In triangle ABC, ∠A is a right angle and m∠B = 45°. Find BC. If your answer is not an integer, leave it in the simplest radical form. The question is multiple choice and the choices are below. A. 20[tex]\sqrt{2}[/tex] ft B. 10 ft C. 20 ft D. 10 [tex]\sqrt{2}[/tex] ft

In Triangle ABC, A Is A Right Angle And MB = 45. Find BC. If Your Answer Is Not An Integer, Leave It

Answers

Answer 1

Answer: D [tex]10\sqrt{2}[/tex]

Step-by-step explanation:

It says that the measure of angle B is 45 degrees. So if we were to put in 45 degrees  we could see that is is opposite AC and BC which we needs to find is the hypotenuse. So since we know the opposite of angle B  is 10 ft we can using that to find the length of BC.  Opposite hypotenuse is the sine function so we will use it to calculate the length of BC.

sin(45) = [tex]\frac{10}{BC}[/tex]       multiply both sides by BC  

BC sin(45) = 10      divide both sides by sin(45)

BC = [tex]\frac{10}{sin(45)}[/tex]

BC = [tex]10\sqrt{2}[/tex]

Answer 2

Answer:

[tex]\huge\boxed{Option\ D : \ BC = 10\sqrt{2}\ ft }[/tex]

Step-by-step explanation:

Since it's a right angled triangle, We'll use trigonometric rations.

Given that m∠B = 45°

So,

Sin B = opposite / hypotenuse

Where m∠B = 45°, opposite = 10 ft and hypotenuse = BC

Sin 45 = 10 / BC

[tex]\sf \frac{\sqrt{2} }{2} = \frac{10}{BC}[/tex]

BC = 20 / √2

Multiplying and Dividing by √2

BC = 20√2 / √(2)²

BC = 20 √2 / 2

BC = 10√2 ft


Related Questions

el deposito de gasolina en una estacion de servicio alcanza para 5 dias si se venden 1400 galones diarios ¿cuantos galones diarios deben venderse para que el deposito cura 7 dias?

Answers

Answer:

u should put this also in English then type it in so it will translate

In Parallelogram DEFG, DH= x+3, HF= 3y, GH= 2x-5, and HE= 5y+2. Find the values of x and y.

Answers

Answer:

y=13  , x=36

Step-by-step explanation:

The diagonal of parallelogram bisect at a point where the sides across the intersection are equal

DH=HF

x+3=3y

x=3y-3   first equation

HE=GH

2x-5=5y+2 ⇒ 2x-5y=7 second equation

solve by substitution: x=3y-3

2x-5y=7

2(3y-3)-5y=7

6y-6-5y=7

y=7+6

y=13

x=3y-3

x=3(13)-3

x=36

In the Rhombus, m<3=80. Find m<2

160
80
50
40

Answers

Answer: C. 50

==============================================

Explanation:

The diagonal cuts the rhombus into two congruent isosceles triangles. We know they are isosceles because the non-diagonal sides are equal in length (since all four sides of a rhombus are the same length).

Let x be the measure of angle 1. This is one base angle. The other base angle is also x as well. The third angle of the bottom triangle is angle 3, which is given to us at 80 degrees. For any triangle the three angles always add to 180.

x+x+80 = 180

2x+80 = 180

2x = 180-80

2x = 100

x = 100/2

x = 50

Angle 1 is therefore 50 degrees.

Angle 2 is also 50 degrees because angles 1 and 2 are congruent alternate interior angles. Any rhombus is a parallelogram (but not the other way around) so the top and bottom lines of the rhombus are parallel, allowing the alternate interior angles to be congruent.

Answer:

m<2 = m<1 = 50°

Step-by-step explanation:

In a Rhombus, Diagonals intersect at 90° as well bisect angles.

Therefore, in a triangle formed by <1, 90° at the diagonal intersection and angle bisection of <3 = 40°.

m<1 = m<2 = 50°

Null hypothesis: There is no difference in the average start-up costs of the 4 different types of shops. Alternative hypothesis: There is a difference in the average start-up costs of the shops

Answers

Answer:

True

Step-by-step explanation:

The null and alternate hypothesis are established terms that are used in statistics. Note that the Null hypothesis often represents the expected outcome, as in this example that– "There is no difference in the average start-up costs of the 4 different types of shops".

