Answer:
3. Object C.
Step-by-step explanation:
The inertia of an object is the measure of the force required to set it in motion. For two objects to have the same motion, the one with the greater mass will require a proportionately greater force to achieve the same motion.
Object C, with a mass of 1,250,000 grams (1,250 kg) will have the greatest inertia.
Please help with both precalc questions! 2 dif problems
Answer:
Step-by-step explanation:
For the first problem you have:
[tex]sin^2(x)-sin(x)=0[/tex]
Factor out a sin(x) to get:
[tex]sin(x)[2sin(x)-1]=0[/tex]
Individually, set both terms equal to zero:
[tex]sin(x)=0[/tex]
[tex]2sin(x)-1-0[/tex]
The first equation is asking "sine of what angle gives zero?" The sine of 0 will give zero, and so will the sine of pi, and 2pi, etc. Therefore, you can generalize this by saying the solution is pi multiplied by an integer 'n' where 'n' can be from zero to infinity:
[tex]x=n\pi[/tex]
where n = 0, 1, 2, 3, 4, 5, etc..
(make sure you specify that 'n' can equal zero.)
For the second equation, add 1 to both sides to get:
[tex]2sin(x)=1[/tex]
Divide both sides by 2 to get:
[tex]sin(x)=\frac{1}{2}[/tex]
Sine of what gives 1/2? Sine of pi/6 gives 1/2, and so does 5pi/6. Therefore, the two solution here would be pi/6 plus a phase shift of 2pi, and 5pi/6 plus a phase shift of 2pi:
[tex]x=\frac{\pi }{6} +2n\pi[/tex]
[tex]x=\frac{5\pi }{6} +2n\pi[/tex]
The second problem states that:
[tex]cos(u)=\frac{4}{5}[/tex]
Cosine is defined as the adjacent side of a right triangle divided by the hypotenuse of the right triangle:
[tex]cos(u)=adjacent/hypotenuse[/tex]
After drawing a triangle, the adjacent side is 4, and the hypotenuse is 5. But first, lets rewrite sin(2u) using the double angle identity to get:
[tex]sin(2u)=2sin(u)cos(u)[/tex]
But we know the value of cosine of 'u', it is 4/5. Therefore:
[tex]sin(2u)=2sin(u)*\frac{4}{5}[/tex]
[tex]sin(2u)=\frac{8}{5} sin(u)[/tex]
To find the sine of 'u', use the triangle you should have constructed when I defined cosine as the adjacent over the hypoptenuse. Sine is defined as the opposite over the hypotenuse. We have:
[tex]sin(u)=opposite/hypotenuse[/tex]
We have the adjacent, we have the hyppotenuse, and we want the opposite. If we find the opposite side, we can find the sin(2u). Use pythagogrean's theorem to find the opposite:
[tex]adjacent^2+opposite^2=hypotenuse^2[/tex]
[tex]4^2+opposite^2=5^2[/tex]
[tex]opposite^2=25-16[/tex]
[tex]opposite=3[/tex]
Finally, we have that:
[tex]sin(u)=\frac{3}{5}[/tex]
Or:
[tex]sin(2u)=\frac{8}{5}*\frac{3}{5} =24/25[/tex]
Hopefully you could follow along. There is a lot going on here, but since youre in pre-calc, you should be able to follow along as long as you follow my steps.
Factorise this expression as fully as possible 12x3 - 9x?
please help
Answer:
12x3-9x
=3-12x9x
=3-21x
=21x-3
The volume of a sphere is 29307 cubic centimeters. What is the radius of the sphere?
Round to the nearest whole number.
Answer:
19 cubic centimeters
Step-by-step explanation:
The equation for the volume of a sphere is [tex](4/3)\pi r^3[/tex].
We can setup the equation as [tex]29307 = \frac{4}{3}\pi r^3[/tex].
Now we need to isolate the r^3. Divide both sides by 4/3 and pi, which leaves [tex]\frac{29307}{(4/3) \pi } =r^3[/tex]
Now we take the cube root of both sides to have a single r on the right side. This comes out to equal 19 cm^3
0=x^2+2x-11 solve by completing the square
Answer:
Below in bold.
