm. Log transformations help linearize and solve equations involving exponents.
Explanation:
To rewrite functions in equivalent forms and solve equations using the properties of exponents and logarithms, one must understand several key rules and relationships. For example, the common logarithm (log) indicates the power to which 10 must be raised to equal a given number.
Two essential properties we use are:
The logarithm of a product of two numbers is the sum of the logarithms of the two numbers (log xy = log x + log y).The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number (log x^n = n log x).Exponential and logarithmic functions are inverses. This relationship allows us to simplify complex expressions and solve exponential equations by taking the logarithm of both sides. For instance, the natural logarithm (ln or loge) and the base e exponential are inverse functions, so ln (e^x) = x and e^(ln x) = x.
A log transformation can linearize functions that involve an exponent by taking the log of both sides of the equation. This technique is valuable in solving equations where the variable is an exponent.
Which triangles are similar?
a
b
c
d
What is the linear function that best fits the data set?
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3.2km/50min X 60min/1hr X 1mi/1.6km
A) 2.4mi/hr
B) 2.4km/hr
C) 12mi/hr
D) 12km/hr
The student's conversion calculation of speed units from kilometers per minute to miles per hour yields a speed of 2.4 miles/hour, so the answer is choice A.
Explanation:The question is a conversion exercise in speed units from kilometers per minute to miles per hour. We have the following information: 3.2 km in 50 min, and we know that 1 mile is equivalent to 1.6 km and 60 min is equivalent to 1 hour. Thus, the conversion is as follows:
3.2 km ÷ 50 min. = 0.064 km/min.
Converting km/min to mi/hr involves multiplying by 60 (minutes in an hour) and dividing by 1.6 (km in a mile), and we get:
(0.064 km/min x 60 min/hr) ÷ 1.6 km/mi. = 2.4 mi/hr.
Hence, the correct answer is (A) 2.4 miles/hour.
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how do I solve (x-5)(x-1)=0