Meanwhile, the Alternative hypothesis tells the opposite of expected outcome– "There is a difference in the average start-up costs of the shops working statement".

Thus, the forcus of the research would be to prove whether the null hypothesis is true or false. If it is true, then we fail to reject the null hypothesis.

how do you find the area of an open cylinder... what is the Formula?? please help​

Answers

Answer:

Cylinder has a formula

π×r²×h

so of it is open

π×r²×h - π×r²

Answer:

pls give brainiest

Step-by-step explanation:

A=2πr×h(r+h)

line passing through points (-4,2) and (0,3)

Answers

Answer:

y-y1=m(x-x1)

or,y-2=1/4(x+4)

or,4y-8=x+4

or,x-4y+12=0 is the required equation.

Step-by-step explanation:

If it helps you, plz mark it as brainliest

Elena drank 3 liters of water yesterday. Jada drank 3⁄4 times as much water as Elena. Lin drank twice as much water as Jada. Did Lin drink more or less water than Elena? Group of answer choices

Answers

Answer:

Lin drank more water

Step-by-step explanation:

Given

Elena = 3 litres

Jada = ¾ of Elena

Lin = 2 times of Jada

Required

Determine if Lin drank more or less water than Elena

First, we have to get the actual amount of water Jada drank.

Jada = ¾ of Elena

Substitute 3 litres of Elena

[tex]Jada = \¾ * 3 litres[/tex]

[tex]Jada = 9/4 litres[/tex]

[tex]Jada = 2\¼\ litres[/tex]

Lin = 2 * Jada

Substitute 2¼ litres for Jada

[tex]Lin = 2 * 2\¼\ litres[/tex]

[tex]Lin = 2 * 9/4 litres[/tex]

[tex]Lin = 9/2 litres[/tex]

[tex]Lin = 4\frac{1}{2} litres[/tex]

Recall that Elena drank 3 litres

Comparing 3 Litres to [tex]4\frac{1}{2}[/tex] litres, we can conclude that Lin drank more water.

Use mathematical induction to prove the statement is true for all positive integers n. 8 + 16 + 24 + ... + 8n = 4n(n + 1)? Please show work

Answers

Answer:

The sum of the series is Sₙ = n/2 [2·a + (n - 1)·d] where a = 8 and d = 8, therefore 8 + 16 + 24 + ... + 8·n = 4·n·(n + 1)

Step-by-step explanation:

The parameters given are;

8 + 16 + 24 + ... + 8·n = 4·n·(n + 1)

The given series of numbers can be checked to find;

16 - 8 = 24 - 16 = 8

Therefore, the series of numbers is an arithmetic progression with first term = 8, and common difference = 8, we have;

The sum of n terms of an arithmetic progression, Sₙ, is given as follows;

Sₙ = n/2 [2·a + (n - 1)·d]

Where;

a = The first term of the series of numbers = 8

d = The common difference = 8

∴ Sₙ = n/2 × [2×8 + (n - 1)×8] = n [2×8/2 + (n - 1)×8/2]  =  n × [8 + (n - 1)×4]

Sₙ =  n × [8 + (n - 1)×4] =  n × [8 + 4·n - 4] = n × [8  - 4 + 4·n] = n × [4 + 4·n]

Sₙ =n × [4 + 4·n] = 4 × n×(n + 1) = 4·n·(n + 1).

Use the substitution method to solve the system of equations. Choose the correct ordered pair.

Answers

Answer:

b

Step-by-step explanation:

Answer:

The answer is D or (10,-9)

Step-by-step explanation:

Since y is already given (and you have to use the substitution method) substitute y into one of the equations. So you should have something like this:

-2x+11=3x+21

After that merely solve for x which should get you x=10. After you get your x value plug 10 in either (of the original) equation and your y value should be -9. For example if you chose y=-2x+11 you should have y= -2(10)+11. In the end your answer should be (10,-9).

If you want to check your work merely plug your answer into both equations (ex: -9=-2(10)+11 --> -9=-9), therefore you know your answer is correct).

Hope this helped!

A toy box in the shape of a rectangular prism has a volume of 6,912 cubic inches. The base area of the toy box is 288 square inches. What is the height of the toy box?