Step-by-step explanation:
x^2 + 2x- 11 = 0
x^2 + 2x = 11
x^2 + 2x + 1 = 11 + 1
(x + 1)^2 = 12
x + 1 = ±√ 12
x = -1 ± √12
= -4.464, 2.464 to the nearest thousandth.
Martín quiere poner una manguera color neón alrededor del helado que está afuera de su nevería para llamar la atención de sus clientes. Considerando las dimensiones del helado como se muestra en la figura, ¿Cuál es la longitud en centímetros de manguera que se requiere para rodear el helado? *
area 80 cm
longuitud 89. 44cm
215. 04 cm
295. 04 cm
304. 48 cm
384. 48 cm
La manguera que necesita Martín para rodear el helado es de 304,48m
Cómo calcular la longitud de la manguera que necesita Martín?Para calcular la longitud de la manguera que necesita Martín para rodear el helado es necesario aplicar la siguiente fórmula matemática:
Longitud de la manguera = π × r + 2 × LLongitud de la manguera = 3,14 × 40 + 2 × 89,44 Longitud de la manguera = 125,6 + 178,88Longitud de la manguera = 304, 48 mDe acuerdo a lo anterior, la longitud de la manguera que necesita Martín es de 304,48m.
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Charlotte is redecorating the master bedroom in her house. She has purchased a new bedroom set and also plans to paint the room and put in new flooring. The room is rectangular, with dimensions of 16 feet (length) by 13 feet (width). The walls in the room are 9 feet tall, and the room contains two doors and two windows. Charlotte has decided to put new carpet in the bedroom. The carpet she chose costs $1.85 per square foot, not including the cost of labor or other related materials. She was given the following information by the local flooring store where she is purchasing the carpet. She is required to purchase a piece of carpet which includes a 3-inch overlap on all sides. Labor and material costs will relate to the area of this piece. The labor costs are $23 per hour, per person. A two-person carpet crew can lay 50 square feet of carpet each hour. The crew that will complete the job at Charlotte's house will be a four-person crew. There is an additional $75 fee to cover the cost of equipment, materials, and supplies. What are the dimensions of the piece of carpet that Charlotte must purchase? Note: Express your answer as a decimal number and do not round.
Answer: 2.23 hours
Step-by-step explanation:
dimensions of the room------------------- >16*13
1 in---------------- >0.0833333 foot
3 in----------------- >x
x=3*.0833333=0.25 ft
Let
C-------------- > dimensions of the piece of carpet that Charlotte must purchase
C-------------- > (16+2*0.25)*(13+2*0.25)---------- > (16.50)*(13.50)=222.75 ft²
The answer a the question 1) is 16.50 feet X 13.50 feet
The answer a the question 2) is 222.75 ft²
3. How many hours should it take for the four-person crew to lay the flooring in Charlotte's bedroom?
if two-person carpet crew can lay 50 square feet of carpet---------- > 1 hour
four person carpet crew can lay 100 square feet of carpet---------- > 1 hour
therefore
if 100 ft² carpet----------------------- > 1 hour
222.75 ft² carpet--------------------- > x
x=222.75/100=2.2275 hours=2.23 hours
The answer is 2.23 hours
Oscar buys his lunch in the school cafeteria. The cost of 15 school lunches is $33.75.
Part 1: If you had to find a graph to represent this rate, would slope would you be looking for?
Part 2: Using the rate you determined, complete this ordered pair: (5, ________)
Answer:
Part 1: 2.25
Part 2: (5, 11.25)
Step-by-step explanation:
Part 1: 33.75/15= 2.25
Part 2: 5*2.25= 11.25
Find the lateral area and surface area of a cone with an altitude of 5 feet and a slant height of 9 and 1/2 feet. Round to the nearest tenth, if necessary.
