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aksik [14]
3 years ago
7

At the beginning of a snowstorm, Grayson had 10 inches of snow on his lawn. The snow then began to fall at a constant rate of 0.

5 inches per hour. Assuming no snow was melting, how much snow would Grayson have on his lawn 3 hours after the snow began to fall? How much snow would Grayson have on his lawn after t hours of snow falling?
Mathematics
1 answer:
maxonik [38]3 years ago
3 0

Answer:

  • Grayson had 10 inches of snow in his lawn
  • the snow falls at a constant rate of 0.5 inches per hour
  • no snow was melting
  • the snow has fallen for 3 hours  

Let y be the height of the snow in the lawn

Grayson had 10 inches at the beginning (at t=0) so y= 10

3 hours passed so y= 10 + 3*0.5 = 11.5 inches

Grayson had 11.5 inches after three hours

Assuming that the snow continued to fall for an unkhown time t

y = 0.5*t + 10

we had 10 at the beginning so we add 10 (+10)

the snow is growing by 0.5 inches in the single hour so we multiply by 0.5

t is the time and it can 4, 5, 6 ...... hours

Just like a function :

  • 0.5 is the slope
  • t is the variable
  • 10 is the y-intercept

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The outer and inner triangles are both equilateral and the circle touches all three sides of the outer triangle. If the area of
Brrunno [24]

Answer:

The area of outer Δ = 40 cm²

Step-by-step explanation:

∵ Area of the small triangle = 10 cm²

If we join the center of the circle with the 3 vertices of the inner Δ

These 3 segments are the radii of the circle

Now the inner triangle has 3 isosceles Δ their sides are r , r and s1 with vertex angle 120° ⇒ (360° ÷ 3 = 120°)

Where r is the radius of the circle and s1 is the side of the inner triangle

<em>By using cosine rule</em>

(s1)² = r² + r² - 2r²cos120 = r² + r² - 2r² (-0.5) = r² + r² + r² = 3r²

∴ s1 = r√3

∵ The radius of the circle ⊥ to the side of the outer Δ because the side of the outer Δ is a tangent to the circle

If we join a vertex of the outer Δ with the center of the circle

We will have a right angle triangle of two legs r and half s2 with angle 60° (120° ÷ 2 )between them ⇒ s2 is the side of outer Δ

∴ tan 60° = 1/2 (s2) ÷ r ⇒ √3 = 1/2 (s2) ÷ r = (s2)/2r

∴ s2 = 2r√3

∴ s2 : s1 = 2r√3 ÷ r√3 = 2 : 1

∴ The side of the outer Δ is double the side of the inner Δ

<em>By using similarity ratio</em>

A2/A1 = (s2/s1)² ⇒ A2 and A1 are the areas of outer and inner triangles

∴ A2 : A1 = (2/1)² = 4/1  

∴ A2 = 4 A1

∴ A2 = 4 × 10 = 40 cm²

5 0
3 years ago
The first element in an arithmetic sequence is 2. Its twenty second is 14. Find the value of n so that a(n)=6
Aleks04 [339]

Answer:

<h2>n = 8</h2>

Step-by-step explanation:

Given the nth term of an arithmetic sequence to be Tn = a+(n-1)d

a = first term of the sequence

n = number of terms

d = common difference.

Given the first element a = 2 and 22nd to be 14

T22 = a+(22-1)d = 14

a+21d = 14

Substtuting a = 2 into the equation to get d

2+21d = 14

21d = 12

d = 12/21

d = 4/7

The nth term of the sequence given a = 2 and d = 4/7 will be expressed as;

Tn = 2+(n-1)4/7

Given Tn = 6

6 = 2+(n-1)4/7

6 = 2+4/7 n - 4/7

6-2+4/7 = 4/7 n

32/7=4/7 n

32 = 4n

n = 32/4

n = 8

8 0
3 years ago
Draw a number line to divide 70÷5
defon
If you need help the answer is 14 use long division or just subtract all depending on what the numbers are.
4 0
3 years ago
Help me answer these questions please​
Wewaii [24]
You plug in x for 3 so it would be 10(3) + 2, and 10 times 3 is 30 and 30 plus 2 is 32
7 0
2 years ago
.////////////PLEASE HELPPPPP
Reptile [31]

Answer:

106°

Step-by-step explanation:

Supplementary angles add up to 180°

180°- 74°

= 106°

6 0
3 years ago
Read 2 more answers
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