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Ad libitum [116K]
3 years ago
15

In remodeling a house an architect finds that by adding the same amount to each dimension of a 15ft by 19ft rectangular room, th

e area would be increased by 98 ft^2. How
much must be added to each dimension?
Let x be the amount that is added to each dimension. After writing an equation in standard form with a > 0, a= ? b= ? and c= ?
(Simplify your answers.)
Mathematics
1 answer:
earnstyle [38]3 years ago
8 0

Answer:

Step-by-step explanation:

new length=15+x

width=19+x

then area=(15+x)×(19+x)=285+15x+19x+x²=x²+34x+285 ft²

original area=15×19=285 ft²

then 285+98=x²+34x+285

or

x²+34x-98=0

x²+34x+17²=98+17²

(x+17)²=98+289=387

x+17=√387=3√43

x=3√43-17 ft

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A company interested in lumbering rights for a certain tract of slash pine trees is told that the mean diameter of these trees i
brilliants [131]

Answer:

97.6% of the trees will have diameters between 7.6 and 18.6 inches.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 12 inches

Standard Deviation, σ = 2.2 inches

We are given that the distribution of diameter of tree is a mound shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

P(diameters between 7.6 and 18.6 inches)

P(7.6 \leq x \leq 18.6) = P(\displaystyle\frac{7.6 - 12}{2.2} \leq z \leq \displaystyle\frac{18.6-12}{2.2}) = P(-2 \leq z \leq 3)\\\\= P(z \leq 3) - P(z < -2)\\= 0.999 - 0.023 = 0.976= 97.6\%

P(7.6 \leq x \leq 18.6) = 97.6\%

97.6% of the trees will have diameters between 7.6 and 18.6 inches.

8 0
3 years ago
What is the diameter of a sphere? A.Twice the radius of the sphere B.The distance between two spheres C.The distance from the ce
dolphi86 [110]

Twice the raidus. okay, Im sure that how you spell Radius but anyway, Hope this helps.


3 0
2 years ago
Can someone help me?
Kitty [74]

Answer:

see explanation

Step-by-step explanation:

Given the width is \frac{1}{3} of the length, then

y - 4 = \frac{1}{3}(2y + 6)

Multiply through by 3 to clear the fraction

3y - 12 = 2y + 6 ( subtract 2y from both sides )

y - 12 = 6 ( add 12 to both sides )

y = 18

Thus

length = 2y + 6 = 2(18) + 6 = 36 + 6 = 42 in

width = y - 4 = 18 - 4 = 14 in

6 0
2 years ago
What is the width of a rectangle with length 5.5 cm and area 220 cm???
Aleks04 [339]
40 cm. Just divide the area by the length. Hope this helps!
7 0
3 years ago
Find two unit vectors orthogonal to both given vectors. i j k, 4i k
Maurinko [17]
The cross product of two vectors gives a third vector \mathbf v that is orthogonal to the first two.

\mathbf v=(\vec i+\vec j+\vec k)\times(4\,\vec i+\vec k)=\begin{vmatrix}\vec i&\vec j&\vec k\\1&1&1\\4&0&1\end{vmatrix}=\vec i+3\,\vec j-4\,\vec k

Normalize this vector by dividing it by its norm:

\dfrac{\mathbf v}{\|\mathbf v\|}=\dfrac{\vec i+3\,\vec j-4\,\vec k}{\sqrt{1^2+3^2+(-4)^2}}=\dfrac1{\sqrt{26}}(\vec i+3\,\vec j-4\vec k)

To get another vector orthogonal to the first two, you can just change the sign and use -\mathbf v.
6 0
3 years ago
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