Answer: first option
Step-by-step explanation:
The formula for calculate the surface area of a cone is the shown below:
Where: s is the slant height and r is the radius.
As you can see in the figure the slant height and the radius are:
s=18 cm and r=6 cm
Therefore when you substitute the values shown above into the formula, you obtain that the result is:
cm²
Actual Distance =120 Km
We have to map 120 Km in the scale of 3 Cm.
i.e, 3 Cm = 120 Km
→ 1 cm = (120÷3) Km
→ 1 cm = 40 Km
So, if you scale 3 cm on the map correspond to 120 km,then
you have to scale , 1 Cm= 40 Km
Drawn the graph for you below.
We have 3 people: Paul, Daniel and Patricia. Let each name denote that person’s current age in years. Remember that % is the symbol for 1/100.
PAUL: (#A) Paul = Patricia – 2
DANIEL:
(#B) Daniel = 125% * Patricia = 125 * (1/100) * Patricia = 1.25 * Patricia
(#C) Ten years ago, Daniel’s age at that time would have been Daniel’s current age – 10. IE “Daniel – 10”.
Ten years ago, Patricia’s age at that time would have been Patricia’s current age – 10. IE “Patricia – 10”.
Ten years ago, Daniel’s age at that time (IE Daniel – 10) was 50% greater than Patricia’s age at the time (Patricia – 10).
IE
Daniel – 10 = 150% * (Patricia – 10)
Daniel – 10 = 1.50 * (Patricia – 10)
Daniel – 10 = 1.50 * Patricia – 1.50 * 10
Daniel – 10 = 1.50 * Patricia – 15
Daniel = 1.50 * Patricia – 15 + 10
Daniel = 1.50 * Patricia – 5
So now we have 3 equations in 3 unknowns:
(A) Paul = Patricia – 2
(B) Daniel = 1.25 * Patricia
(C) Daniel = 1.50 * Patricia – 5
Solve equations B & C simultaneously
1.25 * Patricia = 1.50 * Patricia – 5
1.25 * Patricia – 1.50 * Patricia = – 5
– 0.25 * Patricia = – 5
Patricia = (– 5) / (– 0.25)
Patricia = + 20
So now we can write the 3 people’s ages:
(a) Patricia = 20
(b) Paul = Patricia – 2 = 20 – 2 = 18
(c) Daniel = 1.25 * Patricia = 1.25 * 20 = 25
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<span>Finally, we check our solution against the original question. </span>
Paul is two years younger than Patricia. ……… 20 – 2 = 18 ✔
Daniel is 25% older than Patricia. ……… 25 = 125% * 20 ✔
Ten years ago, Daniel was 50% older than Patricia. 25 – 10 = 150% (20– 10) ✔
Hope that helped :)
Step-by-step explanation:
A left Riemann sum approximates a definite integral as:
Given ∫₂⁸ cos(x²) dx:
a = 2, b = 8, and f(x) = cos(x²)
Therefore, Δx = 6/n and x = 2 + (6/n) (k − 1).
Plugging into the sum:
∑₁ⁿ cos((2 + (6/n) (k − 1))²) (6/n)
Therefore, the answer is C. Notice that answer D would be a right Riemann sum rather than a left (uses k instead of k−1).
n would equal <em>-33</em>.
<em>n=-33</em>
