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Alex Ar [27]
3 years ago
15

B is between A and C, AC = 14 and BC = 11.4. Find AB

Mathematics
1 answer:
djverab [1.8K]3 years ago
8 0

Answer: 2.6

Step-by-step explanation:

1. We know that A to C is 14

2. B to C is 11.4 so we're going to find the remainder to equal 14.

3. 14 minus11.4 which equals 2.6

4. AB is 2.6

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Alenkasestr [34]
Sin (37°) = opposite side/Hypotenuse

sin (37°) =CV/55 →CV = 55.si  (37°)

CV = 55 x (0.601815)
CV= 33
3 0
3 years ago
A punch glass is in the shape of a hemisphere with a radius of 5 cm. If the punch is being poured into the glass so that the cha
Galina-37 [17]

Answer:

28.27 cm/s

Step-by-step explanation:

Though Process:

  • The punch glass (call it bowl to have a shape in mind) is in the shape of a hemisphere
  • the radius r=5cm
  • Punch is being poured into the bowl
  • The height at which the punch is increasing in the bowl is \frac{dh}{dt} = 1.5
  • the exposed area is a circle, (since the bowl is a hemisphere)
  • the radius of this circle can be written as 'a'
  • what is being asked is the rate of change of the exposed area when the height h = 2 cm
  • the rate of change of exposed area can be written as \frac{dA}{dt}.
  • since the exposed area is changing with respect to the height of punch. We can use the chain rule: \frac{dA}{dt} = \frac{dA}{dh} . \frac{dh}{dt}
  • and since A = \pi a^2 the chain rule above can simplified to \frac{da}{dt} = \frac{da}{dh} . \frac{dh}{dt} -- we can call this Eq(1)

Solution:

the area of the exposed circle is

A =\pi a^2

the rate of change of this area can be, (using chain rule)

\frac{dA}{dt} = 2 \pi a \frac{da}{dt} we can call this Eq(2)

what we are really concerned about is how a changes as the punch is being poured into the bowl i.e \frac{da}{dh}

So we need another formula: Using the property of hemispheres and pythagoras theorem, we can use:

r = \frac{a^2 + h^2}{2h}

and rearrage the formula so that a is the subject:

a^2 = 2rh - h^2

now we can derivate a with respect to h to get \frac{da}{dh}

2a \frac{da}{dh} = 2r - 2h

simplify

\frac{da}{dh} = \frac{r-h}{a}

we can put this in Eq(1) in place of \frac{da}{dh}

\frac{da}{dt} = \frac{r-h}{a} . \frac{dh}{dt}

and since we know \frac{dh}{dt} = 1.5

\frac{da}{dt} = \frac{(r-h)(1.5)}{a}

and now we use substitute this \frac{da}{dt}. in Eq(2)

\frac{dA}{dt} = 2 \pi a \frac{(r-h)(1.5)}{a}

simplify,

\frac{dA}{dt} = 3 \pi (r-h)

This is the rate of change of area, this is being asked in the quesiton!

Finally, we can put our known values:

r = 5cm

h = 2cm from the question

\frac{dA}{dt} = 3 \pi (5-2)

\frac{dA}{dt} = 9 \pi cm/s// or//\frac{dA}{dt} = 28.27 cm/s

5 0
2 years ago
Please Help me with this Click to select the following graphic figure. A square circumscribed about a circle:
Sophie [7]

The answer would be the first image.

Step-by-step explanation:

From context, it appears that to be circumscribed is to be drawn about; thus the square circumscribed about the circle is the first graph.

3 0
3 years ago
Plz help this is due tonight
tatuchka [14]

Answer:

7. Answer is 1236.25$

8. Answer is 143.75$

9. Answer is 16.485$

10. Answer is 6.825$

11. Answer is 31.25%

12. Answer is 0.125 for the decimal section and 12.5% for the percent section.

Step-by-step explanation:

7. 7.5 percent of 1150 is 86.25 and 86.25 + 1150 is 1236.25.

8. 15 percent of 125 is 18.75 therefore 125 + 18.75 is equal to 143.75.

9. 3.50 + 2.25 + 9.95 + 15.7 and 5 percent of 15.7 is 0.785 and 15.7 + 0.785 is 16.485.

10. 4.25 plus 2.25 is 6.50 and 5% of 6.50 is 0.325 and 6.50 plus 3.25 is 6.825.

11. 63 plus 25 is 88 so 88 is 68.75 percent of 128 and 100 minus 68.75 is 31.25 so 31.25 is the answer.

12. 1/8 is 12.5 percent so for the percent section it is 12.5 and for the decimal section 0.125

3 0
2 years ago
An executive invests 29,000, some at 8% and the rest at 7% annual interest. If he receives an annual return of $2,230, how much
jeka57 [31]

Answer:

Amount invested in A (8%) = $20,000

Amount invested in B (7%) = $9,000

Step-by-step explanation:

Given:

Total amount invested = $29,000

Interest rate A = 8% = 0.08

Interest rate B = 7% = 0.07

Annual return = $2,230

Find:

Amount invested in each

Computation:

Assume;

Amount invested in A = x

Amount invested in B = 29,000 - x

So,

Interest receive from A = x × 0.08

Interest receive from A = 0.08 x

Interest receive from B = (29000 - x) × 0.07

Interest receive from B = 2,030 - 0.07 x

Annual return = Interest receive from A + Interest receive from B

2,230 = 0.08 x + 2,030 - 0.07 x

x = 20,000

Amount invested in A = $20,000

Amount invested in B = 29,000 - $20,000

Amount invested in B = $9,000

8 0
3 years ago
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