Find the surface area of the rectangular prism.

Answer:

5785.12

Step-by-step explanation:

I showed the picture instead of explaining

Answer:

Step-by-step explanation:

These are really difficult, but one thing I noticed pretty much across the board is that we state our trig ratios in terms of sin and cos using the Pythagorean identity:

[tex]sin^2x+cos^2x=1[/tex], even this one where tangents are involved. Let's begin:

If tan⁻1(x) = u (this is just a substitution to make things easier down the road), then tan(u) = x

If tan⁻1(y) = v, then tan(v) = y.

If that be the case, what we have as a rewrite from our original problem is

sin(u + v) which, according to the identity is:

[tex]sin(u-v)=sin(u)cos(v)-sin(v)cos(u)[/tex] which also tells us that we need those tangents in terms of sines and cosines, as stated earlier. We will take the Pythagorean identity and solve it for both sinx and cosx. Sinx first:

If [tex]cos^2x+sin^2x=1[/tex] then solving for sin:

[tex]\frac{cos^2x}{sin^2x}+\frac{sin^2x}{sin^2x}=\frac{1}{sin^2x}[/tex] (as you can see, I just divided everything by sin-squared):

[tex]cot^2x+1=\frac{1}{sin^2x}[/tex] and

[tex]\frac{1}{tan^2x}+1=\frac{1}{sin^2x}[/tex] and work on eliminating the denominators by multiplying through by sin-squared times tan-squared:

[tex]sin^2x*tan^2x(\frac{1}{tan^2x}+1=\frac{1}{sin^2x})[/tex] which simplifies to

[tex]sin^2x+sin^2x*tan^2x=tan^2x[/tex] and factor out on the left:

[tex]sin^2x(1+tan^2x)=tan^2x[/tex] and solve for sin-squared:

[tex]sin^2x=\frac{tan^2x}{1+tan^2x}[/tex] and take the square root of both sides:

[tex]sinx=\frac{tanx}{\sqrt{1+tan^2x} }[/tex] .  Do the same to solve for cos(x) to get:

[tex]cosx=\frac{1}{\sqrt{1+tan^2x} }[/tex] and now we're ready to fill in our formula for sin(u + v):

[tex]\frac{tanu}{\sqrt{1+tan^2u} }*\frac{1}{\sqrt{1+tan^2v} }[/tex]  -  [tex]\frac{tanv}{\sqrt{1+tan^2} }*\frac{1}{\sqrt{1+tan^2u} }[/tex]  and...

since tanu = x and tanv = y:

[tex]\frac{x}{\sqrt{1+x^2}}*\frac{1}{\sqrt{1+y^2}}-\frac{y}{\sqrt{1+y^2}}*\frac{1}{\sqrt{1+x^2} }[/tex] which, in the end, simplifies to

[tex]\frac{x-y}{\sqrt{1+x^2}*\sqrt{1+y^2} }[/tex] and you're done! Yikes to that!!!!

Answer:

90

Step-by-step explanation:

To solve this problem we need to set up an expression

35x+20

35 is the cost per hour, and 20 dollars is the visit fee.

x is the amount of hours the CT can work

So if we plug in the amount for the number of hours from the problem we get

35(2)+20

Which becomes 70+20 which is 90.

Hope thsi helps!

The computer technician works for 2 hours will take total charges equal to $90 .

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7

According to the question

The computer technician charges $20 per visit plus $35 per hour.

i.e

Let hours he work = x

therefore,

Total charge of computer technician in equation = 20 +  35x  

Now,

As the computer technician works for 2 hours the cost will be

By using equation

Total charge of computer technician in dollars  = 20 + 35x  

where x = 2

so,

= 20 +  35*2  

= $90  

Hence, the computer technician works for 2 hours will take total charges equal to $90 .  

To know more about equation here:

https://brainly.com/question/10413253

#SPJ2

Answer:

4.4 cm

Step-by-step explanation:

Arc length = 2*pi*r*(central angle) / 360

Arc length = 2*(22/7)*3.5*(72/360)=4.4 cm

Answer:

C

Step-by-step explanation:

cot =cos/sin =a/b

cos=a/b*sin

(sin-cos)/(sin+cos) =(sin-sin*a/b)(sin+sin*a/b)

=(1-a/b)/(a+a/b)

=(b-a)/(a+b)

Answer:

f(2) = 8

Step-by-step explanation:

f(x) = x^2 + 8x – 12

Let x = 2

f(2) = 2^2 + 8*2 – 12

     = 4 + 16 -12

        =20-12

        = 8

Answer:

[tex]f(x) = {x}^{2} + 8x - 12 \\ f(2) = (2)^{2} + 8(2) - 12 \\ = 4 + 16 - 12 \\ f(2) = 8[/tex]

I hope I helped you^_^

Answer:

12

Step-by-step explanation:

4s multiples:

4,8,12,16,20,24

6s multiples:

6,12,18,24,30,36

lowest number that is a common multiple between both 4 and 6:

12

Answer: 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can find the answer by multiplying the number of donuts, 12, by the price he sells each donut for, $0.75, and subtracting that answer from the price he paid.

By making the equation 12 × 0.75 = $9 - $3.99 we can find out that he makes $5.01 in profit.

Answer:

B

Step-by-step explanation:

sin(theta) = sqrt(1-cos^2(theta)

sin(theta)=sqrt(1-1/2)=sqrt(1/2)=sqrt(2)/2 but as theta is in IV quadrant, sin(theta) will be negative

Answer:

16 slices

Step-by-step explanation:

4 apples times 4 slices (as there is 4 slices per apple)

So, 4×4=16

Hope this helps :)

(u × v) • w makes sense, since u × v is another vector, and so (u × v) • w is a scalar.

u × (v • w) does not make sense, since v • w is a scalar, and the cross product is not defined between a vector and a scalar.

(u × v) × w makes sense, since u × v is a vector and so is w.

u • (v • w) does not make sense, since v • w is scalar, and the dot product is not defined between a vector and a scalar.

Step-by-step explanation:

As we know that,

In area of triangle , breadth =6inch,similarily ,height =8inch

now ,

Area of triangle = 1/2 ×b×h

= 1/2 × 8 ×6

=24inch^2

also,

In another figure,we can say

a=10 inch,b=16 inch and h=9 inch

similarly,

Area of trapizium = 1/2 h(a+b)

= 1/2 ×9(10+16)

=9/2 ×26

=9×13

=117inch^2

now ,

total area of figure =117 +24 =141inch^2

therefore,total area of figure is 141 inch^2

Answer:

Perimeter of the rectangle is 29x + 1 feet

Step-by-step explanation:

Length of the rectangle = 9.5x + 10 feet

Width of the rectangle = 5x - 9.5 feet

perimeter of rectangle = 2 ( length + width )

perimeter = 2 { (9.5x + 10) + (5x-9.5) }

perimeter = 2 ( 9.5x + 5x + 10 - 9.5 )

perimeter = 2 (14.5x + 0.5)

perimeter =29x + 1 feet

Answer:

range

Step-by-step explanation:

The difference between the largest and smallest value in a data set is the range

Answer:

Range

Step-by-step explanation:

I hope this will help you buddy

Answer:

-6

Step-by-step explanation:

x + 12 = 6

 - 12      - 12

so

12-12=0

6-12=-6

put into equation

x + 0 = -6

x = -6

Answer:

3/4 cup of milk.

Step-by-step explanation:

1 1/2= 6/4. 6÷2=3.

Answer:

3/4

Step-by-step explanation:

Half the recipe means multiply by 1/2

1 1/2 * 1/2

Change the mixed number to an improper fraction

(2*1+1)/2 * 1/2

3/2 * 1/2

3/4

Answer:

x=21

Step-by-step explanation:

We can use a ratio to solve

45          27

------ = ----------

35            x

Using cross products

45x = 35*27

45x = 945

45x/45 = 945/45

x  =21

Answer:

21

Step-by-step explanation:

The ratio of A to B is 45 / 35, which is equal to 9 / 7. To get from B to A, the ratio is 7 / 9.

(7 / 9) x 27

7 x 27 = 189, 189 / 9 = 21

Brainliest, please!

