A box that has a width of 32 inches and a length of 60 inches is used to ship
a part. The part lies along the diagonal of the bottom of the box. What is the
longest possible length of the part?

A. 28in
B. 88in
C. 92in
D. 68in

Answer:

The exact values of sin2Ф and cos2Ф are as follows:

sin2Ф = 0.8983

cos2Ф = 0.4394

Step-by-step explanation:

sin Ф = 9/17 = perp/hyp = y/r

we know that:

r² = x²+y²

17² = x² + 9²

x² = 208

x = 4√13

cos Ф = base/hyp = x/r = (4√13)/17

Solving sin2Ф

we know that:

sin2Ф = 2 sinФ cosФ

= 2*(9/17)*((4√13)/17)

= (72√13)/289

= 0.8983

Solving cos2Ф:

we know that:

cos2Ф = 1 - 2sin²Ф

= 1 - 2(9/17)²

= 1 - 0.5606

= 0.4394

Answer:

X<7

Step-by-step explanation:

It would be x is less than or equal to 7 if the dot to the far right was filled in. The furthest point to the left is an arrow meaning it continues.

Using it's concept, it is found that the domain of the function graphed is given by x < 7.

It is the set that contains the input values for the function. In a graph, it is given by the values of the x-axis.

In this problem, to the left, there is an arrow, hence the function is calculated for all values of x to negative infinity. To the right, there is an open circle at x = 7, hence the domain is x < 7.

More can be learned about the domain of a function at https://brainly.com/question/18475299

#SPJ2

Answer:

Step-by-step explanation:

[tex]\text{The domain:}\\\\D:x>0\\\\\ln x-\ln\dfrac{1}{x}=2\qquad\text{use}\ \log_ab-\log_ac=\log_a\left(\dfrac{b}{c}\right)\\\\\ln\dfrac{x}{\frac{1}{x}}=2\\\\\ln x^2=2\qquad\text{use}\ \log_ab=c\iff a^c=b\ \text{and}\ \ln x=\log_ex\\\\x^2=e^2\iff x=e\in D[/tex]

To solve the given equation Inx - ln(1/x) = 2, combine the logarithms, simplify, and solve for x to find that x = e.

To solve the equation Inx - ln(1/x) = 2:

Rewrite ln(1/x) as -ln(x): Inx + ln(x) = 2

Combine the logarithms: ln(x²) = 2

Solve for x: x² = e², x = e

Answer:

26

Step-by-step explanation:

x is a degree so it can't be no more then 60 so the angle should be 26

The value of x is 60 degrees, as determined through a series of geometric deductions based on the properties of triangles and semicircles. Here option B is correct.

The sum of the angles in a triangle is 180 degrees.

The sum of the angles in a semicircle is 180 degrees.

The angle opposite to the diameter of the circle is 90 degrees.

Therefore, the angle x in the first triangle is 180 - 90 - 52 = 38 degrees.

The angle x in the second triangle is 180 - 38 - x = 142 - x degrees.

The angle x in the second triangle is also equal to the angle x in the semicircle, which is 180 - 52 - x = 128 - x degrees.

Equating the two expressions for the angle x in the second triangle, we get 142 - x = 128 - x.

Solving for x, we get x = 60 degrees. Here option B is correct.

To learn more about value

https://brainly.com/question/24078844

#SPJ3

Answer:

x< -1.8

Step-by-step explanation:

-12x+13>35

We leave the variable alone passing the 13 with opposite sign to the other side and subtracting it from 35.

-12x>22

We divide both by the variable, -12x, and it gives x > -1.8. Since the sign of x changed, we flip the sign and the final result is x < -1.8

ANSWER

[tex]x \: < \: - 1\frac{ 5}{ 6} [/tex]

EXPLANATION

The given inequality is

[tex] - 12x + 13 \: > \: 35[/tex]

Add -13 to both sides to obtain;

[tex]- 12x + 13 - 13 \: > \: 35 - 13[/tex]

Simplify to obtain:

[tex]- 12x + 0 \: > \:22[/tex]

[tex]- 12x \: > \: 22[/tex]

Divide both sides by -12 and reverse the inequality sign.

