PLS HELP. I tried and cant figure it out.

PLS HELP. I Tried And Cant Figure It Out.

Answers

Answer 1

Answer:

I x² +12x I = -32

Step-by-step explanation:

Absolute value equation:

  x = -4  ; x = -8

x + 4 = 0  and     x + 8 = 0

(x +4)(x + 8) = 0

x*x + x*8 + 4*x + 4*8 = 0

     x² + 4x + 8x  + 32 = 0

         x² + 12x   + 32   = 0

Absolute value equation:

  I x² + 12x I = -32


Related Questions

The volume of a cylindrical can of beans is 45 π cubic centimeters. if the diameter is 6 centimeters, what is the height of the can in centimeters?

Answers

Answer:

h = 5 cm

Step-by-step explanation:

Givens

d = 6cm

V = 45cubic cm

Formula

V = pi * r^2 h                                  substitute values into the formula

Solution

d = 2*r

6 = 2*r                                            Divide both sides by 2

6/2 = 2r / 2

3 = r

45 pi cm^3 = pi * (3)^2 * h            Divide both sides by pi

45 pi/pi = pi * 9 * h / pi

45 = 9h                                         Divide both sides by 4

45/4 = 9h/9                                    

5 cm

Find how many matches Peter won. plss answwer (ಥ _ ಥ)

Answers

Answer:

10 is the right answer...

Step-by-step explanation:

thanks

mark me as brainlist....

Find two positive numbers whose product is 81 and whose sum is a minimum. (enter your answers as a comma-separated list. )

Answers

Answer:  18

Step-by-step explanation:  the smallest two positive numbers whose product is 81 are 9 and 9. 9+9 is equal to 18.

Find the producer surplus at the equilibrium point. 3) s(x) = x 3, 0 k x k 3; x = 3

Answers

The producer surplus at the equilibrium point is 1.0146

An equilibrium (or equilibrium point) of a dynamical machine-generated via an autonomous machine of everyday differential equations (ODEs) is a solution that doesn't change with time.

Equilibrium is the country in which the marketplace delivers and calls for stability each different, and as a result, expenses turn out to be solid. usually, an over-deliver of products or services reasons charges to head down, which leads to higher demand—at the same time as a below-supply or scarcity reasons costs to head up resulting in fewer calls.

The equilibrium equations (balance of linear momentum) are given in index form as(1.4)σji,j+bi=ρu¨i, I,j=1,2,3where σij are additives of (Cauchy) stress, ρ is mass density, and bi is body force additives.

Producer Surplus = area of shadestportion

Area of shaded portion = free of rect minus area of OneD

Aves of OABO=Now serving from

"[3√74-3/5]

= √(x+3)" de

=2 (2√6-√5)

(Jon= √46 = Fure=456-255

(x+3)+1

Area of rectangle OA BC =316

= 3√6

producer surplus = 3√6 - (ure -2√5)

= 2√3-66

= 1.0146

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Pick the correct answer
Please help thanks :)

Answers

Answer:

B

Step-by-step explanation:

First create the equation that has slope of -1 in the form of y=mx+b. Because the slope is -1, m=-1, so the equation is y=-x+b. Now we see that we are given the point (-3, 8) as an intersection point. Substitute x and y for -3 and 8 in our equation. With this information, our equation becomes 8=3+b. Solving, b=5. Our equation is now y=-x+5.

Simplifying all of the answer choices, we have

A. y=-x-5

B. y=-x+5

C. y=-x-5

D. and E. as what they already show

The only answer that matches is B.

Use special right triangles to find the value of the variables no decimal answers

Answers

Step-by-step explanation:

This is trigonometry. Focusing on Y initially, we can see that Y is the opposite, and 32 is the hypotenuse. Therefore, we must use sin:

[tex] \sin(60) = \frac{y}{32} [/tex]

[tex]y = \sin(60) \times 32[/tex]

[tex]y \approx28[/tex]

Next X. We can see that X is the adjacent, and 32 is the hypotenuse, so we must use cos:

[tex] \cos(60) = \frac{x}{32} [/tex]

[tex]x = \cos(60) \times 32[/tex]

[tex]x = 16[/tex]

Now let's look at A. We can see that a is the adjacent, and 12 is the opposite, so we must use tan:

[tex] \tan(60) = \frac{12}{a} [/tex]

[tex]a = \frac{12}{ \tan(60) } [/tex]

[tex]a \approx7[/tex]

Now, B. We can see that B is the hypotenuse, and 12 is the opposite, so we must use sin:

[tex] \sin(60) = \frac{12}{b} [/tex]

[tex]b = \frac{12}{ \sin(60) } [/tex]

[tex]b \approx14[/tex]

Answer:

Below in bold.

