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Soloha48 [4]
3 years ago
12

When writing numbers in base 10, we only allow coefficients of 0 through 9. Why is that?​

Mathematics
1 answer:
Margaret [11]3 years ago
7 0

Answer:

Because 0 counts as the first possible number. 0-9 gives you 10 possible numbers.

Step-by-step explanation:

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A tunnel is built in form of a parabola. The width at the base of tunnel is 7 m. On
uysha [10]

Given:

The width at the base of parabolic tunnel is 7 m.

The ceiling 3 m from each end of the base there are light fixtures.

The height to light fixtures is 4 m.

To find:

Whether it is possible a trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel.

Solution:

The width at the base of tunnel is 7 m.

Let the graph of the parabola intersect the x-axis at x=0 and x=7. It means x and (x-7) are the factors of the height function.

The function of height is:

h(x)=ax(x-7)             ...(i)

Where, a is a constant.

The ceiling 3 m from each end of the base there are light fixtures and the height to light fixtures is 4 m. It means the graph of height function passes through the point (3,4).

Putting x=3 and h(x)=4 in (i), we get

4=a(3)((3)-7)

4=a(3)(-4)

\dfrac{4}{(3)(-4)}=a

-\dfrac{1}{3}=a

Putting a=-\dfrac{1}{3}, we get

h(x)=-\dfrac{1}{3}x(x-7)              ...(ii)

The center of the parabola is the midpoint of 0 and 7, i.e., 3.

The width of the truck is 4 m. If is passes through the center then the truck must m 2 m on the left side of the center and 2 m on the right side of the center.

2 m on the left side of the center is x=1.5.

A trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel is possible if h(1.5) is greater than 2.8.

Putting x=1.5 in (ii), we get

h(1.5)=-\dfrac{1}{3}(1.5)(1.5-7)

h(1.5)=-(0.5)(-5.5)

h(1.5)=2.75

Since h(1.5)<2.8, therefore the trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel is not possible.

6 0
2 years ago
21) Rearrange the formula c2 = a2 + b2 for b.
Anvisha [2.4K]
C2 + a2 +2 = b
Would be the new formula
8 0
3 years ago
Which of the following number is divisible by both 2 and 3​
DENIUS [597]

Answer:

6, 12, 18,

Step-by-step explanation:

u didn't said the numbers but here is the explanation

6÷2=3

6÷3=2

12÷3=4

12÷2=6

18÷2=9

18÷3=6

4 0
3 years ago
Read 2 more answers
What is the product of 14/5
MAXImum [283]

Answer:

2.8

Step-by-step explanation:

Just divide and get the answer

3 0
3 years ago
Help please............................
Vesnalui [34]

Step-by-step explanation:

csc x / (cot x + tan x)

Write in terms of sine and cosine.

(1 / sin x) / [(cos x / sin x) + (sin x / cos x)]

Multiply top and bottom by sin x.

1 / [cos x + (sin²x / cos x)]

Multiply top and bottom by cos x.

cos x / (cos²x + sin²x)

Use Pythagorean identity.

cos x / 1

cos x

3 0
3 years ago
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