Answers

Answer:

h= 24 inches

Step-by-step explanation:

(Volume)= (Base Area) * (Height)

6,912= 288h

h=

Which professionals most directly use geometry in their work? A. accountants B. astronomers C. judges D. pharmacists E. politicians\

Answers

Answer:

Astronomers directly use geometry in their work rather than accountants , judges, pharmacist and politicians.

They used geometry to measure velocity , direction, distance, relativity, momentum, and probability. They used it to look at objects in the sky with a telescope by setting a required angle to get a proper view .

But Accountants, judges, pharmacist and politicians are not in use of geometry directly or frequently.

Hence, Option 'B' is correct.

Step-by-step explanation:

Answer: b

Step-by-step explanation:

F(x)=0.5x^2-2 and g(x)=8x^3+2

Answers

Answer:

(f*g)(x) = 4x⁵ - 16x³ + x² - 4

Step-by-step explanation:

To find (f*g)(x), you need to multiply f(x) with g(x).  Use FOIL to multiply.

f(x) = 0.5x² - 2

g(x) = 8x³ + 2

(f*g)(x) = (0.5x² - 2)(8x³ + 2)

(f*g)(x) = 4x⁵ + x² - 16x³ - 4

(f*g)(x) = 4x⁵ - 16x³ + x² - 4

what’s the equation of line ?
y =__x + __

Answers

Answer:

y=3/4x-2

Step-by-step explanation:

two points from graph (0-2) and (8,4)

find slope m: y2-y1/x2-x1

m=4+2/8-0

m=6/8=3/4

x=0 then y=b=-2

y=3/4x-2

Explain what each of them is.

Answers

Answer:

What are natural numbers?

the positive integers or whole numbers include 1, 2, 3, and etc. sometimes zero.

What are whole numbers?

Whole numbers are 0, 1, 2, 3, 4, 5, 6. Whole numbers include positive integers along with 0.

17, 99, 267, 8107 and 999999999 are examples of whole numbers.

What are rational numbers?

A rational number is a number that can be express as the ratio of two integers. A number that cannot be expressed that way is irrational. For example, one third in decimal form is 0.33333333333333

What are irrational numbers?

A real number that can NOT be made by dividing two integers (an integer has no fractional part). "Irrational" means "no ratio", so it isn't a rational number.

Example: π is an irrational number.

What are real numbers?

The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as √2.

Included within the irrationals are the transcendental numbers, such as π

3/v=2/4? i need help plz

Answers

Answer:

v = 6

Step-by-step explanation:

3/v = 2/4

We can use cross products to solve

2v = 3*4

2v = 12

Divide each side by 2

2v/2 = 12/2

v =6

Answer:

v=6

Step-by-step explanation:

If this is making them equal, then you should know that 2/4 is 1/2 , so you could just multiply 3 by both the 1 and the 2 in 1/2 and 1 times 3 is 3 which is what we have and 2 times 3 is 6 which is v.

Which statement about this figure is true ?

a. it has reflection al symmetry with one line of symmetry

b. it has no rotational symmetry

c. it has no rotational symmetry with an angle of rotation of 90 degrees

d. it has no reflectional symmetry

Answers

Its B because if you were to rotate the bottom to left or right it wouldnt be symmetrical

The statement that is true about the given figure, a limaçon, is c. It has no rotational symmetry, with an angle of rotation of 90 degrees.

Let's examine each option and explain why they are true or false:

a. It has reflectional symmetry with one line of symmetry: This option is false. To have reflectional symmetry with one line of symmetry, the figure must be identical on both sides when divided by a line. The given figure, a limaçon, does not exhibit this property.

b. It has no rotational symmetry: This option is true. Rotational symmetry means that the figure remains unchanged after rotation by certain angles. The limaçon does not have any rotational symmetry because it does not appear the same after any rotation.

c. It has no rotational symmetry, with an angle of rotation of 90 degrees: This option is true. A figure with rotational symmetry of 90 degrees would appear the same after a 90-degree rotation. However, the limacon does not exhibit this property.

d. It has no reflectional symmetry: This option is true. Reflectional symmetry requires the figure to have a line of symmetry dividing it into two identical halves. The limaçon does not possess such a line of symmetry.

Based on the explanations above, the correct statement is that the limaçon has no rotational symmetry with an angle of rotation of 90 degrees (option c).