Answer:

64 cm³

Does the answer help you?

Answer:

11341-5=11336

-122+42=-80, when you have different signs always keep in mind that you have to subtract and then get the sign of the big number.

for the third one you firstly have to work with the two negative signs,you have to multiply them, take note that when you multiply a negative by a negative you get a positive, a positive by a positive you get a positive and a negative by a positive you get a negative.

-0.35-(-0.25)

-0.35+0.25

=-0.1

I hope this helps

Answer:

V(t) = 14,000(0.89)^t  

Step-by-step explanation:

Present value of the Dodge Challenger = $14,000

Present percentage value = 100%

Depreciation value = 11%

Number of years = t

Future value = V(t)

V(t) = Present value of the Dodge Challenger(Present percentage value - Depreciation value)^t

= 14,000(100% - 11%)^t

= 14,000(89%)^t

= 14,000(0.89)^t

V(t) = 14,000(0.89)^t

Answer:

45

Step-by-step explanation:

c(x)=2x^2-4x-3

Let x= -4

c(-4)=2(-4)^2-4(-4)-3

      = 2(16) +16-3

       =32+16-3

         45

Answer:

45

Step-by-step explanation:

c(-4) = 2(-4)² - 4(-4) - 3

       = 2(16) + 16 - 3

       = 32 + 13

       = 45

Answer:

I CANT SEE THE QUESTION CAN U UPLOAD IT AGAIN

Step-by-step explanation:

Answer:

one and a half quaters

Step-by-step explanation:

4/4 is a whole

The they take one 1/4

then that gives you 3/4

which is then 1.5/4 left for you

Answer:

3/8

Step-by-step explanation:

Hi! So what really helps me sometimes is to draw a circle and split it. I shaded 1/4 (Lionel's quarter) first. Now, there is 3/4 of the cake left. Helen has half of the rest, which means she has half of 3/4. 1/2 of 3/4 (which is basically 1/2 x 3/4) = 3/8. This means Helen has 3/8 of the cake. I then split my circle into eighths and shaded in 3. This left me with 3/8 of the cake left for Sophie. This means the fraction that remains for her is 3/8.  

I hope this helped :)

Answer:

Step-by-step explanation:

Amount of work done by 15 men is:

Same work can be done by 25 men, in 15 days, so 10 more men should be added.

Answer:

[tex]x = -5 \text{ or } x =3[/tex]

Step-by-step explanation:

We want to find the real solutions to the equation:

[tex]\displaystyle 8^{x^2 + 2x - 15} = 1[/tex]

Recall that any value raised to zero (except for zero itself) is one.

In other words, the exponent must equal zero:

[tex]x^2 + 2x - 15 = 0[/tex]

Solve for x. Factor:

[tex](x+5)(x-3) = 0[/tex]

Zero Product Property:

[tex]x + 5 = 0\text{ or } x - 3 = 0[/tex]

Solve for each case. Hence:

[tex]x = -5 \text{ or } x =3[/tex]

In conclusion, our two real solutions are:

[tex]x = -5 \text{ or } x =3[/tex]

Answer:

[tex]f^{-1}[/tex](x) = 0.5x + 2

Step-by-step explanation:

let y = f(x) and rearrange making x the subject , that is

y = 2x - 4 ( add 4 to both sides )

y + 4 = 2x ( divide both sides by 2 )

[tex]\frac{y+4}{2}[/tex] = x

Change y back into terms of x with x = [tex]f^{-1}[/tex] (x)

[tex]f^{-1}[/tex] (x) = [tex]\frac{x+4}{2}[/tex] = 0.5x + 2

Answer: F -1(x)  = 0.5 x + 2

Step-by-step explanation:

Just took the test on edmentum and got a 100

Answer:

3 sqrt(3)

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp / adj

tan 60 = x/3

3 tan 60 = x

3 sqrt(3) = x

Answer:

x = 3[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Using the tangent ratio in the right triangle and the exact value

tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , then

tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{3}{x}[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )

x = 3[tex]\sqrt{3}[/tex]

Answer:

| h-52 | < or equal to 1

Step-by-step explanation: