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3 years ago

Im h--> 0 ((Sqrt 9+h)-3)/h

1 answer:

6 0

$\lim_{h \to 0} \frac{ \sqrt{9+h}-3}{h} = \frac{ \sqrt{9+0} -3}{0}= \frac{0}{0} \\ \lim_{h \to 0} \frac{ \sqrt{9+h}-3}{h}* \frac{ \sqrt{9+h}+3 }{ \sqrt{9+h} +3}= \\ = \lim_{h \to 0} \frac{9+h-9}{h( \sqrt{9+h} +3)} = \\ \lim_{n \to 0} \frac{h}{h( \sqrt{9+h}+3) }= \\ = \frac{1}{ \sqrt{9} +3}$ =
= 1/6

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Micah places a mirror on the ground 24 feet from the base of a tree. He walks

irina [24]

The height of tree is 8 feet

<h3><u>Solution:</u></h3>

Given, Micah places a mirror on the ground 24 feet from the base of a tree

At that point, Micah's eyes are 6 feet above the ground

And he is 9 feet from the image in the mirror.

To find : height of tree = ?

Let "n" be the height of tree

From the question, we can see there is a directly proportional relationship between heights and distances.

Proportional relationships are relationships between two variables where their ratios are equivalent.

$\frac{\text { height of micah eyes above ground }}{\text { distance of micah from mirror }}=\frac{\text { height of tree above the ground }}{\text { distance of tree from mirror }}$

$\begin{array}{l}{\frac{6 \text { feet }}{9 \text { feet }}=\frac{n \text { feet }}{24 \text { feet }}} \\\\ {\frac{6}{9}=\frac{n}{24}} \\\\ {\text { n }=\frac{1}{3} \times 24} \\\\ {\text { n }=8}\end{array}$

Hence, the height of the tree is 8 feet

6 0

3 years ago

A school fundraiser has a minimum target of $600. Faculty donated $200 and there are 10 student clubs that are participating wit

Advocard [28]

Answer:

just do 400/10= $40 so the student clubs should each pay $40 to get $600 because the faculty already payed $200 so they only need $400 more dollars which is why the answer should just be

f = $40 per student club

Step-by-step explanation:

3 0

3 years ago

a triangle playground has angles with measures in ratio 3: 4: 5. what is the measure of the smallest angle?

forsale [732]

Between 3 and 4 obviously

3 0

3 years ago

Read 2 more answers

The number of apples in the box was less than 80. It is possible to divide all the apples evenly among 3, 4, and 5 children. How

ANEK [815]

Answer:

60 apples

Step-by-step explanation:

There are some number of apples in the box which is less than 80.

Now, it is given in the condition that all the apples can be divided evenly among 3, 4, and 5 children.

Therefore, the number of apples is a common multiple of 3, 4, and 5 which is less than 80.

Now, multiples of 3 less than 80 are 78, 75, 72, 69, 66, 63, 60, etc.

And, multiples of 4 less than 80 are 76, 72, 68, 64, 60, 56, etc.

Again, multiples of 5 less than 80 are 75, 70, 65, 60, 55, etc.

Therefore, the common multiple less than 80 is 60.

Hence, there were 60 apples in the box. (Answer)

6 0

3 years ago

The data set below shows the temperature, in degrees Fahrenheit, of a mug of tea compared tothe time in minutes after being pour

Verizon [17]

Given the model of the Exponential Regression:

$y=174.4(0.987)^x$

By definition:

$Residual=Observed\text{ }y\text{ }value-Predicted\text{ }y\text{ }value$

You can see in the table the observed y-values (the temperature in Fahrenheit)

In order to find the Predicted y-values, you need to substitute all the x-values given in the table (the time in minutes) into the equation and then evaluate. You get:

$y=174.4(0.987)^5\approx163.35$ $y=174.4(0.987)^8\approx157.07$ $y=174.4(0.987)^{11}\approx151.02$ $y=174.4(0.987)^{15}\approx143.32$ $y=174.4(0.987)^{18}\approx137.80$ $y=174.4(0.987)^{22}\approx130.77$ $y=174.4(0.987)^{25}\approx125.74$ $y=174.4(0.987)^{29}\approx119.33$ $y=174.4(0.987)^{32}\approx114.73$ $y=174.4(0.987)^{35}\approx110.32$

Now you have these points:

$(5,163.35),(8,157.07),(11,151.02),(15.143.32)(18,137.800),(22,130.77),(25,125.74),(29,119.33),(32,114.73),(35,110.32)$

Therefore, you can plot them on the Coordinate Plane:

By definition, when the residual plot shows a pattern, a non-linear regression model is appropriate for the data. Therefore, the Exponential Regression Model is a good fit.

Hence, the answer is:

- Residual Plot:

- First option.

6 0

2 years ago