Learn more about symmetry here:

https://brainly.com/question/32342060

#SPJ4

A researcher wants to use a confidence interval to estimate the proportion of college students in his state who plan to vote in the 2020 presidential election. He plans to randomly sample 120 college students, and plans to construct a 95% or 99% confidence interval. Which of these confidence intervals will be wider, and why

Answers

Answer:

99% confidence interval will be wider because as the level of confidence increase the width increases as well and the standard error decreases

Step-by-step explanation:

The  confidence interval is directly proportional to the sample size  hence the 99% confidence interval will be wider than the 95% confidence interval of the sample of 120 college students

using a 99% confidence interval gives a more accurate result than a 95% confidence because the standard error decreases with increase in confidence interval

Some time ago , Keith's height and his nephew's height were at a ratio of 15:7. Then, Keiths height increased by 16% and his nephew,s height doubled. Keith is now 34 cm taller than his nephew, what is their total current height

Answers

Answer:

The answer is below

Step-by-step explanation:

The ratio of Keith's height and his nephew's height is 15:7. Let keith height be x cm and his nephews height be y cm.

[tex]\frac{x}{y}=\frac{15}{7} \\x=\frac{15}{7}y[/tex]

Keiths height increased by 16% , therefore Keith new height is (100% + 16%) × x = 1.16x

The nephew height is doubled, therefore his new height is 2y.

Given that Keith is now 34 cm taller than his nephew

1.16x = 2y + 34

but x = (15/7)y

[tex]1.16(\frac{15}{7} )y=2y+34\\\\\frac{87}{35} y=2y+34\\\\\frac{87}{35} y-2y=34\\\\\frac{17}{35}y=34\\ \\y=\frac{34*35}{17}\\ \\y=70\ cm[/tex]

The nephews new height = 2y = 2(70) = 140 cm

Keith new height = 2y + 34 = 140 + 34 = 174 cm

Their total current height = 140 cm + 174 cm = 314 cm

what is the value of digit 9 in 3.45×0.27×0.3 ? ​

Answers

Answer:

[tex]\boxed{\pink{0.27945}}[/tex]

Step-by-step explanation:

[tex]3.45 \times 0.27 \\ = 0.9315 \times 0.3 \\ = 0.27945[/tex]

Answer: thousandths place

Step-by-step explanation:

                                      ↓

3.45 x 0.27 x 0.3 = 0.27945

                                     

The place values to the right of the decimal point are:

one to the right (2): tenths

two to the right (7): hundredths

three to the right (9): thousandths

four to the right (4): ten thousandths

five to the right (5): hundred thousandths

Solve for b. -11b+7 = 40 b=

Answers

Answer:

B= -3

Step-by-step explanation:

Move the terms that do not contain b to the right then solve. Hope this helps!

Answer:

[tex]\large \boxed{{b=-3}}[/tex]

Step-by-step explanation:

[tex]-11b +7=40[/tex]

Subtract 7 from both sides.

[tex]-11b +7-7=40-7[/tex]

[tex]-11b=33[/tex]

Divide both sides by -11.

[tex]\displaystyle \frac{-11b}{-11} =\frac{33}{-11}[/tex]

[tex]b=-3[/tex]

Euphrosynelight needs 2x-7 while her friend needs 5x+2 how much in total

Answers

Answer:

7x-5

Hope this helped; mark brainliest if it did! :)

I need help pls will give you five stars and a big thank you comrade

Answers

Answer:

B, f(x) = ( x+2) ^2(x-1) (x+3)

Step-by-step explanation:

Looking at the x- intercepts, the line passes at 2, -1, and 3, so B is you answer (:

Hannah’s mom bought a variety pack of chips. There were a total of 12 bags. Her mom put the bags in a jar. There were 5 barbecue,3 plain,3 sour cream, and 1 tortilla.

What is the probability of Hannah selecting a bag of barbecue chips if she doesn’t look in the jar?

A.) 5/12
B.) 5/7
C.) 12/5
D.) 1/12
E.) 7/12

Answers

Answer:

5/12

Step-by-step explanation:

There is a total of 12 bags,  5 of which are bbq

P ( bbq) = number of bbq/ total

             = 5/12

The function f(x) = 50(0.952)x, where x is the time in years, models a declining feral cat population. How many feral cats will there be in 9 years?

Answers

Answer: B) 32

Work Shown:

f(x) = 50(0.952)^x

f(9) = 50(0.952)^9

f(9) = 32.1146016801717

f(9) = 32 approximately

Side note: the exponential function is in the form a*b^x with b = 1+r = 0.952, which solves to r = -0.048. The negative r value means we have a 4.8% decrease each year.

Another note: you don't even need to use math to answer this question. Note how 50 is the starting population and the population is declining. Only choice B has a value smaller than 50, so we can rule out the others right away.

Answer:

  32

Step-by-step explanation:

The initial value of the population is f(0) = 50(0.952^0) = 50. If the population is declining, it must be less than 50 in 9 years. The only answer choice that is less than 50 is ...

  about 32 feral cats

_____

You can evaluate f(9) to choose the same answer:

  f(9) = 50(0.952^9) ≈ 32.114 ≈ 32

can you solve;
3/7+5/21

Answers

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[tex]\frac{3}{7}+\frac{5}{21}[/tex]

[tex]= \frac{3}{7}+\frac{5}{21}[/tex]

[tex]= \frac{9}{21}+\frac{5}{21}[/tex]

[tex]= \frac{9 + 5}{21}[/tex]

[tex]= \frac{14}{21}[/tex]

[tex]= \frac{2}{3}[/tex] (Decimal: 0.666667)

Answer : [tex]\boxed{\frac{2}{3} }[/tex] (Decimal: 0.666667)

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3/7+5/21=2/3

Find the least common denominator or LCM of the two denominators:
LCM of 21 and 7 is 21

For the 1st fraction, since 21 × 1 = 21,
5
21
=
5 × 1
21 × 1
= 5/21

Likewise, for the 2nd fraction, since 7 × 3 = 21,
3
7
=
3 × 3
7 × 3
= 9/21

Add the two fractions:
5
21
+
9
21
=
5 + 9
21
= 14/21

Simplify and get 2/3

Which statement best explains why the sine of an acute angle is equal to the cosine of the angles complement

Answers

Answer:

Option (B)

Step-by-step explanation:

From the figure attached,

ΔABC is a right triangle.

Cosine and Sine ratios from the given triangle will be,

SinA = [tex]\frac{\text{Opposite side}}{Hypotenuse}[/tex]

        = [tex]\frac{a}{c}[/tex]

CosB = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

         = [tex]\frac{a}{c}[/tex]

Therefore, both the ratios (Sine and Cosine) will be equal as [tex]\frac{a}{c}[/tex]

Option (B) will be the correct option.

Two mechanics worked on a car. The first mechanic worked for hours, and the second mechanic worked for hours. Together they charged a total of . What was the rate charged per hour by each mechanic if the sum of the two rates was per hour?

Answers

Answer:

The rate charged by first mechanic per hour= x =$85

The rat charged by second mechanic per hour =y = $70

Step-by-step explanation:

Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of $1900. What was the rate charged per hour by each mechanic if the sum of the two rates was $155 per hour?

Solution

Let

x= hourly rate of the first mechanic

y= hourly rate of the second mechanic

Derive two equations to solve for the two unknowns

10x + 15y = 1900 (1)

x + y = 155 (2)

From (2)

x + y = 155

x=155-y

Substitute x=155-y into (1)

10x + 15y = 1900

10(155-y) + 15y =1900

1550 -10y + 15y =1900

5y =1900-1550

5y=350

Divide both sides by 5

y= 70

Substitute y=70 into (2)

x + y = 155

x + (70) =155

x=155 - 70

= 85

x= 85

The rate charged by first mechanic per hour= x =$85

The rat charged by second mechanic per hour =y = $70

another one another one...........

Answers

Answer:

B

Hope it helped you out

Tysm

Figure ABCD is a rectangle Find the value of x

Answers

Step-by-step explanation:

Since this is a rectangle these two equations for the length have to equal each other.

2x+4=7x-1

We now need to get all of the x's on one side and constant numbers on the other side.

add 1 to both sides and subtract 2x from both sides.

5=5x

divide 5 from both sides.

x=1


please i need help asap lol

A baseball league is holding registration for both a men's league and a women's league. Only a total of 546 players can register, and each team consists of exactly 13 players. If 25 women's teams have already registered, which inequality could be used to find m, the number of men's teams that can register? A. 25(13) + 13m 546 C. 25(13 + 13m) 546

Answers

Answer:

546 - 25 x 13 (divided by) 13

546 - (25 x 13) / 13

Step-by-step explanation:

25 x 13 = 325

546 - 325 = 221

221 / 13 = 17

17 mens teams can register.