Check the picture below.
we know the LA is 9 and 1/2 or namely 19/2 and the height is 5, so
[tex]\stackrel{slant~height}{\cfrac{19}{2}}~~ = ~~\stackrel{slant~height}{\sqrt{r^2+h^2}}\implies \left( \cfrac{19}{2} \right)^2~~ = ~~r^2+5^2\implies \cfrac{361}{4}~~ = ~~r^2+25 \\\\\\ \cfrac{361}{4} - 25~~ = ~~r^2\implies \cfrac{261}{4}=r^2\implies \sqrt{\cfrac{261}{4}}=r\implies \boxed{\cfrac{3\sqrt{29}}{2}=r} \\\\[-0.35em] ~\dotfill\\\\ LA=\pi r\stackrel{slant~height}{\sqrt{r^2+h^2}}\implies LA=\pi \left( \cfrac{3\sqrt{29}}{2} \right)\cfrac{19}{2}\implies \boxed{LA=\cfrac{57\pi \sqrt{29}}{4}}[/tex]
[tex]~\dotfill\\\\ SA=\pi r\sqrt{r^2+h^2}~~ + ~~\pi r^2\implies SA=LA~~ + ~~\pi r^2 \\\\\\ SA=\cfrac{57\pi \sqrt{29}}{4}~~ + ~~\cfrac{3\pi \sqrt{29}}{2}\implies \boxed{SA=\cfrac{63\pi \sqrt{29}}{4}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill LA\approx 241.1\qquad SA\approx 266.5~\hfill[/tex]
what is 5 2/3 x 13? I'm not really good with fractions
Answer:
The answer is 221/2 or 73 ⅔
Step-by-step explanation:
5 ⅔ = (3 × 5 + 2) ÷ 3 = 17/3
Now,
17/3 × 13 = 221/2 = 73 ⅔
Thus, The answer is 221/2 or 73 ⅔
Select the correct answer. which expression is equivalent to ^3sqrt56x^7y^5
The exponent expression ∛(56x⁷y⁵) is equivalent to the expression 2x²y∛(7xy²).
What is an exponent?Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.
The expression will be given as
[tex]\sqrt[3]{56x^7y^5}[/tex]
The expression can be written as
[tex]\rightarrow \sqrt[3]{2*2*2*7 \ x^3 \ x^3 \ x \ y^3 \ y^2 }\\\\\rightarrow 2*x*x*y * \sqrt[3]{7xy^2} \\\\\rightarrow 2x^2 y \sqrt[3]{7xy^2 }[/tex]
More about the exponent link is given below.
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HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Simplify the following expression: (52)^8
How many solutions are there to this nonlinear system
Answer:
well its two
Step-by-step explanation:
but A nonlinear system could be representative of two circles that overlap and intersect in two locations, hence two solutions. A nonlinear system could be representative of a parabola and a circle, where the vertex of the parabola meets the circle and the branches also intersect the circle, hence three solutions.
Which expression is equivalent to sin7π/6?
Answer:
-6
Step-by-step explanation:
The answer is: 7π6=−π6
π= 3.14 or 22/7
so 7x3.14= 21.98
than divide by 6
An equilateral triangle with side length 19 cm is shown in the diagram, work out the height of the triangle. Give your answer rounded to 1 DP. The diagram is not drawn accurately.
Answer:
h = 16.5
Step-by-step explanation:
Remark
The formula below really is the Pytharagan formula disguised.
h^2 = hypotenuse (side)^2 - (1/2 side)^2
Givens
side = 19 cm
Solution
h^2 = 19^2 - (1/2*19)^2 Substitute given into formula
h^2 = 361 - (9.5)^2 square 9.5
h^2 = 361 - 90.25 Subtract
h^2 = 270.75 Take the square root of both sides
√h^2 = √270.75
Answer: h = 16.5
С
2 ft.
4 ft.
What is the perimeter? If necessary, round to the nearest tenth.
Answer:
10.47 to the nearest hundredth
Step-by-step explanation:
By Pythagoras
c^2 = 2^2 + 4^2 = 20
c = √20
c = 4.47
Perimeter = 2 + 4 + 4.472
The perimeter of the right-angled triangle is 6 + 2√(5) feet.
What is Pythagoras' theorem?Pythagoras' Theorem states that the square of the hypotenuse side of a right-angled triangle is equal to the sum of the squares of the other two sides.
Given that a right-angled triangle.
The perpendicular length is 2 feet, the base length is 4 feet.
We need to use the Pythagorean theorem to find the length of the hypotenuse, and then add up the lengths of all three sides to get the perimeter.
In this case, we can use it to find the length of the hypotenuse c:
2² + 4² = c²
4 + 16 = c²
20 = c²
c = √(20) = 2√(5)
Now we can add up the lengths of all three sides to get the perimeter:
Perimeter = a + b + c
Perimeter = 2 + 4 + 2√(5)
Perimeter = 6 + 2√(5) feet
Therefore, the perimeter = 6 + 2√(5) feet
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simplify (-3x)^2
please I need to know this answer
Answer:
9x²
Step-by-step explanation:
(- 3x)²
= - 3x × - 3x
= - 3 × - 3 × x × x
= 9 × x²
= 9x²
The linear function f(x)=ax+b is graphed in the coordinate plane. Two equal intervals are compared,[-3,3] and [9,15]. What conclusion can be drawn from each interval of 6?
The linear function f(x) = ax + b has a constant rate
The conclusion from the each interval is that the function values changes at a constant rate
How to determine the conclusion?
The linear function is given as:
f(x) = ax + b
The interval is given as:
[-3,3] and [9,15]
Since the function is a linear function, the conclusion from the each interval is that the function values changes at a constant rate
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Which is an exponential decay function?
f(x) =
4
O f(x) =
13 (7)
O =1 (
O fx)=9)*
f
O flx) = (-3)
9
() =
An exponential decay function is flx) = (-3)9, the correct option is D.
What is exponential growth or decay function?Consider the function:
[tex]y = a(1\pm r)^m[/tex]
where m is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.
If there is plus sign, then there is exponential growth happening by r fraction or 100r %
If there is negative sign, then there is exponential decay happening by r fraction or 100r %
We are given that;
f(x) =4
An exponential decay function is a function of the form:
f(x) = ab^x
where a and b are positive constants and b < 1.
The value of b determines how fast the function decreases as x increases. The smaller the value of b, the faster the decay.
To find which option is an exponential decay function, we need to compare their values of b.
Option A has f(x) = 4(1/3)x. This means that b = 4^(1/3), which is approximately 1.587. Since b > 1, this is not an exponential decay function.
Option B has f(x) = 13(7)^x. This means that b = 7, which is greater than 1. This is not an exponential decay function.
Option C has f(x) = (9/5)^x. This means that b = 9/5, which is also greater than 1. This is not an exponential decay function.
Option D has f(x) = (-3)(9)^(-x). This means that b = 9^(-1), which is equal to 1/9. Since b < 1, this is an exponential decay function.
Therefore, by exponential growth and decay the answer will be flx) = (-3)9
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It cost $120 to buy the materials for crown molding in the completed office. (Crown molding is the decorative border where the walls meet the ceiling. It will go all the way around all four walls.) Using the same materials, how much will it cost to buy all of the crown molding for the bedroom? Round up to the nearest whole dollar.
$26 $79 $47 $75
Answer:75
Step-by-step explanation:
Find x
20x + 5 = 5x +65
Answer:
x=4
Step-by-step explanation:
20x-5x=65-5
15x=60
x=60/15
x=4
Answer:
x = 4Step-by-step explanation:
In the question we are given with an equation that is 20x + 5 = 5x + 65 . And we are asked to find the value of x.
Solution :
[tex] \longmapsto \: 20x + 5 = 5x +65[/tex]
Step 1 : Subtracting 5 on both sides :
[tex] \longmapsto \: 20x + \bold{ \cancel{5}} - \bold{ \cancel{5}}= 5x + \bold{65 }- \bold{5}[/tex]
On further calculations, we get :
[tex] \longmapsto \: 20x = 5x + 60[/tex]
Step 2 : Subtracting 60 on both sides :
[tex] \longmapsto \:20x - 60 = 5x + \bold{ \cancel{60}}- \bold{ \cancel{60}}[/tex]
On further calculations, we get :
[tex] \longmapsto \:20x - 60 = 5x[/tex]
Step 3 : Transposing 5x to left hand side and -60 to right hand side :
[tex] \longmapsto \:20x - 5x = 60[/tex]
On further calculations , we get :
[tex] \longmapsto \:15x = 60[/tex]
Step 4 : Divide by 15 on both sides :
[tex] \longmapsto \: \frac{ \cancel{15}x}{ \cancel{15} } = \cancel{ \frac{60}{15} }[/tex]
On further calculations, we get :
[tex] \longmapsto \: \red{ \boxed{x = 4}}[/tex]
Therefore , value of x is 4 .Now, we are verifying our answer by substituting value of x in given equation :
20x + 5 = 5x + 6520 ( 4 ) + 5 = 5 ( 4 ) + 6580 + 5 = 20 + 6585 = 85L.H.S = R.H.SHence, Verified .Therefore , our answer is correct
#Keep Learningcan someone please help me with this
Answer:
(D) 29.3
Step-by-step explanation:
The answer is all the days added together and then divided by 10.
20+30+40+38+25+22+39+22+26+31=293.
293/10=29.3
using rounding to the nearest 10 which number is best estimate of 432 - 169
Find the surface of the figure.
Answer:
64 square in.
Step-by-step explanation:
4*4=16
4*6*1/2*4= 48
16+48= 64
Answer:
64in^2
Step-by-step explanation:
Surface area of pyramid =
[tex] \frac{1}{2}( p \times l) + b[/tex]
plugging the numbers in, 1/2(16*6)+16
SA= 64
Complete the steps to evaluate log798, given log72 ≈ 0.356. how can you rewrite log798 using the product property?
The expression [tex]\rm log_{7} 98[/tex] using the product property is [tex]\rm log_{7} 49 + \rm log_{7} 2[/tex].
What is a logarithm?A logarithm is the exponentiation inverse function that can be expressed by the exponent or power to which a base must be raised to yield a number.
It is given that [tex]\rm log_{7} 2[/tex] = 0.356
We can write [tex]\rm log_{7} 98[/tex] in terms of [tex]\rm log_{7} 2[/tex]
[tex]\rm log_{7} 98[/tex] = [tex]\rm log_{7} (49\times 2)[/tex]
In logarithm, the product will change in addition
[tex]\rm log_{7} 98[/tex] = [tex]\rm log_{7} (49\times 2)[/tex]
= [tex]\rm log_{7} 49 + \rm log_{7} 2[/tex]
Hence, the expression [tex]\rm log_{7} 98[/tex] using the product property is [tex]\rm log_{7} 49 + \rm log_{7} 2[/tex]
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Answer:
log7 2 + log7 49
log7 49= 2
Step-by-step explanation:
Question 2 Which relationship is NOT a function?
Answer:
Top left optionStep-by-step explanation:
According to definition of the function, each input must have exactly one output.
One of the given relationships - T-shirt prices reveals two outputs.
All the rest show one-to-one relationship.
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
77
Step-by-step explanation:
A=B x H divide by 2
A= 14 x 11 /2 = 77
Select the correct answer.
ΔABC is reflected across the x-axis and then translated 4 units up to create ΔA′B′C′. What are the coordinates of the vertices of ΔA′B′C′ ?
A.
A′(-3, 3), B′(-1, 1), C′(-2, 3)
B.
A′(3, -3), B′(1, -1), C′(2, -3)
C.
A′(3, -5), B′(1, -7), C′(3, -5)
D.
A′(-3, 3), B′(-1, 1), C′(-2, -3)
Answer:
The correct to the question about is simply C. A is ruled out because it doesn't represent refections
in a cyclic quadrilateral ABRS, if AR=BS, prove that AS=RB and AB is parallel to SR
pls help and do quick!
find x
Answer:
x = 90
Step-by-step explanation:
If the line is straight.
Angles on a straight line add up to 180
2x = 180
x = 90
helpp Its for calculus
Answer:
its 18
Step-by-step explanation:
Answer:
the answer is 18
Step-by-step explanation:
