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Tanzania [10]
3 years ago
5

The sum of d and 67 is equal to f. Let f = 83.

Mathematics
2 answers:
Fynjy0 [20]3 years ago
6 0
F=d+67
83=d+67
83-67=d
16=d
Maslowich3 years ago
5 0

Answer:

d = 16

Step-by-step explanation:

f - 67

83 - 67 = 16

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The product of w and 2 is greater than or equal to 19.
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Equation Form:

w x 2 \geq 19

Divide both sides by 2:

w \geq 9.5

So, w must be equal to or greater than 9.5 for this equation to work.

5 0
2 years ago
Colton is going to invest in an account paying in interest rate of 6.3% compounded continuously how much wood coating need to in
fredd [130]

Answer:

8284

Step-by-step explanation: I had the same question

5 0
3 years ago
Twice a year, for all four years of college, you used your credit card to pay for books and supplies, which amounts to $516 a se
mixer [17]

Answer:

$11,728

Step-by-step explanation:

Twice a year, for 4 years is 8 times

516×8 = 4128

Yearly for 4 years is 4 times

700×4 = 2800

Every month for 4 years is 48 times

100×48 = 4800

Minimum expenditure:

4128 + 2800 + 4800 = $11,728

4 0
3 years ago
A 12-meter ladder leans against a building forming a 30° angle with the building.
KatRina [158]

Answer:

will show you two (2) ways to solve this problem.

A diagram is needed to see what is going on....

 

Without loss of generality (WLOG)

The wall is on the right. The ladder leans against the wall

with a POSITIVE slope, from SW to NE (quadrant 3 to quadrant 1).

The measure from the bottom of the ladder to the wall is 6.

 

 

Option 1:

 

The ladder, ground and wall form a right triangle.

 

The hypotenuse (ladder) is 14 feet.

 

 The bottom of the ladder is 6 feet from the wall,

  so the base of this right triangle is 6 feet.

 

The top of the ladder to the ground represents

the missing leg of the right triangle.

 

The pythagorean theorem applies, which says

 6^2 + h^2 = 14^2   where h is the height

                                 of the top of the ladder to the ground

 

36 + h^2 = 196

 

 h^2 = 196 - 36

 

h^2  = 160

 

h = sqrt(160)

 

   = sqrt(16 * 10)

 

    = sqrt(16)* sqrt(10)

 

    = 4*sqrt(10) <--- exact answer

 

    = 4 * 3.16227766016838....

 

     = 12.64911....

 

    12.65 <--- rounded to 2 digits as directed

 

----------------------------------------------

Option #2: using trig

 

With respect to the angle formed by the bottom of the

ladder with the ground

  cos T = 6/14 = 3/7  

 T = inverse-cosine(3/7) = 64.623006647 degrees

 

 sin(64.623006647) = h/14

 

 h = 14*sin(64.62300647) = 12.6491106 <--- same answer                        

hope this helps

Step-by-step explanation:

5 0
2 years ago
a famer has 120 feet of fencing with whcih to enclose two adjacent rectangular pens as shown. what dimeensions should be used th
Nat2105 [25]

The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.

Let the area be y .

Area = (base) × (height)

Base = 2x

Height = h

Let the area of the rectangular pens be y .

∴ y = 2xh

Perimeter of all the fencing = 4x+3h

∴ 4x+3h = 120

now we solve for h

3h = 120-4x

h = 40 - 4/3 x

Now we will substitute this value in the above first equation:

y = 2xh

or, y = 2x (40 - 4/3 x)

or, y = 80x - 8/3 x²

Now for the maximum area we have to find the first order differentiation of y

now,

dy /dx = 80 - 16/3 x

At dy/dx = 0 we get the value of x for which y is maximum.

80 - 16/3 x = 0

or, - 16/3 x = -80

or, x = 15 feet

Hence height =  40 - 4/3 x = 40 - 20 = 20feet

Maximum area = 2xh = 2×15×40 = 1200 square feet

The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.

Disclaimer : The missing figure for the question is attached below.

To learn more about area visit:

brainly.com/question/27531272

#SPJ4

6 0
1 year ago
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