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2 years ago

The length of a rectangle is (x - 9) feet. Its width is x feet. Write an expression you could use to find the perimeter

Mathematics

1 answer:

steposvetlana [31]2 years ago

6 0

Answer:

The expression for the perimeter of the rectangle is: $P = 4x - 18$

Step-by-step explanation:

Perimeter of a rectangle:

A rectangle has length l and width w. It's perimeter is given by:

$P = 2(l + w)$

In this question:

$l = x - 9, w = x$

$P = 2(x - 9 + x) = 2(2x - 9) = 4x - 18$

The expression for the perimeter of the rectangle is: $P = 4x - 18$

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It's a word problem junkie. Is a bus driver who earns 1600 dollars per month login is a is a manager who earns 6800 dollars per

Vlad [161]

Answer: bus driver

Step-by-step explanation:

Given: Earning of bus driver = 1600 dollars per month

Earning of manager = 6800 dollars per month

Amount donated by bus driver = 1200 dollars

Amount donated by manager = 4500 dollars

Percentage of amount donated by bus driver = $\dfrac{1200}{1600}\times100 \%=\dfrac{3}{4}\times100\%=75\%$

Percentage of amount donated by manager = $\dfrac{4500}{6800}\times100 \%\approx66.18\%$

Clearly, 75> 66.18

So, bus driver donated higher percentage of money.

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2 years ago

What is 12%expressed as a fraction? 3/25 1/8 6/25 1/4

Alexxx [7]

3/25 because it's 12% expressed as a fraction

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2 years ago

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

2 years ago

Read 2 more answers

Factor: 36x^2-64 thanks!

Marina CMI [18]

Answer:

4(3x+4)(3x-4)

Step-by-step explanation:

4(9x^2-16)

3 0

2 years ago

Read 2 more answers