Any help is appreciated

The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 cm2/m

Mnenie [13.5K]

Answer:

The base is reducing at a rate of 3.4cm per min.

Step-by-step explanation:

Let The Height of the Triangle, h

Area of the triangle = A

Area of a Triangle, $A= \frac{1}{2}bh$

When $A=190 cm^2, h=10cm$

$190= \frac{1}{2}*b*10\\b=38cm$

$\frac{dA}{dt}=\frac{1}{2}h\frac{db}{dt}+ \frac{1}{2}b\frac{dh}{dt}\\\frac{dh}{dt}=1 cm/min, \frac{dA}{dt}=2cm^2/min,$

$2=\frac{1}{2}*10*\frac{db}{dt}+ \frac{1}{2}*38*1\\2=5\frac{db}{dt}+19\\2-19=5\frac{db}{dt}\\-17=5\frac{db}{dt}\\\frac{db}{dt}=-\frac{17}{5} =-3.4 cm/min$

The base is reducing at a rate of 3.4cm per min.

8 0

3 years ago

Blanca runs 8 laps around the track each day to train for an endurance race. She times each lap to practice her pacing for the r

Artist 52 [7]

Answer:

A graph shows lap time (seconds) labeled 82 to 98 on the horizontal axis and the number of laps on the vertical axis. 1 lap was 82 to 84 seconds. 4 laps were 84 to 86 seconds. 2 laps were 86 to 88 seconds. 4 laps were 88 to 90 seconds. 6 laps were 90 to 92 seconds. 5 laps were 92 to 94 seconds. 2 laps were 94 to 96 seconds. 0 laps were 96 to 98 seconds

Step-by-step explanation:

The given table is presented as follows;

$\begin{array}{ccc}Day \ 1 \ lap \ times \ (seconds)&Day \ 2 \ lap \ times \ (seconds)&Day \ 3 \ lap \ times \ (seconds)\\83&87&85\\92&90&86\\91&92&91\\89&91&93\\94&92&91\\93&95&89\\88&90&88\\84&85&84\end{array}$ The number of laps in the range 82 to 84 seconds = 1

The number of laps in the range 84 to 86 seconds = 4

The number of laps in the range 86 to 88 seconds = 2

The number of laps in the range 88 to 90 seconds = 4

The number of laps in the range 90 to 92 seconds = 6

The number of laps in the range 92 to 94 seconds = 5

The number of laps in the range 94 to 96 seconds = 2

The number of laps in the range 96 to 98 seconds = 0

Therefore, the histogram that represents Blanca's lap times for the three days of practice is described as follows;

A graph shows lap time (seconds) labeled 82 to 98 on the horizontal axis and the number of laps on the vertical axis. 1 lap was 82 to 84 seconds. 4 laps were 84 to 86 seconds. 2 laps were 86 to 88 seconds. 4 laps were 88 to 90 seconds. 6 laps were 90 to 92 seconds. 5 laps were 92 to 94 seconds. 2 laps were 94 to 96 seconds. 0 laps were 96 to 98 seconds

5 0

2 years ago

Solve 4(4f-9)=-(2-f)

Whitepunk [10]

Answer:

f = $\frac{7}{15}$

Step-by-step explanation:

1. 4(4f - 9) = -(2-f) distribute the negative

2. 4(4f - 9) = -2 + f Distribute the 4

3. 16f - 9 = -2 + f Subtract f on both sides

4. 15f - 9 = -2 Add 9 on both sides

5. 15f = 7 Divide both equations by 15

6. $\frac{15f}{15} = \frac{7}{15}$

f = $\frac{7}{15}$

8 0

3 years ago

Do yall eat a...... s..... s......

guapka [62]

No. and i will keep it like that

5 0

3 years ago

A polling company reported that % of surveyed adults said that Complete parts (a) through (d) below.

SOVA2 [1]

Answer:

a) 376.66

b) Option 2: No, the result from part (a) could not be the actual number of adults who said that rising gas prices are "quite annoying" because a count of people must result in a whole.

c) 377

d) 40.77%

Step-by-step explanation:

a) 37% of 1018 is;

37/100 × 1018 = 376.66

b) Thus, the result in a above is not a whole number. Thus;

No, the result from part (a) could not be the actual number of adults who said that rising gas prices are "quite annoying" because a count of people must result in a whole.

c) from a above a, we got a value of 376.66.

Now the actual number would be preferably an integer. Thus, actual number is approximately 377.

d) percentage of respondents said that cellular phones are not at all harmful = 415/1018 × 100% = 40.77%

8 0

3 years ago