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Verizon [17]
2 years ago
14

What is the midpoint between (-4,4),(-2,2)

Mathematics
1 answer:
Otrada [13]2 years ago
3 0
The answer is b (-3,3)
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Find the number a such that the line x = a bisects the area under the curve y = 1/x2 for 1 ≤ x ≤ 4. 8 5​ (b) find the number b s
IceJOKER [234]

a. We're looking for a such that

\displaystyle\int_1^a\frac{\mathrm dx}{x^2}=\int_a^4\frac{\mathrm dx}{x^2}

-\dfrac1x\bigg|_{x=1}^{x=a}=-\dfrac1x\bigg|_{x=a}^{x=4}

1-\dfrac1a=\dfrac1a-\dfrac14

\dfrac54=\dfrac2a\implies\boxed{a=\dfrac85}

b. Integrating with respect to y will make things easier.

y=\dfrac1{x^2}\implies x=\dfrac1{\sqrt y}

(where we take the positive square root because we know x>0)

Now we want to find b such that

\displaystyle\int_0^b\frac{\mathrm dy}{\sqrt y}=\int_b^1\frac{\mathrm dy}{\sqrt y}

2\sqrt y\bigg|_{y=0}^{y=b}=2\sqrt y\bigg|_{y=b}^{b=1}

2\sqrt b=2-2\sqrt b

4\sqrt b=2\implies\boxed{b=\dfrac14}

3 0
2 years ago
Circle J is located in the first quadrant with center (a, b) and radius s. Felipe transforms Circle J to prove that it is simila
iVinArrow [24]
The correct answer for the question that is being presented above is this one: "c. translate circle J by (x-a, y-b) and dilate by a factor of t/s." Circle J is located in the first quadrant with center (a, b) and radius s. Felipe transforms Circle J to prove that it is similar to any circle centered <span>at the origin with radius r.</span>
3 0
2 years ago
A small company's net income for the first six months of the year was $76,500 and for the last six months it was $100,000 what i
Talja [164]
<span>The<u> correct answer</u> is:

153/200.

Explanation<span>:

The amount for the first 6 months is 76500 and the amount for the last 6 months is 100000. This makes the ratio 76500/100000.

Both of these end with two 0's; this means they are both divisible by 100. 76500/100 = 765 and 100000/100 = 1000; this makes the ratio 765/1000.

Since these end with a 5 or a 0, they are divisible by 5; 765/5 = 153 and 1000/5 = 200; this makes the ratio 153/200.

153 is only divisible by 3 or 9; 153/3 = 51 and 153/9 = 17. None of these will divide evenly into 200, so we stop at 153/200.</span></span>
4 0
2 years ago
Read 2 more answers
Harper has $15.00 to spend at her grocery store. She is going to buy bags of fruit that cost $4.75 each and one box of crackers
Andrej [43]
First write the inequality:    15\leq4.75x +3.50

Then to solve, first subtract 3.50 from both sides to get:

11.50\leq4.75x

Then divide by 4.75 to get 2.42, and since you can't buy .42 of a bag  of fruit, you round down. So your final answer would be 2 bags of fruit.
7 0
2 years ago
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4.Find the square roots of the following decimal numbers
alisha [4.7K]

Answer:

I) 32.5

ii) 100.1

Step-by-step explanation:

I) 1056.25 = √1056.25

= 32.5

ii) 10020.01= √10020.01

=100.1

4 0
2 years ago
Read 2 more answers
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