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noname [10]
3 years ago
6

Carter is building a model sailboat. The boat will have two triangular sails. One sail will have a base of 24 inches and a heigh

t of 56 inches. The other sail will have a base of 14 inches and a height of 33 inches. What is the minimum amount of material Carter needs to build the sails? 1,806 inches2 1,344 inches2 903 inches2 672 inches2
Mathematics
2 answers:
Black_prince [1.1K]3 years ago
7 0

Find the area of each triangle and then add them together.

The formula for area of a triangle is 1/2 x base x height.

Area 1 = 1/2 x 24 x 56 = 672 square inches.

Area 2 = 1/2 x 14 x 33 = 231 square inches.

Total area = 672 + 231 = 903 square inches.

vovikov84 [41]3 years ago
7 0

Answer:

903 in^2.

Step-by-step explanation:

Area of the larger sail = 1/2*24*56 = 672 in^2.

Area of the smaller sail = 1/2*14*33 = 231 in^2.

Minimum amount of material = 672 + 231 = 903 in^2.

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A spring has a natural length of 7 m. If a 4-N force is required to keep it stretched to a length of 11 m, how much work W is re
bezimeni [28]

Answer:

18 J is the work required to stretch a spring from 7 m to 13 m.

Step-by-step explanation:

The work done is defined to be the product of the force F and the distance d  that the object moves:

W=Fd

If F is measured in newtons and d<em> </em>in meters, then the unit for is a newton-meter, which is called a joule (J).

This definition work as long as the force is constant, but if the force is variable like in this case, we have that the work done is given by

W=\int\limits^b_a {f(x)} \, dx

Hooke’s Law states that the force required to maintain a spring stretched x    units beyond its natural length is proportional to

f(x)=kx

where k is a positive constant (called the spring constant).

To find how much work W is required to stretch it from 7 m to 13 m you must:

Step 1: Find the spring constant

We know that the spring has a natural length of 7 m and a 4 N force is required to keep it stretched to a length of 11 m. So, applying Hooke’s Law

4=k(11-7)\\\\\frac{k\left(11-7\right)}{4}=\frac{4}{4}\\\\k=1

Thus F=x

Step 2: Find the the work done in stretching the spring from 7 m to 13 m.

Recall that the natural length is 7 m, so when we stretch the spring from 7 m to 13 m, we are stretching it by 6 m beyond its natural length.

Work needed to stretch it by 6 m beyond its natural length

W=\int\limits^6_0 {x} \, dx \\\\\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1\\\\\left[\frac{x^{1+1}}{1+1}\right]^6_0\\\\\left[\frac{x^2}{2}\right]^6_0=18

18 J is the work required to stretch a spring from 7 m to 13 m.

5 0
3 years ago
Elle can buy 2 quarts of milk for $3 or 1 gallon of milk for $3, Which Is The Better Deal.... Because Im not sure..
GrogVix [38]
1 gallon is equal to 4 quarts. 

So you can either get 2 quarts for $3, or 4 quarts for 3$

1 gallon is the better deal.
5 0
3 years ago
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You are comparing to wireless services. Verizon changes $35 a month and $5 per gigabyte of data.
ikadub [295]
A) Gigabytes = x
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7 0
3 years ago
A man flies a kite at a height of 15 ft. The wind is carrying the kite horizontally from the man at a rate of 5 ft./s. How fast
Misha Larkins [42]

Answer:

4.4 ft/s

Step-by-step explanation:

Height = 15ft

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Distance from the man to the kite= 32ft

dh/dt = 5 ft/s

h = √32^2 - 15^2

h = √ 1025 - 225

h = √800

h = 28.28ft

D = √15^2 + h^2

dD/dt = 1/2(15^2 + h^2)^-1/2 (2h) dh/dt

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= (28.28 / √1024.7584)5

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= 0.88*5

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3 years ago
Efectuati impartirea 12xy:3x
adelina 88 [10]

In this question , we have to simplify the given ratio, which is

12xy:3x

First we have to see which factor is common in numerator and denominator,

We can write 12 as 3 times 4, that is

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So the common factor is 3x.

In the next step, we cancel out 3x

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And that's the required simplified form .

7 0
3 years ago
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