What is the greatest possible error when measuring to the nearest quarter of an inch?

Please someone help me with this I’m very confused

mote1985 [20]

Answer:

a. n= 1x +7

b. n= 12 + 4x

Step-by-step explanation:

4 0

2 years ago

Evaluate the integral by making an appropriate change of variables.

VARVARA [1.3K]

By inspecting the integrand, the "obvious" choice for substitution would be

u = y + x

v = y - x

Solving for x and y, we would have

x = (u - v)/2

y = (u + v)/2

in which case the Jacobian and its determinant are

$J=\begin{bmatrix}x_u&x_v\\y_u&y_v\end{bmatrix}=\dfrac12\begin{bmatrix}1&-1\\1&1\end{bmatrix}\implies|\det J|=\left|\dfrac12\right|=\dfrac12$

The trapezoid R has two of its edges on the lines x + y = 8 and x + y = 9, so right away, we have 8 ≤ u ≤ 9.

Then for v, we observe that when x = 0 (the lowest edge of R), v = y ; similarly, when y = 0 (the leftmost edge of R), v = -x. So

-x ≤ v ≤ y

-(u - v)/2 ≤ v ≤ (u + v)/2

-u + v ≤ 2v ≤ u + v

-u ≤ v ≤ u

So, the integral becomes

$\displaystyle\iint_R5\cos\left(7\frac{y-x}{y+x}\right)\,\mathrm dA=\int_8^9\int_{-u}^u\frac52\cos\left(\frac{7v}u\right)\,\mathrm dv\,\mathrm du$

$=\displaystyle\frac52\int_8^9\frac u7(\sin7-\sin(-7))\,\mathrm du$

$=\displaystyle\frac57\sin7\int_8^9u\,\mathrm du$

$=\displaystyle\frac5{14}\sin7(9^2-8^2)=\boxed{\frac{85}{14}\sin7}$

4 0

2 years ago

darren has 3/4 of a gallon of soil.he needs to plant 5 small plants.if he splits the soil evenly between the plants.how much soi

nika2105 [10]

Number of plants = 5

Amount of soil present for 5 plants = 3/4 gallons

Now here we have to find how much soil will each plant get.

So we have to apply unitary method here to find how much would each plant get the share of soil.

Soil required by 5 plants = 3/4 gallons

Soil required by 1 plant = 3/4 divided by 5 = 3/20 gallons

Answer: Each plant will get 3/20 gallons of soil.

7 0

2 years ago

Read 2 more answers

What is the surface area of the composite figure? Round to the nearest tenth.

pychu [463]

Answer:

Find the area of the base of the cylinder using A = (pi)r 2 . Subtract your answer from the 80 square inches for the cube and the area of the cylinder. 4. Add the surface areas of each figure to get the total area of the composite figures.

7 0

2 years ago

A cylinder has a radius of 3 cm. Sand is poured into the cylinder to form a layer 2 cm deep. What is the volume of sand in the c

netineya [11]

Answer:

Volume=56.54cm³

Step-by-step explanation:

$Solution,\\\\Radius(r)=3cm\\\\Height(h)=2cm\\\\Now,\\\\Volume=\pi r^{2} h\\\\Volume=\pi *(3cm)^{2} *2cm\\\\Volume=18\pi cm^{3} =56.54cm^{3}$

3 0

1 year ago