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4 years ago

The left hand and the right hand sums are shown here.which could be the actual area under the curve for that interval?

Mathematics

1 answer:

yawa3891 [41]4 years ago

5 0

Answer:

C_ 3.67

Step-by-step explanation:

The right-sum and left-sum are kinda opposite to each other when it comes to estimating the area value of the actual curve. As in...

If the right-sum is over estimating, then the left-sum must be underestimating.

If the left-sum is over estimating, then the right-sum must be underestimating.

So our actual value must lie somewhere between the value calculated by the right-hand-sum and the left-hand-sum

The question gave left-sum being 3.65 and right-sum being 3.683, so our value must lie between two two numbers. The only answer choice that is between 3.65 and 3.683 is 3.67.

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The integers of -5 and 5 are called

qwelly [4]

The integers are called the opposites because they are on the opposite side of zero.

3 0

3 years ago

The surface area of a cylinder is increasing at a rate of 9 pi square meters per hour. The height of the cylinder is fixed at 3

Alekssandra [29.7K]

Answer:

$9\pi \text{ cubic meters per hour}$

Step-by-step explanation:

Since, the surface area of a cylinder,

$A= 2\pi r^2 + 2\pi rh$ ................(1)

Where,

r = radius,

h = height,

If $A= 36\pi\text{ square meters}, h = 3\text{ meters}$

$36\pi = 2\pi r^2 + 2\pi r(3)$

$18 = r^2 + 3r$

$\implies r^2 + 3r - 18=0$

$r^2 + 6r - 3r - 18 = 0$ ( by middle term splitting )

$r(r+6)-3(r+6)=0$

$(r-3)(r+6)=0$

By zero product property,

r = 3 or r = - 6 ( not possible )

Thus, radius, r = 3 meters,

Now, differentiating equation (1) with respect to t ( time ),

$\frac{dA}{dt}= 4\pi r\frac{dr}{dt} +2\pi(r\frac{dh}{dt} + h\frac{dr}{dt})$

∵ h = constant, ⇒ dh/dt = 0,

$\frac{dA}{dt} = 4\pi r \frac{dr}{dt} +2\pi h \frac{dr}{dt}$

We have, $\frac{dA}{dt}=9\pi\text{ square meters per hour}, r = h = 3\text{ meters}$

$9\pi = 4\pi (3) \frac{dr}{dt}+2\pi (3)\frac{dr}{dt}$

$9\pi = (12\pi + 6\pi )\frac{dr}{dt}$

$9\pi = 18\pi \frac{dr}{dt}$

$\implies \frac{dr}{dt} =\frac{1}{2}\text{ meter per hour}$

Now,

Volume of a cylinder,

$V=\pi r^2 h$

Differentiating w. r. t. t,

$\frac{dV}{dt}=\pi ( r^2 \frac{dh}{dt}+h(2r)\frac{dr}{dt})=\pi ((3)(6) (\frac{1}{2})) = 9\pi \text{ cubic meters per hour}$

6 0

3 years ago

PLEASE HELP DUE IN 30 MINUTES!!!

liubo4ka [24]

Answer:

I'm pretty sure the answer to the third question is C

Step-by-step explanation:

We are solving for h(g(x)).

We already know that g(x) is equal to x^2+4.

So know, we can simplify our expression, h(g(x)), to h(x^2+4).

We also know that h(x)=1/x

we simply substitute x for x^2+4, giving us an answer of 1/(x^2+4)

6 0

4 years ago

What are the solution(s) of –x2 + 2x + 3 = x2 – 2x + 3?

Leviafan [203]

-x^2+2x+3=x^2-2x+3 add x^2 to both sides

2x+3=2x^2-2x+3 subtract 2x from both sides

3=2x^2-4x+3 subtract 3 from both sides

2x^2-4x=0 factor

2x(x-2)=0

So x=0 and 2

3 0

3 years ago

Read 2 more answers

Question 1

AveGali [126]

Answer:

2.30/7.5

Step-by-step explanation:

4.30-2=2:30

2.5-10=7.5

8 0

4 years ago