Please help

Find the missing part.

y = __ √_ ????

the first blank is a fraction with two numbers on top

According to the question

sinA =  

         Method : 1( By Theorem )

sinA =  

Let,

     Height from angle A = 3 x

     Hypotenuse of triangle = 5 x

        By Pythagoras Theorem

Hypotenuse^2 = height^2 + base^2

( 5 x )^2 = ( 3 x )^2 + ( base )^2

25x^2 - 3x^2 = ( base )^2

16x^2 = base^2

( 4x )^2 = ( base )^2

4x = base

Therefore, cosA =  

                          =

                          =  

And, tanA =  

                =  

                =  

               Method : 2 ( Identities )

We know, sin^2 A + cos^2 A = 1

          Substituting value,

( 3 / 5 )^2 + cos^2 A = 1

cos^2 A = 1 - 9 / 25

cos^2 A = ( 25 - 9 ) / 25

cos^2 A = 16 / 25

cos^2 A = ( 4 / 5 )^2

cos A = 4 / 5

tanA = sinA / cosA

       = ( 3 / 5 ) / (  4 / 5 )

       =3/4

Answer:

=34602838637675

Step-by-step explanation:

=−519601+(62626626)(552526)

=−519601+34602839157276

=34602838637675

Answer:

x=9

Step-by-step explanation:

bc 9x2=18 and 18+10=28

Answer:

x = 9

Step-by-step explanation:

2x + 10 - 10 = 28 - 10

2x = 18

x = 9

Step-by-step explanation:

In order to get the answer first you figure out the type of equation. In this case this is a linear equation, y=mx+b

The B or the y-intercept/base is the first step. Here, it says a fee of 14.50 is needed for each order.

The mx part will be the .08 cents needed for each copy.

y= .08x+14.50 is the equation....

The copies needed is 40 which is the x in the situation:

y=.08(40)+14.50....

.08 * 40 is 3.2 then add the base of 14.50 which is: 17.70 all together

Answer:

C

Step-by-step explanation:

trust me c is the correct answer

\(\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)+4\implies \log_2\left( \cfrac{1}{2^4} \right)+4\implies \log_2(2^{-4})+4\implies -4+4\implies \text{\LARGE 0}\)

\(\rule{34em}{0.25pt}\\\\ \textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b\qquad\qquad \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)=y\implies 2^y=\cfrac{1}{16}\implies 2^y=2^{-4}\implies y=-4\)

In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

To determine the percentage change within the number of wolves each year, we ought to look at the development rate of the work w(x) = 14 * 1.08^x.

The development rate in this case is given by the example of 1.08, which speaks to the figure by which the number of wolves increments each year. In this work, the coefficient 1.08 speaks to a development rate of 8% per year.

To calculate the percentage change, we subtract 1 from the growth rate and increase by 100 to change over it to a rate:

Percentage change = (1.08 - 1) * 100 = 0.08 * 100 = 8%.

In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

Learn more about percentage below.

https://brainly.com/question/24304697

#SPJ4

Answer: x = 10

see in the picture, ΔACE has:

+) BF//AE

+) B and F are  midpoints.

=> BF is the median line of the triangle ACE

=> BF = 1/2. AE

=> AE = 2BF

⇔ 5x - 4 = 2.23 = 46

⇔ 5x = 46 + 4 = 50

⇔ x = 50/5 = 10

Step-by-step explanation:

Answer:

i got you.

whats up

Step-by-step explanation:

The volume of the solid with the given semi-circular base with radius 5 units is equal to 333.33 cubic units.

As given in the question,

Radius of the semicircular base = 5 units

Equation of the circle is given by :

x² + y² = r²

⇒ x² + y² = 5²

⇒ x² + y² = 25

⇒ x = √25 - y²

Cross section is perpendicular to the base and it is parallel to the diameter  are squares:

Diameter is double of the radius

s = 2x

 = 2√25 - y²

Volume of the given solid is equal to :

V = \(\int\limits^5_0 {s^{2} } \, dy\)

  = \(\int\limits^5_0 {( 2\sqrt{25 - y^{2} }) ^{2} } \, dy\)

 = \(\int\limits^5_0 {( 4({25 - y^{2} }) } \, dy\)

= 100y - 4y³/3 (for limit 0 to 5)

=  ( 500 - 500/3 ) - 0

= 500 ( 1 - 1/3 )

= 500( 2/3 )

= 1,000/3

= 333.33 cubic units.