Step-by-step explanation:

The first triangle is a 30-60-90 triangle,

so the sides are in the ratio 2 : 1 : √3,  where 2 is the hypotenuse, the 1 is adjacent to 60 degree angle and the √3 is opposite the 60 degree angle.

So x = 1/2 * 32 = 16

and y = 16√3  or 27.71 to nearest hundredth.

The second one is the same special triangle, so

√3/2 = 12/b

b = 24/√3

 = 8√3  or 13.86  to nearest hundredth.

a = 1/2 b = 4√3 or 6.93 to nearest hundredth.

NEED HELP SOLVING

has to be simplified

Answers

hey! the answer is…

3/2c^3-1/12c^2 -4-c^4-c

i also added a picture of how the answer should be written just in case you don’t understand what’s above!

A coin-operated drink machine was designed to discharge a mean of 7 ounces of coffee per cup. In a test of the machine, the discharge amounts in 18 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 7.04 ounces and 0.17 ounces, respectively. If we assume that the discharge amounts are normally distributed, is there enough evidence, at the 0.1 level of significance, to conclude that the true mean discharge,u, differs from ounces? Perform a two-tailed test. Then fill in the table below. I need the two critical values at the 0.1 level of significace. Also need the answers to al other questions and whether we accpe for reject.

Answers

Using the t-distribution, it is found that since the test statistic is between -1.7341 and 1.7341, we do not reject(accept) the null hypothesis, hence there is not enough evidence to conclude that the true mean discharge differs from 7 ounces.

What are the hypothesis tested?

At the null hypothesis, it is tested if the mean is of 7 ounces, that is:

[tex]H_0: \mu = 7[/tex]

At the alternative hypothesis, it is tested if the mean is different of 7 ounces, that is:

[tex]H_1: \mu \neq 7[/tex]

What is the test statistic?

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.

The values of the parameters are given by:

[tex]\overline{x} = 7.04, \mu = 7, s = 0.17, n = 18[/tex]

Hence the value of the test statistic is found as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{7.04 - 7}{\frac{0.17}{\sqrt{18}}}[/tex]

t = 1

What is the decision?

Considering a two-tailed test, as we are testing if the mean is different of a value, with 18 - 1 = 17 df and a significance level of 0.1, the critical value is of [tex]t^{\ast} = 1.7341[/tex]

Since the test statistic is between -1.7341 and 1.7341, we do not reject(accept) the null hypothesis, hence there is not enough evidence to conclude that the true mean discharge differs from 7 ounces.

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Rounding off 6 400mm​

Answers

The rounding off a given number implies approximating the number to the required value. Thus the answer to the given question is 6 000 mm.

Rounding off a given number implies approximating the number to the required value. This can be done in two major ways: rounding up or rounding down.

Rounding up implies considering the required digit if it is up to or greater than 5, which turns to 1. Rounding down requires no consideration of digits less than 5 which turns to 0.

Thus considering the given question, Since the second digit is 4 which is lesser than 5, then it turns to a zero. So that;

rounding off 6 400 mm would give 6 000 mm.

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A bag contains 3 red marbles, 7 blue marbles, and 2 green marbles. what is the probability of choosing a blue marble when one marble is drawn?

Answers

Answer: 7/12

Step-by-step explanation: There is a total of 3+7+2 = 12 marbles in the bag. 7 are blue marbles so there is a 7/12 chance of getting a blue marble when one marble is drawn.

Answer:

7/12

or an 84%

Step-by-step explanation:

particular company's net sales, in billions, from 2008 to 2018 can be modeled by the expression t2 + 14t + 85, where t is the number of years since the end of 2008. What does the constant term of the expression represent in terms of the context?

Answers

The constant in the expression represents that the company earned  85 billion dollars in 2008.

What does the constant represent?

The expression given in the question is known as a quadratic function. A quadratic function is a function that usually has a single variable and it is raised to the power of 2. The graph of a quadratic function is a curve called a parabola. Parabolas may curve upward or downward

An example of a quadratic function is ax² + bx + c

Where: a,b, c are real numbers not equal to zero

c = constant.

The constant in this question is 85. It is the amount earned in 2008

Here are the options:

The company earned  85 billion dollars from 2008 to 2018

The company earned  85 billion dollars in 2008

The company earned 14  billion dollars from 2008 to 2018.

The company earned  14 billion dollars in 2008.

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The slope-intercept form given (6,-5) & perpendicular to -5x - 7y = -17.

Answers

Answer:

[tex]y=\dfrac{7}{5}x-\dfrac{67}{5}[/tex]

Step-by-step explanation:

Slope-intercept form of a linear equation:

 [tex]y=mx+b[/tex]

where:

m is the slope.b is the y-intercept.

Rearrange the given equation so that it is in slope-intercept form:

[tex]\implies -5x-7y=-17[/tex]

[tex]\implies -7y=5x-17[/tex]

[tex]\implies y=-\dfrac{5}{7}x+\dfrac{17}{7}[/tex]

Therefore, the slope of the given equation is -⁵/₇.

If two lines are perpendicular to each other (at right angles), the product of their slopes will be -1.  Therefore, their slopes will be negative reciprocals of each other.

Therefore, the slope of the line perpendicular to the given equation is:

[tex]\sf m=\dfrac{7}{5}[/tex]

Substitute the found slope and the given point (6, -5) into the slope-intercept formula and solve for b:

[tex]\implies -5=\dfrac{7}{5}(6)+b[/tex]

[tex]\implies -5=\dfrac{42}{5}+b[/tex]

[tex]\implies b=-\dfrac{67}{5}[/tex]

Substitute the found slope and the found value of b into the slope-intercept formula to create the equation for the perpendicular line:

[tex]\implies y=\dfrac{7}{5}x-\dfrac{67}{5}[/tex]

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Find a b, 6a 9b, |a|, and |a − b|. (simplify your vectors completely. ) a = −9, 12 , b = 6, 4

Answers

The values of a + b, 6a + 9b, |a|, and |a − b| are −3i + 16j, 0i + 108j, 15 and 17 respectively. This can be obtained by using vector addition, vector subtraction and formula to find magnitude of a vector.

Find the values of a + b, 6a + 9b, |a|, and |a − b|:

Given that,

a = <−9, 12> , b = <6, 4>

These vectors can be rewritten as,

a = <−9, 12> = −9i + 12j

b = <6, 4> = 6i + 4j

To find a + b,we add both vectors a and b together,

a + b = −9i + 12j + 6i + 4j

a + b = −9i + 6i + 12j + 4j

a + b = (−9 + 6)i + (12 + 4)j

a + b = −3i + 16j

To find 6a + 9b, we first find 6a and 9b then add them both together,

6a = 6 (−9i + 12j )

6a = −54i + 72j

9b = 9(6i + 4j)

9b = 54i + 36j

Now add 6a and 9b together,

6a + 9b = −54i + 72j  + 54i + 36j

6a + 9b = −54i + 54i + 72j + 36j

6a + 9b = 0i + 108j

To find |a|, use the formula to find the magnitude of a vector,

If a = a₁i + a₂j, |a| = √a₁² + a₂²

Here, a = −9i + 12j

|a| = √(−9)² + (12)²

|a| = √81 + 144 = √225

|a| = 15

To find |a − b|, first subtract b from a and find the magnitude of the resultant,

a - b = −9i + 12j - (6i + 4j)

a - b = −9i - 6i + 12j - 4j

a - b = −15i + 8j

Now use the formula to find the magnitude of a vector,

|a − b| = √(-15)² + (8)²

|a − b| = √225 + 64 = √289

|a − b| = 17

Hence the values of a + b, 6a + 9b, |a|, and |a − b| are −3i + 16j, 0i + 108j, 15 and 17 respectively.

       

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In a certain company, there were five candidates running for President. After the vots were tallied, it turned out that Victor, like in the election, finished in thir place, and david beat him. Greg said that he didn't come in first, but he also didn't come in last. Mac in an interview, said that in this election he wasn't able to win, but at least he was one place hight than his old rival Bill. What place did each candidate come in?

Answers

Considering the situation described, the classification of the elections is given as follows, according to their order of finish:

David, Greg, Victor, Mac, Bill.

How to find the classification of the elections?

We take the situation that is described, and build the classification from it. The classification has the following format:

P1 - P2 - P3 - P4 - P5

With P1 being the first placed candidate, P2 being the second placed candidate, and so on until P5 which is the fifth placed candidate.

From the text given in this problem, we have that:

Victor finished in third place, and David beat him, hence P3 = Victor, David = P1 or P2.Greg didn't come in first nor in last, hence, considering that Victor is P3, Greg = P2 or P4.Mac didn't win, but he finished higher than Bill, hence, considering that Mac didn't win and that Victor is P3, Mac = P4, Bill = P5.From the bullet points above, we can conclude that David = P1, Greg = P2.

Hence the classification of the election is given by:

David, Greg, Victor, Mac, Bill.

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A hamster is 2 1/2 inches long a rabbit is 3 1/2 times as long as a hamster how long is the rabbit

Answers

2.5 * 3.5 = 8.75 or 8 3/4 inches long

-6 - (2x + 7) = -2(x +6) -1

Answers

Answer:

Infinite solutions

Step-by-step explanation:

You can put in any number for x and the 2 sides of the equation will equal each other.

Answer:

The equation has not solution, both parts of the equation correspond to the same line.

Step-by-step explanation:

-6 -(2x+7) = -2(x+6) - 1

-6 -2x - 7 = (-2*x + (-2*6)) - 1

-6 - 2x - 7 = -2x - 12 - 1

-2x - 13 = -2x - 13

-2x = - 2x

The hollenbecks own a square lot with area 3600 square meters. they plan to fence just three sides of this lot. how many meters of fence must they purchase?

Answers

Answer: 180 meters

Step-by-step explanation: To solve this we need to find the square root of 3600. 6x6 = 36 so we know the square root is 60. That means that each side of the square lot is 60 meters. If they fence 3 sides they will need to purchase 60x3= 180 meters of fence.

Which test point holds true for the inequality 3/2y-2x>=1? Where does the shaded area lie for this inequality? The test point holds true for this inequality. The shaded area for the inequality lies the boundary line.

Answers

The test That holds true for this inequality is given as 1/4 and 1

How to solve for the inequality

3/2 y - 2x > 1

The goal is to make y the subject

then

3/2 y > 2x + 1

We have to divide through the equation by 3/2

Such that  y  > 4/3 x + 2/3

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Select the correct answer. What is the value of the limit ? lim x 5 square x^2 +4

Answers

By direct evaluation, we will see that the limit is equal to 29.

How to find the limit?

Here we want to find the limit of the given expression when x tends to 5.

[tex]\lim_{x \to \ 5} x^2 + 4[/tex]

We can directly evaluate the expression in x = 5 and see if we get a real value different than zero.

By direct evaluation, we get:

[tex]\lim_{x \to \ 5} x^2 + 4 = 5^2+ 4 = 29[/tex]

Notice that the limit does give a whole number, then in this way, we conclude that the limit of the given expression when x tends to 5 is equal to 29.

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Answer:

square 29

Step-by-step explanation:

How many natural numbers between $150$ and $300$ are divisible by $9$?

Answers

Answer:

There are 17 natural numbers divisible.

There are 17 natural numbers between 150 and 300 that are divisible by 9.

To find the number of natural numbers between 150 and 300 that are divisible by 9, we need to find the count of multiples of 9 within this range.

The first multiple of 9 greater than or equal to 150 is 153 (9 x 17), and the last multiple of 9 less than or equal to 300 is 297 (9 x 33).

Now, we can calculate the number of multiples of 9 between 153 and 297 (inclusive):

Number of multiples of 9 = (Last multiple - First multiple) / 9 + 1

Number of multiples of 9 = (297 - 153) / 9 + 1

Number of multiples of 9 = 144 / 9 + 1

Number of multiples of 9 = 16 + 1

Number of multiples of 9 = 17

So, there are 17 natural numbers between 150 and 300 that are divisible by 9.

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Which graph represents a reflection across the x-axis of g(x) = Three-fourths(3)x?

Answers

See attached images for the graph.

PLS SOLVE ASAP. I will mark brainlest.

Answers

Answer:

• [tex](w \cdot u) (7)[/tex] =  [tex]\bf 8[/tex]

• [tex](u \cdot w) (7)[/tex]  =  [tex]\bf 22[/tex]

Step-by-step explanation:

We are given:

[tex]u(x) = x^2 + 6[/tex]

[tex]w(x) = \sqrt{x + 9}[/tex].

• [tex](w \cdot u) (7)[/tex]. read as "w of u of 7", means we have to input 7 into the function [tex]u(x)[/tex], and use the output we get as input for the function [tex]w(x)[/tex] :

[tex](w \cdot u) (7)[/tex]

⇒ [tex]w(u(7))[/tex]

⇒ [tex]w(7^2 + 6)[/tex]

⇒ [tex]w(55)[/tex]

⇒ [tex]\sqrt{55 + 9}[/tex]

⇒ [tex]\sqrt{64}[/tex]

⇒ [tex]\bf 8[/tex]

• Similarly, we can evaluate [tex](u \cdot w) (7)[/tex] :

[tex](u \cdot w) (7)[/tex]

⇒ [tex]u(w(7))[/tex]

⇒ [tex]u(\sqrt{7 + 9})[/tex]

⇒ [tex]u(\sqrt{16})[/tex]

⇒ [tex]u(4)[/tex]

⇒ [tex]4^2 + 6[/tex]

⇒ [tex]\bf 22[/tex]

The answers are :

(w o u)(7) = 8

(u o w)(7) = 22

To find the first answer, substitute u(x) in w(x), and set x = 7.

u(7) = 7² + 6 u(7) = 49 + 6u(7) = 55

w(u(7)) = √(55 + 9)w(u(7)) = √64w(u(7)) = 8(w o u)(7) = 8

To find the second answer, substitute w(x) in u(x), and set x = 7.

w(7) = √(7 + 9)w(7) = √16w(7) = 4

u(w(7)) = 4² + 6u(w(7)) = 16 + 6u(w(7)) = 22(u o w)(7) = 22

Given △BAD AB = 3x - 4 ED = 24 CA = 12 BE = 3x Find x to the nearest hundredth.

Answers

Answer:

  x = 10.67

Step-by-step explanation:

The triangles shown are similar, so corresponding sides are proportional. This lets us write a relation that can be solved for x.

Setup

For the given figure, we can write the proportion ...

  AB/CA = DB/ED . . . . . . where DB = ED +BE

  (3x-4)/12 = (24 +3x)/24 . . . . . . substitute given values

Solution

Multiplying by 24 gives ...

  2(3x -4) = 3x +24

  6x -8 = 3x +24 . . . . . eliminate parentheses

  3x = 32 . . . . . . . . add 8-3x

  x = 32/3 = 10 2/3 ≈ 10.67 . . . . . divide by 3 and convert to decimal

The value of x to the nearest hundredth is 10.67.

the sum of two numbers is 123. when the larger number is added to 5 times the smaller, the sum is 343. find the numbers.​

Answers

Create a system of equations
x + y = 123
5x + y = 343

I use substitution
y = 123 - x
5x + 123 - x = 343
4x + 123 = 343
4x = 220
x = 55

Plug in
x + y = 123
55 + y = 123
y = 68

Check
5x + y = 343
5(55) + 68 = 343
275 + 68 = 343
343 = 343

The two numbers are 68 and 55.

Given that the sum of two numbers is 123. when the larger number is added to 5 times the smaller, the sum is 343.

We need to find the numbers,

Let's call the two numbers x and y. According to the given information, we have the following two equations:

x + y = 123 (The sum of the two numbers is 123)

x + 5y = 343 (When the larger number is added to 5 times the smaller, the sum is 343)

Now, we can solve these two equations simultaneously to find the values of x and y.

Let's rearrange equation 1 to express x in terms of y:

x = 123 - y

Substitute this value of x into equation 2:

(123 - y) + 5y = 343

Now, solve for y:

123 + 4y = 343

4y = 343 - 123

4y = 220

y = 220 / 4

y = 55

Now that we have the value of y, we can find the value of x using equation 1:

x = 123 - y

x = 123 - 55

x = 68

So, the two numbers are 68 and 55.

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pls help i don’t know how to do this

Answers

Answer: [tex]\displaystyle\\\frac{2\pi }{3},\ \frac{5\pi }{3} .[/tex]

Step-by-step explanation:

[tex]\displaystyle\\tan\theta=-\sqrt{3}\ \ \ \ 0\leq \theta\leq 2\pi \\\theta =\frac{2\pi }{3}+\pi N\ \ \ (N=0,\ 1,\ 2,\ 3\ ...)\\ N=0\\\theta=\frac{2\pi }{3} +\pi *0\\\theta=\frac{2\pi }{3}\ \ \ \ ( 0\leq \theta\leq 2\pi)\\ N=1\\\theta=\frac{2\pi }{3}+\pi *1 \\\theta=\frac{2\pi }{3} +\pi \\\theta=\frac{2\pi +3\pi }{3} \\\theta=\frac{5\pi }{3} \ \ \ ( 0\leq \theta\leq 2\pi)\\[/tex]

[tex]N=2\\\theta=\frac{2\pi }{3}+2\pi \\ \theta=\frac{2\pi +3*2\pi }{3}\\ \theta=\frac{2\pi +6\pi }{3} \\\theta=\frac{8\pi }{3} \\\theta=2\frac{2}{3} \pi \ \ \ \ (\notin0\leq \theta\leq 2\pi).\\[/tex]

I'm thinking of a number. If I add 4 to the number and then multiply the result by 3,the answer is the same as subtracting 5 from the number and then multiplying the result by 2.
(a) in terms of x?
(b) solve the equation n find the number what I'm thinking of

Answers

Answer:

x=-22

Step-by-step explanation:

Let's substitute the number you are thinking of with x

(x+4)*3=(x-5)*2

3x+12=2x-10

x+12=-10

x=-22

Alexa is a basketball player at East High. At a recent game, she made some three point shots and some two point shots. Alexa scored a total of 18 points and made 3 times as many two point shots as three point shots. Determine the number of three point shots Alexa made and the number of two point shots she made.​

Answers

Answer:

6 2 point shots 2 3 points

Step-by-step explanation:

3 two point shot 1 3 point shot = 9

6 two point shot 2 3 point shot =18

AArea of a circle Take a rope, tie it at one corner of a door knob and then. find out how much area can be covered if you cart move around. Also mention the name of 2D figure obtained. Tie a stone on one end of the rope and then rotate it. . Find the area of obtained figure take the length of rope as a radius.​

Answers

Answer:

A=113 cm²

Step-by-step explanation:

If the length of the rope is 6 cm

then the radius of the circle we draw is 6 cm.

Area of the circle is A = π·r²

A = π·6² ≈ 3.14· 36 ≈ 113cm²

A soap company started a promotion in which each packet of detergent powder will have 20% extra powder at the
same price, Jenna buys a 2 kg packet of the detergent powder. How much total detergent powder will be in the packet?

Answers

2.4kg.,

..

hope it helps

Answer is 2.4 kg total detergent powder
Step by step
She buys 2kg of powder plus 20% extra powder
2 x 20%
2 x .20 = .4
Add the .4 to the original 2kg
Total 2.4 kg
Problem solved

Austin keeps a right conical basin for the birds in his garden as represented in the diagram. The basin is 40 centimeters deep, and the angle between the sloping sides is 77°. What is the shortest distance between the tip of the cone and its rim?​

Answers

177.8 centimeters.

What is the formula for cos θ?The symbol for it is Cosθ, and it has the following form: adjacent/hypotenuse = cosθ. In other words, it divides the length of the hypotenuse by the length of the neighboring side, which is the side next to the angle (the longest side of a right triangle).When working with right-angled triangles, the Cos Theta Formula is particularly helpful. The Cosine of an angle in a right triangle is always equal to the hypotenuse's length divided by the length of the neighboring side. This makes it an excellent tool for resolving Cosine-related issues.

The shortest distance between the tip of the cone and its rim:

cos θ= base/Hypotenuse

cos 77°=[tex]\frac{40}{H}[/tex]

[tex]0.22495=\frac{40}{H}[/tex]

[tex]H=177.8[/tex]

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The shortest distance between the tip of the cone and its rim exits 51.11cm.

What is the shortest distance between the tip of the cone and its rim?​

If you draw a line along the middle of the cone, you'd finish up with two right triangles and the line even bisects the angle between the sloping sides. The shortest distance between the tip of the cone and its rim exists in the hypotenuse of a right triangle with one angle calculating 38.5°. So, utilizing trigonometry and allowing x as the measurement of the shortest distance between the tip of the cone and its rim.

Cos 38.5 = 40 / x

Solving the value of x, we get

Multiply both sides by x

[tex]$\cos \left(38.5^{\circ}\right) x=\frac{40}{x} x[/tex]

[tex]$\cos \left(38.5^{\circ}\right) x=40[/tex]

Divide both sides by [tex]$\cos \left(38.5^{\circ}\right)$[/tex]

[tex]$\frac{\cos \left(38.5^{\circ}\right) x}{\cos \left(38.5^{\circ}\right)}=\frac{40}{\cos \left(38.5^{\circ}\right)}[/tex]

simplifying the above equation, we get

[tex]$x=\frac{40}{\cos \left(38.5^{\circ}\right)}[/tex]

x = 51.11cm

The shortest distance between the tip of the cone and its rim exits 51.11cm.

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