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2 years ago

Berniece solved the following equation:

Mathematics

1 answer:

aniked [119]2 years ago

5 0

Answer:

Step 4.

Step-by-step explanation:

To isolate the x variable, she subtracts 8 from both sides making it another subtraction property of equality justification.

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Which is greater 6,200 ft or 1 mi 900 ft?

Tasya [4]

1 mi and 900 ft,1 mile = 5280 ft

8 0

3 years ago

Read 2 more answers

(5/4 × 54/48) + (5/4 × 105/75)

Kitty [74]

101/32 or 3 5/32 or 3.15625

(5/4 × 54/48) = 45/32

(5/4 × 105/75) = 7/4

7/4 x 8 top & bottom =56/32

45+56=101

Hope this helps!

8 0

2 years ago

Find the expansion of cos x about the point x=0

ycow [4]

Answer:

Cos x = 1 - $\frac{x^2}{2!}$ + $\frac{x^4}{4!}$ - $\frac{x^6}{1!}$ + ...

Step-by-step explanation:

We use Taylor series expansion to answer this question.

We have to find the expansion of cos x at x = 0

f(x) = cos x, f'(x) = -sin x, f''(x) = -cos x, f'''(x) = sin x, f''''(x) = cos x

Now we evaluate them at x = 0.

f(0) = 1, f'(0) = 0, f''(0) = -1, f'''(0) = 0, f''''(0) = 1

Now, by Taylor series expansion we have

f(x) = f(a) + f'(a)(x-a) + $\frac{f''(a)(x-a)^2}{2!}$ + $\frac{f'''(a)(x-a)^3}{3!}$ + $\frac{f''''(a)(x-a)^4}{4!}$ + ...

Putting a = 0 and all the values from above in the expansion, we get,

Cos x = 1 - $\frac{x^2}{2!}$ + $\frac{x^4}{4!}$ - $\frac{x^6}{1!}$ + ...

8 0

3 years ago

If vector u has its initial point at (-7, 3) and its terminal point at (5, -6), u =

attashe74 [19]

First of all, let θθ be some angle in (0,π)(0,π). Then

θθ is acute ⟺⟺ θ<π2θ<π2 ⟺⟺ cosθ>0cos⁡θ>0.θθ is right ⟺⟺ θ=π2θ=π2 ⟺⟺ cosθ=0cos⁡θ=0.θθ is obtuse ⟺⟺ θ>π2θ>π2 ⟺⟺ cosθ<0cos⁡θ<0.

Now, to see if (say) angle AA of the triangle ABCABC is acute/right/obtuse, we need to check whether cos∠BACcos⁡∠BAC is positive/zero/negative. But what is cos∠BACcos⁡∠BAC? It is the angle made by the vectors AB−→−AB→ and AC−→−AC→. (When you are computing the angle at a particular vertex vv, you should make sure that both the vectors corresponding to the two adjacent sides have that vertex vv as the initial point.) We will first compute these two vectors:

AB−→−=(0,0,0)−(1,2,0)=(−1,−2,0)AB→=(0,0,0)−(1,2,0)=(−1,−2,0)AC−→−=(−2,1,0)−(1,2,0)=(−3,−1,0)AC→=(−2,1,0)−(1,2,0)=(−3,−1,0)Therefore, the angle between these vectors is given by:cos∠BAC=AB−→−⋅AC−→−|AB−→−||AC−→−|=…(1)(1)cos⁡∠BAC=AB→⋅AC→|AB→||AC→|=…Can you take it from here? From the sign of this value, you should be able to decide if angle AA is acute/right/obtuse.

Now, do the same procedure for the remaining two angles BB and CC as well. That should help you solve the problem.

A shortcut. Since you are not interested in the actual values of the angles, but you need only whether they are acute, obtuse or right, it is enough to compute only the sign of the numerator (the dot product between the vectors) in formula (1). The denominator is always positive.

6 0

3 years ago

A hat contains 5 red balls, 14 green balls, and 11 yellow balls. Alexa chooses one ball at random from the hat. What is the prob

dem82 [27]

Answer:

The answer is A) 5/6

Step-by-step explanation:

first you add all the balls together

then you add just the yellow and green balls together

the fraction would be 25/30

simplify it and you get 5/6

4 0

3 years ago