[tex] \frac{ - 12x}{ - 12} \: < \: \frac{ 22}{ - 12} [/tex]

[tex]x \: < \: \frac{ 22}{ - 12} [/tex]

This simplifies to

[tex]x \: < \: - \frac{ 11}{ 6} [/tex]

We rewrite as mixed number

[tex]x \: < \: - 1\frac{ 5}{ 6} [/tex]

Step-by-step explanation:

Here,

radius of hemisphere and cylinder(r)=7 cm

height of the cylinder(h)= 10 cm

Now the volume of cylinder(V1) is,

[tex]\pi {r}^{2} h \\ = \pi \times {7}^{2} \times 10 \\ = 1540 \: {cm}^{3} \\ [/tex]

And the volume of hemisphere(V2) is,

[tex] \frac{2}{3} \pi {r}^{3} = \frac{2}{3} \times \pi \times {7}^{3} \\ = 718.67 \: {cm}^{3} [/tex]

Total volume=V1+V2=1540+718.67= 2258.67 cu.cm

Surface area of cylinder(A2)=

[tex]2\pi \: rh + 2\pi {r}^{2} = 2\pi \: r(h + r) \\ = 2 \times \pi \times 7 \times (10 + 7) \\ = 44 \times 17 \\ = 748 \: {cm}^{2} [/tex]

Surface area of hemisphere(A2)=

[tex]2\pi {r}^{2} = 2 \times \pi \times {7}^{2} = 308 \: {cm}^{2} [/tex]

Then total Surface area=A1+A2

=748+308=1056 sq.cm

1. First, let us find the volume. Now the total volume is simply given by adding the volume of the cylinder to that of the hemisphere.

Let us revisit the formulas for the volume of a cylinder and hemisphere.

Cylinder: V = πr^(2)h

Hemisphere: V = (2/3)πr^3

Thus, the total volume is given by πr^(2)h + (2/3)πr^3

Using the values provided in the diagram, we can now say that:

Total volume = π(7)^(2)*10 + (2/3)π(7)^3

= 490π + 686π/3

= 2156π/3 cm cubed

Using π = 22/7, we can now see that:

Total volume = 2156*(22/7) / 3

= 2258.67 cm cubed (to two decimal places)

2. Now let's find the total surface area. Let's review the formulas for total surface area for a cylinder and a hemisphere:

Cylinder: SA = 2πr^2 + 2πrh (this is the area of the top and bottom, plus the area of the rectangle that is wrapped around)

However, since the top of the cylinder is covered by the hemisphere, we don't need to count its area in the surface area, thus we must use SA = πr^2 + 2πrh

Hemisphere: SA = πr^2 + 2πr^2 = 3πr^2 (this is the area of the bottom of the hemisphere plus the area of half of the sphere)

However, since the bottom of the hemisphere is on the cylinder, we don't count this in the total surface area either, therefor we must use SA = 2πr^2

Thus, total surface area is given by:

πr^2 + 2πrh + 2πr^2

= 3πr^2 + 2πrh

Now we can substitute the values of the radius and cylinder height into the formula above. So:

TSA = 3πr^2 + 2πrh

TSA = 3π(7)^2 + 2π(7)(10)

= 147π + 140π

= 287π cm squared

Using π = 22/7, we can now see that:

TSA = 287*(22/7)

= 902 cm squared

Answer:

80 dollars.

Step-by-step explanation:

Let the amount that A get be [tex]x[/tex] dollars.

B will get the rest of the 336 dollars. That will be [tex]336 - x[/tex] dollars.

[tex]\displaystyle \frac{5}{16}[/tex] of what B get will be the same as what A gets. In other words,

[tex]\displaystyle \frac{5}{16}(336-x) = x[/tex].

Add [tex]\displaystyle \frac{5}{16}x[/tex] to both sides of the equation:

[tex]\displaystyle \frac{5}{16}\times 336 = (1 + \frac{5}{16})x[/tex].

[tex]\displaystyle x = \frac{\displaystyle \frac{5}{16}\times 336}{\displaystyle 1 + \frac{5}{16}} = 80[/tex].

In other words, A gets 80 dollars.

Answer:

80

Step-by-step explanation:

Answer:

(2, 6)

Step-by-step explanation:

For each of the 3 given points, substitute the coordinates into y - x > -3 and determine whether the resulting inequality is true or false:

(6, 2):  2 - 6 > - 3, or -4 > -3.  This is FALSE, so (6, 2) is not a solution.

(2, 6):  6 - 2 > - 3, or 4 > -3.  This is TRUE, so (2, 6) is a solution.

Answer: (2,6)

Step-by-step explanation:

The coordinates are in the form (x,y)

(6,2)    2-6=-3,  -3≡-3  thus not the answer

(2,6)    6-2=3,  3>-3  

(2,-1)   -1-2=-3,  -3≡-3  thus not the answer

Hope it helped!

Answer:

The answer is 16,500

Step-by-step explanation:

Answer:

THE ANSWER IS 16500!

Step-by-step explanation:

hopes this helped

Answer:

a = 6, b = 5, c = 3

Step-by-step explanation:

Given

[tex]\frac{1}{6}[/tex] ÷ [tex]\frac{3}{5}[/tex]

Leave the first fraction, change division to multiplication and turn the second fraction upside down, that is

[tex]\frac{1}{6}[/tex] × [tex]\frac{5}{3}[/tex]

Compare with

[tex]\frac{1}{a}[/tex] × [tex]\frac{b}{c}[/tex]

To obtain a = 6, b = 5 and c = 3

Answer:

=30 ft³

Step-by-step explanation:

From the scenario given the formula for density of the fish pod is

ρ= no. of fish/ volume

Making volume the subject of the formula we obtain the following equation:

Therefore volume = no.of fish/ρ

Using the values provided in the question:

=12 fish/0.4 fish/ft³

=30 ft³

= 4.8

Answer:

Step-by-step explanation:

Volume = 30 ft³

density = population/area

.4  =  12/ft³

(.4)(ft³) = 12/ft³ × ft³/1

.4 ft³ = 12

.4ft³ /.4 = 12/.4

ft³ = 30

30 ft³

to get the equation of a straight line, all we need is two points on it... say hmmm this one has (0 , 6) and (6 , 2), so let's use those.

[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{2-6}{6-0}\implies \cfrac{-4}{6}\implies -\cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-6=-\cfrac{2}{3}(x-0) \\\\\\ y-6=-\cfrac{2}{3}x\implies y=-\cfrac{2}{3}x+6[/tex]

The cosine value provided is incorrect as it exceeds the maximum cosine function value. However, with a valid cosine value and the condition that sinθ < 0, the sine value can be found using the Pythagorean identity. The negative square root is taken due to sinθ being less than zero.

The given condition is cosθ = 3√3 with the additional information that sinθ < 0. However, the cosine value seems incorrect as the maximum value for the cosine function is 1, therefore cosθ = 3√3 cannot be true. Assuming there is a typo and considering the correct range for cosine, the answer can be derived using the Pythagorean identity:

cos2θ + sin2θ = 1.

Since sinθ < 0, it indicates that the angle θ is in either the third or fourth quadrant. In both quadrants, cosine values can still be positive. After getting the correct cosine value within the range of -1 to 1, you would find sinθ by rearranging the Pythagorean identity:

sin2θ = 1 - cos2θ.

Then, take the square root and apply the negative sign since sinθ < 0.

The answer you are looking for could either be 16 or 40.  To solve the equation, you would follow the steps of PEMDAS. Since the 2 above the equation is an exponent, you'd first solve there.  

Fill in "a" and "b", the equation will now say 2^2 * 3 + 4 = ?. Assuming that the exponent is meant to go with the 2 alone, 2 * 2 = 4. This leaves the equation to say 4 * 3 + 4 = ? Multiply 3 and 4 to get 12, then add 4 to get 16.  

OR  

Fill in "a" and "b". This time, we're assuming that the exponent is going with 2 * 3 (originally 2a). Multiply 2 and 3 to get 6, then square 6 to get 36. Finally, add 4 to 36 to get 40.  

I'm not quite sure where the exponent was meant to go, but I hope this helps!

Answer:

log_2((x^4+4x^3)/3)

Step-by-step explanation:

First step would be distribute that - into the ( )

3log_2(x)-log_2(3)+log_2(x+4)

Now take care of coefficients of the logs... bring them up as powers of the inside

log_2(x^3)-log_2(3)+log_2(x+4)

or

+log_2(x^3)-log_2(3)+log_2(x+4)

Now for the product and quotient rule! If it has a + in front of it, it will go on top. If it has a - in front of it, it will go on bottom.

Like this:

log_2 (x^3(x+4)/3)

or

log_2((x^4+4x^3)/3)

So inside that log base 2 thing the top is x^4+4x^3

and that bottom is 3

Answer:

[tex]log_{2}(\frac{x^{3}(x+4)}{3})[/tex].

Step-by-step explanation:

[tex]3log_{2}x-(log_{2}3-log_{2}(x+4))[/tex]

[tex]log_{2}x^{3}-log_{2}(\frac{3}{x+4})[/tex]

[tex]log_{2}(\frac{x^{3}}{\frac{3}{x+4}})[/tex]

[tex]log_{2}(\frac{x^{3}(x+4)}{3})[/tex].

Answer: B (x, y, z)

Step-by-step explanation:

In a two-dimensional plane, a coordinate is represented as (x, y).

In a three-dimensional plane, a coordinate is represented the same as the two-dimensional plane, except we need to add the third coordinate (z).

--> (x, y, z)

Answer:

B. (x,y,z).

Step-by-step explanation:

We represent the coordinate of  a point in one dimension as x on the line. We represent the coordinate of a point in two dimension (plane) as (x,y). Similarly we represent  the coordinate of a point which lie in the space (three dimension) as (x,y,z) .Here x is the x-coordinate of the point,

          y is the y-coordinate of the point,

and   z is the z-coordinate of the point. Hence (x,y,z) represent a point a point in a three dimensional Cartesian System.

Answer:

Bullet will hit the ground after 70 seconds.

Step-by-step explanation:

A bullet is fired straight up from a BB gun with initial velocity 1120 ft/s at an initial height of 8 ft. Using the value of velocity the equation becomes:

h(t)= -16t² + 1120t + 8

We need to find time when bullet hit the ground.  

As we know when bullet hit the ground height would be 0  

So, we set h=0 and solve for t .

0 = -16t² + 1120t + 8

Using quadratic formula:

[tex]t= \frac{-1120 \pm \sqrt{(1120)^{2}-4(-16)(8)} }{2(-16)}\\\\ t=70.007 , -0.007[/tex]

Since negative value of the time is not possible, we conclude that the bullet will hit the ground after 70 seconds.

Answer:

t≈70 seconds

Step-by-step explanation:

h=−16t2+v0t+8

We know the velocity, v0, is 1,120 feet per second.

The height is 0 feet. Substitute the values.

0=−16t^2+1,120t+8

Identify the values of a, b, and c.

a=−16,b=1,120,c=8

Then, substitute in the values of a, b, and c.

t=−(1,120)± √(1,120)2−4⋅−16⋅(8

                     2 ⋅ −16

Simplify.

t=−1,120± √1,254,400+512

             - 32

t= −1,120± √1,254,912

             -32

Rewrite to show two solutions.

t= −1,120+ √ 1,254,912 .                   t= −1,120+ √ 1,254,912

            -32                                                               - 32

  t≈70 seconds,t≈−0.007 seconds

Answer: Inconsistent.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

Solve for "y" in each equation:

Equation 1

[tex]-\frac{1}{2}x=3-y\\\\y=\frac{1}{2}x+3[/tex]

Equation 2

[tex]-7+y=\frac{1}{2}x-2\\\\y=\frac{1}{2}x-2+7\\\\y=\frac{1}{2}x+5[/tex]

You can notice that the slope of the Equation 1 is:

[tex]m_1=\frac{1}{2}[/tex]

And the slope of the Equation 2 is:

[tex]m_2=\frac{1}{2}[/tex]

Observev that [tex]m_1=m_2[/tex], then you can conclude that the lines are parallel and the System of equations has No solution.

When there is no solution the classification  of the system of equations is: "Inconsistent".

The area of a parallelogram is base times height.    Each side can be a base, and has a particular height associated with it.

Here the height associated with the 1.5 base is 2.7, and the height associated with the 3.6 base is h.  So

[tex]1.5(2.7)=3.6 h[/tex]

[tex]h=15(27)/360= 1.125[/tex]

Answer: 1.125 units

Without the necessary details related to the parallelogram's area or base and side lengths, it is impossible to calculate the precise height of the parallelogram. The snippets provided relate to different mathematical problems and do not apply to the calculation of a parallelogram's height.

To find the height h of the parallelogram, we have several different pieces of information provided in the snippets, and each one appears to address a distinct mathematical problem. However, none of the given pieces align directly with calculating the height of a parallelogram.

To calculate the height of a parallelogram, usually the area and the base length are given, or you would use trigonometric relationships if angles and side lengths are known. Since none of these crucial pieces of information are provided, we will focus on demonstrating a general approach to solve such a problem through a proportion method that was mentioned:

Set up a proportion to find the height of the actual model.

For example, if a scale model uses a 1 cm height to represent 0.5 m in reality, and the actual height in the model is 75 cm, then using the proportion:

This approach would yield the height x in the actual model. However, we cannot precisely find the height h of the provided parallelogram without specific details related to its area or base and side lengths.

https://brainly.com/question/9297560

#SPJ2

Answer:

The length = 56 feet and the width = 17 feet.

Step-by-step explanation:

We can set up 2 equations to solve this. Let the length of the rug be x, then

x = 3w + 5    where w = the width.   ( looks like you got the width and the length mixed up. The length is the longest side)

The perimeter = 2x + 2w = 146 so we have the 2 equations:

x = 3w + 5

2x + 2w = 146

Now we substitute for x in the second equation:

2(3w + 5) + 2w = 146

6w + 10 + 2w = 146

8w = 136

w = 17 feet,

and x = 3(17) + 5 =  56 feet.

Answer:

Length is 17 feet and Width is 56 feet.

Step-by-step explanation:

P=2L+2W

146=2L+2(3L+5)

146=2L+6L+10

146=8L+10L

146-10=8L+10-10

136=8L

136\8=8\8

17=L

W=3L+5

  =3(17)+5

  =56

Answer:

4 1/4 gallons

Step-by-step explanation:

5 gallons are needed.

Convert one gallon into quarts and one quart into pints.

3 quarts and 2 pints, minus 3 quarts and 1 pint.

The result is 4 gallons and 1 pint.

He needs 4 galloons and 1 pint .

The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Given:

A painter needs 5 gallons of paint to finish a house.

He has 3 quarts and 1 pint.

Now, Convert one gallon into quarts and one quart into pints.

3 quarts and 2 pints

= 0.75 + 0.125

= 0.875 gallons

So, amount of paint needs = 5- 0.875    

                                            = 4.125

Hence, 4 gallons and 1 pint paint does he need.

Learn more about Unit Conversion here:

https://brainly.com/question/19420601

#SPJ2

Answer:

d = 10.8167

Step-by-step explanation:

The distance between two points can be easily found by using the following expression

d = √((x1-x2)^2 + (y1-y2)^2)

where

(x1,y1) = (6,-4)

(x2,y2) = (0,5)

d = √((6-0)^2 + (-4-5)^2)

d = √(36 + 81)

d = √(117)

d = 10.8167

Answer:

The distance between the points (6,-4) and (0,5) = 10.82 units

Step-by-step explanation:

Points to remember

Distance formula

Length of a line segment with end points (x1, y1) and (x2, y2) is given by,

Distance = √[(x2 - x1)² + (y2 - y1)²]

To find the distance between given points

Here, (x1, y1)  =  (6, -4) and (x2, y2)  = (0, 5)

Distance = √[(x2 - x1)² + (y2 - y1)²]

 = √[(0 - 6)² + (5 - -4)²]

 =√[(-6)² + (9)²]

 = √[36 + 81]

 = √[117

 = 10.82

The distance between the points (6,-4) and (0,5) = 10.82 units

36 donuts (2 1/2 dozen) = $8.00

So, you divide 8 by 36 and you get about 22¢ for each donut. Then, you do .22 x 12 which equals $2.64.

One dozen donuts = $2.64

The cost of the one dozen donuts will be $2.64.In one dozen their is 12 donuts.

Arithmetic is an area of mathematics involving the study of numbers and the different operations that can be performed on them.

[tex]\rm 1 \ dozen = 12 \ donuts \\\\ 2\frac{1}{2} dozen = 2\frac{1}{2} \times 12\\ \\\\ 2\frac{1}{2} dozen = 36 \ donuts[/tex]

36 donuts=  $8.00

1 donuts =  $ 0.22

1 dozen donuts cost  = 12 × $ 0.22

1 dozen donuts cost  = $ 2.64

Hence,the cost of the one dozen donuts will be $2.64.

To learn more about the arithmetic operation, refer to the link;

https://brainly.com/question/25834626

#SPJ2

Answer:

linear function

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

[tex]p = \frac{8}{v} [/tex]

when we plug in 4 for P

we want to multiply V to (8/V) and 4 to get rid of the fraction

then we get

[tex]4v = 8[/tex]

we want V by itself so we defide 8 by 4.

8/4 should be simplified.

so we end up with 2.

Answer:

(-3, infinity)

Step-by-step explanation:

The domain of the log function is (0, infinity).  In other words, x must be greater than 0.

To determine the domain of f(x) = log2(x + 3) + 2, we set (x + 3) greater than 0 and solve for x:  That set is x > -3, or (-3, infinity).

Answer:

the answer is x>-3

A full circle is 360 degrees.

XY is 45 degrees.

Multiply the circumference by the fraction of the angle:

104 x (45/360) = 13

The answer is A. 13 cm.

Answer:

Arc length = 13 cm.

Step-by-step explanation:

Given  : A circle with circumferences = 104 cm , central angle = 45°.

To find :  what is the length of arc AB.

Solution : We have given  circle with circumference = 104 cm , central angle = 45°.

Arc length = [tex]\frac{theta }{360} * circumference[/tex].

 Plug the values circumference = 104 cm , central angle = 45°.

Arc length = [tex]\frac{45 }{360} * 104[/tex].

Arc length = 0.125 * 104

 Arc length  = 13 cm .

Therefore,  Arc length = 13 cm.