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ASHA 777 [7]
3 years ago
10

At 6:00 the outside air temperature was 15°F. By 8:00 the temperature had dropped 9°F, and by 11:00 I had dropped another 12°. W

hat was the temperature at 11:00?
Mathematics
1 answer:
laila [671]3 years ago
8 0

Answer:

- 6°F

Step-by-step explanation:

Given :

Temperature at 6:00 = 15°F

Temperature dropped by 9°F by 8:00

Temperature by 8:00 = 15°F - 9°F = 6°F

Temperature dropped another 12°F by 11:00

Hence, Temperature at 11:00 will be :

6°F - 12°F = - 6°F

Temperature at 11:00 = - 6°F

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Determine if each of the following sets is a subspace of Pn, for an appropriate value of n.
snow_tiger [21]

Answer:

1) W₁ is a subspace of Pₙ (R)

2) W₂ is not a subspace of Pₙ (R)

4) W₃ is a subspace of Pₙ (R)

Step-by-step explanation:

Given that;

1.Let W₁ be the set of all polynomials of the form p(t) = at², where a is in R

2.Let W₂ be the set of all polynomials of the form p(t) = t² + a, where a is in R

3.Let W₃ be the set of all polynomials of the form p(t) = at² + at, where a is in R

so

1)

let W₁ = { at² ║ a∈ R }

let ∝ = a₁t² and β = a₂t²  ∈W₁

let c₁, c₂ be two scalars

c₁∝ + c₂β = c₁(a₁t²) + c₂(a₂t²)

= c₁a₁t² + c²a₂t²

= (c₁a₁ + c²a₂)t² ∈ W₁

Therefore c₁∝ + c₂β ∈ W₁ for all ∝, β ∈ W₁  and scalars c₁, c₂

Thus, W₁ is a subspace of Pₙ (R)

2)

let W₂ = { t² + a ║ a∈ R }

the zero polynomial 0t² + 0 ∉ W₂

because the coefficient of t² is 0 but not 1

Thus W₂ is not a subspace of Pₙ (R)

3)

let W₃ = { at² + a ║ a∈ R }

let ∝ = a₁t² +a₁t  and β = a₂t² + a₂t ∈ W₃

let c₁, c₂ be two scalars

c₁∝ + c₂β = c₁(a₁t² +a₁t) + c₂(a₂t² + a₂t)

= c₁a₁t² +c₁a₁t + c₂a₂t² + c₂a₂t

= (c₁a₁ +c₂a₂)t² + (c₁a₁t + c₂a₂)t ∈ W₃

Therefore c₁∝ + c₂β ∈ W₃ for all ∝, β ∈ W₃ and scalars c₁, c₂

Thus, W₃ is a subspace of Pₙ (R)

8 0
3 years ago
A pentagon has angle measures of 105°, 101°, 112° and 113°. What must the fifth angle measure?
Taya2010 [7]
Add them. Pentagram interior angle is 540. 105+101+112+113=431. 540-431=109 Hence, 109 is the answer. Please brainliest.
8 0
3 years ago
Read 2 more answers
Please help !!
lesya692 [45]
The answer would be B
8 0
3 years ago
How many different ways can you write a fraction that has a numerator of 2 as a sum of fractions
Rzqust [24]
At least you can write it as the sum of half of it twice, that is:
2/x = 1/x + 1/x
whatever x number you have, for example:
2/5 = 1/5 + 1/5

But then, you can express a fraction in many different ways, for example again:
2/5 = <span>1/5 + 1/5 = 2/10 + 2/10
</span>= 1/10 + 1/10 + 1/10 + 1/10
so there are an infinite ways of expressing such a fraction.
7 0
3 years ago
2. Sandi can run for one hour at a constant speed of 348 cm per second. Marci can run for one
Zanzabum

Answer:

Marci is the faster runner.

Step-by-step explanation:

Sandi can run 348 cm in a second. Let's find out how many cm she can run in a minute: in a minute there are 60 seconds. So lets multiply 348cm times 60, this gives you 20,880. That is how much she travels in a minute, now let's find out how much she runs in an hour: if she runs 20,880 cm in an minute and there are 60 minutes in an hour, then all you have to do is multiply 20,880 times 60, this gives you 1,252,800. That is how many cm she runs in an hour. Now let's change from cm to miles. There are 160,934 cm in a mile. If we divide 1,252,800 by 160,934 this will give you

7 0
1 year ago
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