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4 years ago

14

The cost for new carpet is $8.55 per square yard,plus an installation fee. If 700 square yards of carpet cost $6164 after instal

lation, write a linear equation to find the cost of 1000 yards.

1 answer:

8090 [49]4 years ago

3 0

$8,805.71 because 700=6164 which means 1000=8,805.71 by Multiplying 1000×6164 which equals 6,164,000 and this result you decide by 700

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Write and evaluate the definite integral that represents the volume of the solid formed by revolving the region about the x-axis

guapka [62]

Answer: V = $\frac{64}{3}\pi$

Step-by-step explanation: A solid formed by revolving the region about the x-axis can be considered to have a thin vertical strip with thickness Δx and height y = f(x). The strip creates a circular disk with volume:

V = $\pi. y^{2}.$ Δx

Using the <u>Disc</u> <u>Method</u>, it is possible to calculate all the volume of these strips, giving the volume of the revolved solid:

V = $\int\limits^a_b {\pi. y^{2} } \, dx$

Then, for the region generated by y = - x + 4:

V = $\int\limits^4_0 {\pi.(-x+4)^{2} } \, dx$

V = $\pi.\int\limits^4_0 {(x^{2}-8x+16)} \, dx$

V = $\pi.(\frac{x^{3}}{3}-4x^{2}+16x )$

V = $\pi.(\frac{4^{3}}{3}-4.4^{2}+16.4 - 0 )$

V = $\frac{64}{3}.\pi$

The volume of the revolved region is V = $\frac{64}{3}.\pi$

8 0

3 years ago

You start driving north for 9 miles, turn right, and drive east for another 40 miles. At the end of driving, what is your straig

Vsevolod [243]

The straight line distance from the starting point is 41 miles.

<u>Explanation:</u>

Given:

Distance covered towards north, n = 9 miles

Distance covered towards east, e = 40 miles

Distance from the origin to the end, x = ?

If we imagine this, then the route forms a right angle triangle

where,

n is the height

e is the base

x is the hypotenuse

Using pythagoras theorm:

(x)² = (n)² + (e)²

(x)² = (9)² + (40)²

(x)² = 1681

x = 41 miles

Therefore, the straight line distance from the starting point is 41 miles.

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3 years ago

1.Given point (-6, -3) and a slope of 4, write an equation in point-slope form.

bazaltina [42]

Step-by-step explanation:

1) c

2) c

use the value of slope and the coordinates and substitute in the equation of line.

8 0

3 years ago

Can someone help me with this.. It is timed I WILL MARK YOU AS BRAINLIEST

DENIUS [597]

(2p+13)(p−3)/2p-7

3 0

3 years ago

Read 2 more answers

Natasha_Volkova [10]

Answer:

Step-by-step explanation:

For a triangle the area is

$A=\frac{1}{2}bh$

If our triangle is isosceles and the 2 congruent sides each measure 4 and they include an angle of 40 degrees, let's say that the vertex angle is 40 and the sides that are not the base each measure 4. If we drop an altitude from the vertex to the base, we cut the triangle into 2 right triangles, with the vertex angle being 20 degrees and the hypotenuse being 4. To find the base, then, which is opposite the angle, we use the sin ratio:

$sin(20)=\frac{b}{4}$ and

4sin(20) = b so

b = 1.368

But we need the whole base, and that is only half of it. So

2b = 2.736

To find the height, which is adjacent to the angle, we use the cos ratio:

$cos(20)=\frac{h}{4}$ and

4cos(20) = h so

h = 3.759

Now we have enough info to find the area of the triangle using the triangle area formula from above:

$A=\frac{1}{2}(2.736)(3.759)$ and

A = 5 meters squared.

7 0

3 years ago