Answer:

[tex]25(13)+13m\leq 546[/tex]

A

Step-by-step explanation:

Each team can only consists of thirteen players. Therefore, by letting w represent the number of women's teams and m the number of men's teams, the total number of players is represented by the equation:

[tex]13w+13m[/tex]

The total number of players cannot surpass 546. In other words, it must be less than or equal to. Therefore:

[tex]13w+13m\leq 546[/tex]

We are given that that 25 women's teams have already signed up. To find out the possible number of men's teams that can sign up, we can substitute 25 for w and then solve for m.

Therefore:

[tex]25(13)+13m\leq 546[/tex]

In conclusion, the answer is A.

Other Questions
(will give brainliest) find the value of x Listed below are selected line items from the Cost of Quality Report for Watson Products for last month. Category Amount Rework $725 Equipment maintenance 1,154 Product testing 786 Product repair 695 What is Watson's total prevention and appraisal cost for last month? Who was considered Judaisms greatest prophet?MosesAbrahamIsaacJacob Modern farming methods require moreinputs which are manufactured in industry. Do youagree? Huipiles are ________. Mr. Franklin uses a machine that has an efficiency of 80%. The machine applies a force of 800 N through a distance of 20 m. Mr. Franklin applies a force of 50 N on the machine. Through what distance does Mr. Franklin apply the force? 4 m 16 m 260 m 400 m Which type of energy is producedby vibrations traveling in waves?A. chemical energyB. nuclear energyC. sound energy In the liquidation of a partnership, any gain or loss on the realization of non-cash assets should be allocated:_____.a. first to creditors and the remainder to partners. b. to the partners on the basis of their capital balances. c. only after all creditors have been paid. d. to the partners on the basis of their income-sharing ratio. according to author stephan covey affective communication is driven by: for the functions f(x) = 4x^4+4x^3-8x^2-13x-5 and g(x) = x+1, find (f/g)(x) and (f/g)(2) I MIND TRICK PLZ HELP LOL Troy and Abed are running in a race. Troy finishes the race in 12 minutes. Abed finishes the race in 7 minutes and 30 seconds. If Troy is running at an average speed of 3 miles per hour and speed varies inversely with time, what is Abeds average speed for the race? What property is demonstrated here? (3x-5) x 4 = 3 x (-5 x 4) A) commutative property of addition B) associative property of multiplication C) commutative property of multiplication D) associative property of addition (haven't learned this yet so I have no clue) j. A computer on a network that acts as the central storage location forprograms and data used on the network The Fime Corporation uses a standard costing system. The following data have been assembled for December: Actual direct labor-hours worked 6,200 hours Standard direct labor rate $7 per hour Labor efficiency variance $2,100 Unfavorable The standard hours allowed for Decembers production is: At Groovy Rags, a trendy retail store, manager Eon Forcer doesn't waste any time thinking about whether the employees on his shift get their breaks at a reasonable time. In fact, he claims he is hard pressed to determine which one has "worked hard enough" to even deserve a break. Earlier today, Eon remarked, "I've never met one that likes this job! They're only biding their time and here for the money." Eon's managerial style would be classified as _______. Kyle buys $30,000 of company XYZ's shares, at a share price of $50. A year later, XYZ's share price is $55, and Kyle sells all his shares. How many dollars did Kyle's investment gain The data collected from an experiment shows that as the temperature outside goes up, the number of swimmers at the local poolgoes up. This data shows a/anSelect one:O a direct relationshipb. indirect relationshipc. inverse relationshipO d. no relationship A spring is hung from the ceiling. When a block is attached to its end, it stretches 2.5 cm before reaching its new equilibrium length. The block is then pulled down slightly and released. What is the frequency of oscillation? tolong donk cari apa jawabannya Your mother calls you and asks you to help with a major family decision. Your maternal grandfather is 70 years old and has been diagnosed with a condition that will kill him some time in the next five years. He can have a procedure that will correct the disease and not leave him with any long-term problems, but the procedure has a 10% mortality rate. He wants to have the procedure, but your mother does not want him to. How would you help mediate this issue?