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ss7ja [257]
2 years ago
7

To solve the equation: 14 = t +72 This is a(n)

Mathematics
1 answer:
krek1111 [17]2 years ago
3 0

Answer:

t=-58

Step-by-step explanation:

14=t+72\\14-72=t+72-72\\-58=t

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a tap can fill a bucket in 2 minutes, another in 3 minutes. If both are turned on how long does it take to fill the bucket?
Rama09 [41]

Answer:

It takes 1 minute 12 seconds to fill the bucket if both taps are turned on.

Step-by-step explanation:

  1. One tap fills the bucket in 2 minutes, thus fills 1/2 of the bucket in one minute.
  2. Other tap fills the bucket in 3 minutes, thus fills 1/3 of the bucket in one minute.
  3. Both together fill 1/2+1/3=5/6 of the bucket in one minute.
  4. If they can fill 5/6 of the bucket in 1 minute, they fill 1/6 of the bucket in 1/5 minute.
  5. They can fill the bucket (6/6) in 1+1/5 minute
  6. This is 1 minute 12 seconds
6 0
3 years ago
Find the dimensions of the rectangle with area 256 square inches that has minimum perimeter, and then find the minimum perimeter
mezya [45]

Answer:

Dimensions: A=a\cdot b=256

Perimiter: P=2a+2b

Minimum perimeter: [16,16]

Step-by-step explanation:

This is a problem of optimization with constraints.

We can define the rectangle with two sides of size "a" and two sides of size "b".

The area of the rectangle can be defined then as:

A=a\cdot b=256

This is the constraint.

To simplify and as we have only one constraint and two variables, we can express a in function of b as:

b=\frac{256}{a}

The function we want to optimize is the diameter.

We can express the diameter as:

P=2a+2b=2a+2*\frac{256}{a}

To optimize we can derive the function and equal to zero.

dP/da=2+2\cdot (-1)\cdot\frac{256}{a^2}=0\\\\\frac{512}{a^2}=2\\\\a=\sqrt{512/2}= \sqrt {256} =16\\\\b=256/a=256/16=16

The minimum perimiter happens when both sides are of size 16 (a square).

4 0
3 years ago
A sign standing 6 feet tall is situated 18 feet away from a flag pole. at a certain time of day the sign's shadow is 3 feet long
alexdok [17]
Observe attached picture.

On picture we have:
A = height of flagpole = x ft
B = length of flagpole's shadow = 24 ft
C = height of sign = 6 ft
D = length of sign's shadow = 3 ft

When we draw a picture representing this problem we can also add another line marked in red. This way we can see that we have two right-angle triangles. We can see that both have same angle marked with α.

We can apply trigonometry rules to find height of flagpole.

From small triangle containing sign we can find tangens function:
tan \alpha = \frac{C}{D}
Similarly we can do for large triangle containing flagpole:
tan \alpha = \frac{A}{B}

We see that these two equations have same left sides. This means that their right sides must also be same:
\frac{C}{D} = \frac{A}{B}
We can solve for A:
CB=AD \\ A= \frac{CB}{D}  \\ A= \frac{6*24}{3}  \\ A=48 ft

Height of flagpole is 48 feet.

8 0
3 years ago
Can someone please help me out thankss
Tamiku [17]

Answer:

3x +5x =90 +30

8x =120

x =15

6 0
3 years ago
Find the equation of the line.<br> Use exact numbers.
Marina CMI [18]

Answer:

Y=3x+3

The y intercept is 3 and use rise over run to find m.

8 0
2 years ago
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