Therefore, the volume of the given solid with the given measures is equal to 333.33.

The above question is incomplete, the complete question is :

Use the general slicing method to find the volume of the following solid.

The solid with a semicircular base of radius 5 whose cross sections perpendicular to the base and parallel to the diameter are squares. Place the semicircle on the xy-plane so that its diameter is on the x-axis and it is centered on the y-axis. Set up the integral that gives the volume of the solid. Use increasing limits of integration.

Learn more about volume here

brainly.com/question/13338592

#SPJ4

Answer: B C D

Step-by-step explanation:

Answer:

12.5cm

Step-by-step explanation:

Each side of the pentagonal  garden has a length of 2.5 cm.

A pentagon has 5 sides.

Since the garden has congruent sides, all its lengths are equal.

Therefore:

Distance Walked by Tanya

= 5 X 2.5

=12.5cm

Tanya has walked 12.5cm in total.

The distance between the point (5,12) and the line y = 5x + 12 is 4.90 units

If a point P with the coordinates (x₁, y₁), and we need to know its distance from the line represented by ax + by + c = 0

Then the distance of a point from the line is given by the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

Given: the point (5,12) and the line y = 5x + 12. The line can be written as

5x-y+12 = 0. Thus:

x₁ = 5, y₁ = 12, a = 5, b = -1, c = 12. Substitute these into the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

d = (5×5 + (-1×12) + 12) / √(5² + (-1)²)

d = 25/√26 = 4.90 units

Therefore, the distance between the point and the line is 4.90 units. Option D is the answer

Learn more about distance between a point and a line on:

https://brainly.com/question/18276750

#SPJ1

Answer:

not sure but I think its 7

Step-by-step explanation:

2+6+7+9+9+9=42

42÷6=7

Answer:

8

Step-by-step explanation:

A family of 5 monkeys eat 2 bananas a day.

to figure out how much the monkeys will eat in 4 days

multiply 2 by 4.

make sure the question is not for each monkey or the answer will be

(2 by 4) by 5. witch would be 40

however for the case your saying the answer would be 8

Answer:

\(8(3x + 10) = 28x - 14 - 4x \\ 8 \times 3x + 8 \times 10 = 28x - 14 - 4x \\ 24x + 80 = 24x - 14 \\ 0x = 94 \\ x = > has \: no \: solution\)

If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.

The rate is the ratio of one value, expression, measurement, or quantity compared to another.

The rate represents the quotient of the numerator and the denominator.

The rate is expressed as a percentage by multiplication with 100.

The number of students who took the ACET this year = 27,813

The number of students who were admitted into the Ateneo = 2,836

The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)

= 10.2%

Thus, we can conclude that the acceptance rate or percentage is Option B.

Learn more about determining the percentage at https://brainly.com/question/24877689.

#SPJ1

Answer:

To make a box-and-whisker plot, we first need to order the data from smallest to largest:

4, 5, 6, 10, 15, 16, 21

Next, we can find the median, which is the middle value of the ordered data set. In this case, the median is 10.

Then, we can find the lower quartile (Q1) and the upper quartile (Q3). The lower quartile is the median of the lower half of the data set, and the upper quartile is the median of the upper half of the data set. To find Q1 and Q3, we can split the data set into two halves:

4, 5, 6, 10 and 15, 16, 21

The median of the lower half is (5+6)/2 = 5.5, and the median of the upper half is (16+21)/2 = 18.5. Therefore, Q1 = 5.5 and Q3 = 18.5.

Now we can draw the box-and-whisker plot. The box represents the middle 50% of the data, with the bottom of the box at Q1 (5.5), the top of the box at Q3 (18.5), and the line inside the box at the median (10). The whiskers extend from the box to the smallest and largest values inthe data set that are not outliers. To determine whether there are outliers, we can use the following formula:

Outlier = Q1 - 1.5 * (Q3 - Q1) or Q3 + 1.5 * (Q3 - Q1)

Plugging in the values, we get:

Outlier = 5.5 - 1.5 * (18.5 - 5.5) = -13.25 or Outlier = 18.5 + 1.5 * (18.5 - 5.5) = 37.25

Since there are no values in the data set that are less than -13.25 or greater than 37.25, there are no outliers.

Therefore, the box-and-whisker plot for the given data is:

            |       4

     ___|___

    |              |

    |              |

    |        5.5 |-----  

    |              |      |

    |              |      |

    |------------|  10 |  

    |              |       |

    |      15.5 |------

    |       |      |

     ___|___

            |       21

The box spans from Q1 (5.5) to Q3 (18.5), with the median line inside the box at 10. The whiskers extend from the box to the minimum value of 4 and the maximum value of 21, since there are no outliers.

Hope this helps!

The ratio of the given 240 kg to 6 kg will be 40:1.

What is Ratio?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings. Mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another. Two quantities are compared using division in a ratio. In this case, the dividend is referred to as the "antecedent" and the divisor as the "consequent."

the ratio 240 kg to 6 kg.

It will be simple 240/6 :: 40 :1

Hence the ratio of the given data will be 40:1

Learn more about Ratio, by the following link.

https://brainly.com/question/12024093

#SPJ1

The function has a relative minimum at (-1.278, -0.509) and a relative maximum at (1.278, 2.509).

How to find  x-intercepts?

To find the x-intercepts, we set y = 0 and solve for x:

(x⁴/4) - x² + 1 = 0

This is a fourth-degree polynomial equation, which is difficult to solve analytically. However, we can use a graphing calculator or software to find the approximate x-intercepts, which are approximately -1.278 and 1.278.

To find the y-intercept, we set x = 0:

y = (0/4) - 0² + 1 = 1

So the y-intercept is (0, 1).

To find the vertical asymptotes, we set the denominator of any fraction in the function equal to zero. There are no denominators in this function, so there are no vertical asymptotes.

To find the horizontal asymptote, we look at the end behavior of the function as x approaches positive or negative infinity. The term x^4 grows faster than x^2, so as x approaches positive or negative infinity, the function grows without bound. Therefore, there is no horizontal asymptote.

To find the critical points, we take the derivative of the function and set it equal to zero:

y' = x³- 2x

x(x² - 2) = 0

x = 0 or x = sqrt(2) or x = -sqrt(2)

These are the critical points.

To determine the intervals where the function is increasing and decreasing, we can use a sign chart or the first derivative test. The first derivative test states that if the derivative of a function is positive on an interval, then the function is increasing on that interval. If the derivative is negative on an interval, then the function is decreasing on that interval. If the derivative is zero at a point, then that point is a critical point, and the function may have a relative maximum or minimum there.

Using the critical points, we can divide the real number line into four intervals: (-infinity, -sqrt(2)), (-sqrt(2), 0), (0, sqrt(2)), and (sqrt(2), infinity).

We can evaluate the sign of the derivative on each interval to determine whether the function is increasing or decreasing:

Interval (-infinity, -sqrt(2)):

Choose a test point in this interval, say x = -3. Substituting into y', we get y'(-3) = (-3)³ - 2(-3) = -15, which is negative. Therefore, the function is decreasing on this interval.

Interval (-sqrt(2), 0):

Choose a test point in this interval, say x = -1. Substituting into y', we get y'(-1) = (-1)³ - 2(-1) = 3, which is positive. Therefore, the function is increasing on this interval.

Interval (0, sqrt(2)):

Choose a test point in this interval, say x = 1. Substituting into y', we get y'(1) = (1)³ - 2(1) = -1, which is negative. Therefore, the function is decreasing on this interval.

Interval (sqrt(2), infinity):

Choose a test point in this interval, say x = 3. Substituting into y', we get y'(3) = (3)³ - 2(3) = 25, which is positive. Therefore, the function is increasing on this interval.

Therefore, the function is decreasing on the intervals (-infinity, -sqrt(2)) and (0, sqrt(2)), and increasing on the intervals (-sqrt(2), 0) and (sqrt(2), infinity).

To find the inflection points, we take the second derivative of the function and set it equal to zero:

y'' = 3x² - 2

3x² - 2 = 0

x² = 2/3

x = sqrt(2/3) or x = -sqrt(2/3)

These are the inflection points.

To determine the intervals where the function is concave up and concave down, we can use a sign chart or the second derivative test.

Using the inflection points, we can divide the real number line into three intervals: (-infinity, -sqrt(2/3)), (-sqrt(2/3), sqrt(2/3)), and (sqrt(2/3), infinity).

We can evaluate the sign of the second derivative on each interval to determine whether the function is concave up or concave down:

Interval (-infinity, -sqrt(2/3)):

Choose a test point in this interval, say x = -1. Substituting into y'', we get y''(-1) = 3(-1)² - 2 = 1, which is positive. Therefore, the function is concave up on this interval.

Interval (-sqrt(2/3), sqrt(2/3)):

Choose a test point in this interval, say x = 0. Substituting into y'', we get y''(0) = 3(0)² - 2 = -2, which is negative. Therefore, the function is concave down on this interval.

Interval (sqrt(2/3), infinity):

Choose a test point in this interval, say x = 1. Substituting into y'', we get y''(1) = 3(1)²- 2 = 1, which is positive. Therefore, the function is concave up on this interval.

Therefore, the function is concave up on the interval (-infinity, -sqrt(2/3)) and (sqrt(2/3), infinity), and concave down on the interval (-sqrt(2/3), sqrt(2/3)).

To find the relative extrema, we can evaluate the function at the critical points and the endpoints of the intervals:

y(-sqrt(2)) ≈ 2.828, y(0) = 1, y(sqrt(2)) ≈ 2.828, y(-1.278) ≈ -0.509, y(1.278) ≈ 2.509

Therefore, the function has a relative minimum at (-1.278, -0.509) and a relative maximum at (1.278, 2.509).

To know more about equations visit :-

https://brainly.com/question/22688504

#SPJ1

Answer: 1.32

Step-by-step explanation:

The average speed of the body in the given interval is 32 + 2z ft/s.

The average speed v of a body in an interval of z seconds can be calculated using the formula v = d/t, where d is the distance traveled and t is the time taken.

In this case, the distance d is (32z + 2z^ 2 ) ft and the time taken is z seconds.

Therefore, the average speed v of the body in this interval is:

v = (32z + 2z^ 2 ) ft / zs

v = 32 + 2z ft/s

Therefore, the average speed of the body in the given interval is 32 + 2z ft/s.

Learn more about average speed here:

https://brainly.com/question/9493607

#SPJ4

The exact solutions of the qudratic equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by

3 (x = (-1 ± √3) / 3) .So, option a is the correct answer.

To find the solutions of the quadratic equation 3x^2 - 6x + 2 = 0, we can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 3, b = -6, and c = 2. Substituting these values into the formula, we have:

x = (-(-6) ± √((-6)^2 - 4(3)(2))) / (2(3))

x = (6 ± √(36 - 24)) / 6

x = (6 ± √12) / 6

x = (6 ± 2√3) / 6

x = (3 ± √3) / 3

Therefore, the exact solutions of the equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by 3 (x = (-1 ± √3) / 3)

So, option a is the correct answer.

To learn more about : quadratic

https://brainly.com/question/1214333

#SPJ11

In mathematics, a sequence is an ordered list of elements, often denoted by brackets or parentheses.

The term "a sequence of length n" refers to a sequence that contains a specific number of elements, where the number of elements is denoted by "n."

When the domain of a function is the set of natural numbers (N), it is called an infinite sequence. An infinite sequence can be thought of as an ordered list that continues indefinitely.

Read more on sequences here https://brainly.com/question/6561461

#SPJ1

1 + 2 + 3 + 4 + 5 + 95 + 96 + 97 + 98 + 99. = 500

Answer:

500

Step-by-step explanation:

rearrange the sum as

(99 + 1) + (98 + 2) + (97 + 3) + (96 + 4) + (95 + 5)

= 100 + 100 + 100 + 1000 + 100

= 5 × 100

= 500

The equation of a circle with diameter endpoints of (13, -1) and (15, 9) will be x² + y² - 28x - 8y + 186 = 0.

Given that:

Endpoints of diameter, (13, -1) and (15, 9)

The equation of the circle when endpoints of diameter are given is written as,

(x - x₁)(x - x₂) + (y - y₁)(y - y₂) = 0

The equation of the circle is calculated as,

(x - 13)(x - 15) + (y + 1)(y - 9) = 0

x² - 28x + 195 + y² - 8y - 9 = 0

x² + y² - 28x - 8y + 186 = 0

The equation of a circle with diameter endpoints of (13, -1) and (15, 9) will be x² + y² - 28x - 8y + 186 = 0.

More about the equation of the circle link is given below.

https://brainly.com/question/10618691

#SPJ1

Answer:

Angle 1 and angle 8

angle 2 and angle 7

angle 3 and angle 6

angle 4 and angle 5

I think its tat.

Step-by-step explanation: