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3 years ago

PLEASE HELP DUE BY MIDNIGHT ILL GIVE YOU BRAINLINEST and 17 POINTS

Mathematics

1 answer:

Leto [7]3 years ago

3 0

Answer:
1). 40ft^2
2). 32.1 cm^2
3). 28 in^2
4). 44 cm^2
5). 148.8m^2
6). 110.7 cm^2

Explanation:

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Solve 7x + 6 < 3(x - 2).

slava [35]

7x + 6 < 3(x - 2)
7x + 6 < 3x - 6
7x - 3x < -6 - 6
4x < - 12
x < - 3

Answer is {x | x < -3}.

7 0

3 years ago

3. What is the area of the circle shown below? Diameter: 28 inches Pi=3.14

Artyom0805 [142]

Step-by-step explanation:

Given diameter (d) = 28 inches

π = 3.14

Radius (r) = 28/2= 14 inches

Now

Area of the circle

= πr²

= 3.14 * 14²

= 615.44 inch ²

6 0

3 years ago

Read 2 more answers

The height of a tree at time t is given by a twice-differentiable function H, where H(t) is measured in meters and t is measured

il63 [147K]

A) Use the mean value theorem.

$H'(6)\approx\dfrac{H(7)-H(5)}{7-5}=\dfrac{11-6}2=\dfrac52\text{ meters/year}$

Since $H(t)$ gives the tree's height in meters at time $t$ , the value of $H'(6)$ informs us how quickly the tree is growing exactly after 6 years have passed. (i.e. the instantaneous rate of change of the tree's height)

b) We use the mean value theorem again. Observe that $H(5)-H(3)=6-2=4$ , and that $5-3=2$ . By the MVT, there must be some $3$ such that

$H'(t)=\dfrac42=2$

c) The average height of the tree is given by the integral

$\displaystyle\frac1{10-2}\int_2^{10}H(t)\,\mathrm dt$

If you can remember the formula for the area of a trapezoid, then this is pretty easy to compute. With five data points, you end up with four trapezoids constructed by the four adjacent subintervals. The "bases" are given by the values of $H(t)$ at each pair of endpoints, and the "heights" are the lengths of the subintervals. For the integral itself, we get

$\dfrac{2+1.5}2(3-2)+\dfrac{6+2}2(5-3)+\dfrac{11+6}2(7-5)+\dfrac{15+11}2(10-7)=\dfrac{263}4$

So the average height of the tree (in meters) is

$\displaystyle\frac1{10-2}\int_2^{10}H(t)\,\mathrm dt\approx\frac{263}{32}$

d) When $G=50$ , the diameter of the base can be determined to be

$50=\dfrac{100x}{1+x}\implies x=1$

We're told that $\dfrac{\mathrm dx}{\mathrm dt}=0.03$ . $G$ is a function of $x$ which is in turn a function of $t$ , so when we differentiate, we use the chain rule:

$\dfrac{\mathrm dG}{\mathrm dt}=\dfrac{\mathrm dG}{\mathrm dx}\cdot\dfrac{\mathrm dx}{\mathrm dt}$

$\implies\dfrac{\mathrm dG}{\mathrm dt}=\dfrac{100}{(1+x)^2}\cdot\dfrac3{100}=\dfrac3{(1+x)^2}$

When the height of the tree is 50 meters, we found the diameter to be 1 meter, so at this point

$\dfrac{\mathrm dG}{\mathrm dt}=\dfrac34\text{ meters/year}$

4 0

3 years ago

Read 2 more answers

21π Rational Irrational

lesantik [10]

Answer: Rational

Step-by-step explanation:

21 $\pi$ is rational because it is $\pi$ times 21 which is 65.9734457254 and numbers that terminate or repeat are rational.