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3 years ago

Rectangle w/area of 91 has dimensions of (x+2) and (2x+3). Solve for dimensions.

Mathematics

1 answer:

Leviafan [203]3 years ago

8 0

Answer:

5unit

Step-by-step explanation: since area of rectangle = length*width

Here length is (x+2) and width is(2x+3)

(x+2)(2x+3)=91

On further solving

2x^2+75x-85=0

2x^2-10x+17x-85=0

2x(x-5)+17(x-5)=0

(2x+17)(x-5)=0

x=5unit

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The length of a vegetable garden is 4 feet longer than its width. If the area of the garden is 140 square feet, find its dimensi

Lena [83]

Length is 14 and the width is 10

4 0

3 years ago

• A cylindrical tank can hold 2279.64 cubic feet of water. The radius of the tank is 11 feet. What is the height of the tank?

tia_tia [17]

Answer:

Step-by-step explanation:

so you want to know the formula for the volume of a cylinder

volume (cylinder) = area of the circular base * height

2279.64 = area of a circle + height

area of a circle is $\pi$ $r^{2}$

they tell us the radius is 11 feet so r = 11

circle = $\pi$ $11^{2}$ = 38013271

2279.64 = 38013271 * height

2279.64 / 38013271 = height

5.996958 = height in feet

8 0

3 years ago

Will give brainiest Answer ASAP

balandron [24]

Answer:

Step-by-step explanation:

When you have an exponent inside and a exponent outside of the parentheses, you multiple them together. Since you're trying to get it equal to d^10, just divide it by 2 and you will get 5.

8 0

3 years ago

According to a study conducted by the Toronto-based social media analytics firm Sysomos, of all tweets get no reaction. That is,

Svetllana [295]

Answer:

a) E(X) = 71

b) V(X) = 20.59

Sigma = 4.538

Step-by-step explanation:

The question is incomplete:

According to a 2010 study conducted by the Toronto-based social media analytics firm Sysomos, 71% of all tweets get no reaction. That is, these are tweets that are not replied to or retweeted (Sysomos website, January 5, 2015).

Suppose we randomly select 100 tweets.

a) What is the expected number of these tweets with no reaction?

b) What are the variance and standard deviation for the number of these tweets with no reaction?

This can be modeled with the binomial distribution, with sample size n=100 and p=0.71, as the probability of no reaction for each individual tweet.

The expected number of these tweets with no reaction can be calcualted as the mean of the binomial random variable with these parameters:

$E(X)=n\cdot p=100\cdot 0.71=71$

The variance for the number of these tweets with no reaction can be calculated as the variance of the binomial distribution:

$V(X)=np(1-p)=100\cdot0.71\cdot0.29=20.59$

Then, the standard deviation becomes:

$\sigma=\sqrt{V(X}=\sqrt{20.59}=4.538$

5 0

3 years ago

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.? y = 2 + se

sertanlavr [38]

Answer:

The volume of the solid is: $\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}$

Step-by-step explanation:

GIven that :

$y = 2 + sec \ x , -\dfrac{\pi}{3} \leq x \leq \dfrac{\pi}{3} \\ \\ y = 4\\ \\ about \ y \ = 2$

This implies that the distance between the x-axis and the axis of the rotation = 2 units

The distance between the x-axis and the inner ring is r = (2+sec x) -2

Let R be the outer radius and r be the inner radius

By integration; the volume of the of the solid can be calculated as follows:

$V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(4-2)^2 - (2+ sec \ x -2)^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(2)^2 - (sec \ x )^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [4 - sec^2 \ x ]dx$

$V = \pi [4x - tan \ x]^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) - 4(-\dfrac{\pi}{3})+ tan (-\dfrac{\pi}{3})] \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) + 4(\dfrac{\pi}{3})- tan (\dfrac{\pi}{3})] \\ \\ \\ V = \pi [8(\dfrac{\pi}{3}) - 2 \ tan (\dfrac{\pi}{3}) ]$

$\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}$

7 0

3 years ago