Answer:
(5) The perpendicular height of the triangle is 8.48 mm.
(6) The 1184.86 cm far up the wall the ladder reach.
Step-by-step explanation:
Part (5):
When a perpendicular is drawn in an isosceles triangle then the perpendicular divided the base into 2 equal parts.
The figures is shown below.
In ΔABC,
CB = 6 mm
So,
CD = BD = 3 mm
Now calculating the perpendicular height of the triangle.
Using Pythagoras theorem in ΔADC:
Thus, the perpendicular height of the triangle is 8.48 mm.
Part (6):
The figure is shown below.
Converting meter to centimeter:
1 m = 100 cm
So,
12 m = 1200 cm
Using Pythagoras theorem in ΔXYZ:
Thus, 1184.86 cm far up the wall the ladder reach.
Answer:
Step-by-step explanation:
This is a pretty basic related rates problem. I'm going to go through this just like I do in class when I'm teaching it to my students.
We see we have a snowball, which is a sphere. We are talking about the surface area of this sphere which has a formula of
In the problem we are given diameter, not radius. What we know about the relationship between a radius and a diameter is that
d = 2r so
Now we can have the equation in terms of diameter instead of radius. Rewriting:
which simplifies to
and a bit more to
(the 4's cancel out by division). Now that is a simple equation for which we have to find the derivative with respect to time.
Now let's look at the problem and see what we are given as far as information.
The rate at which the surface area changes is -3.8, and we are looking for 
, the rate at which the diameter is changing, when the diameter is 13. Filling in:
and solving for the rate at which the diameter is changing:
and divide to get
Obviously, the negative means that the diameter is decreasing.
Answer:
No.
Step-by-step explanation:
The numbers aren't going up at a constant rate. Say each lap costs 2 dollars. On lap 4, you have paid 8 dollars total. On lap 9, you have paid 18 dollars total. But the 10th lap is free, which means you pay 0 dollars. In order for this pattern to be constant, you would need to pay 20 dollars, but instead you pay 0.
There is a relationship between confidence interval and standard deviation:
Where
is the mean,
is standard deviation, and n is number of data points.
Every confidence interval has associated z value. This can be found online.
We need to find the standard deviation first:
When we do all the calculations we find that:
Now we can find confidence intervals:
We can see that as confidence interval increases so does the error margin. Z values accociated with each confidence intreval also get bigger as confidence interval increases.
Here is the link to the spreadsheet with standard deviation calculation:
https://docs.google.com/spreadsheets/d/1pnsJIrM_lmQKAGRJvduiHzjg9mYvLgpsCqCoGYvR5Us/edit?usp=sharing
Answer:
$35.7
Step-by-step explanation:
you can convert 15% to a decimal by dividing by 100.
15/100 = .15
if you multiply the decimal by the cost of the shirt you get how much the discount is.
0.15 * $42 = 6.30
so a 15% discount on a $42 shirt is $6.30 off. So you subtract the discount from the total cost.
$42 - $6.30 = $35.70 that is the sale price of the shirt.
