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dimulka [17.4K]
2 years ago
12

Find the exact length of side a

Mathematics
1 answer:
pantera1 [17]2 years ago
5 0

The figure is a scalene triangle, and the exact length of side a is √13

<h3>How to determine the exact length of side a?</h3>

To calculate the length of a, we make use of the following law of cosine

a² = b²  + c² - 2bc * cos(A)

Using the values in the figure, we have:

a² = 3√2²  + 5² - 2 * 3√2 * 5 * cos(45)

Evaluate the expression

a² = 18  + 25 - 30

Evaluate the sum and the difference

a² = 13

Take the square root of both sides

a = √13

Hence, the exact length of side a is √13

Read more about law of cosines at:

brainly.com/question/4372174

#SPJ1

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ZanzabumX [31]
Consider the function f(x)=x^{1/3}, which has derivative f'(x)=\dfrac13x^{-2/3}.

The linear approximation of f(x) for some value x within a neighborhood of x=c is given by

f(x)\approx f'(c)(x-c)+f(c)

Let c=64. Then (63.97)^{1/3} can be estimated to be

f(63.97)\approxf'(64)(63.97-64)+f(64)
\sqrt[3]{63.97}\approx4-\dfrac{0.03}{48}=3.999375

Since f'(x)>0 for x>0, it follows that f(x) must be strictly increasing over that part of its domain, which means the linear approximation lies strictly above the function f(x). This means the estimated value is an overestimation.

Indeed, the actual value is closer to the number 3.999374902...
4 0
3 years ago
A sandbox in the shape of a rectangular prism is 2 feet deep and 6 feet wide. Filled to the top it can hold 72 cubic feet of san
Sedbober [7]

Answer:

height=6 ft

Step-by-step explanation:

-The volume of a rectangular prism is given by the formula:

V=lwh

#We make h the subject of the formula the solve for it:

V=lwh\\\\\frac{V}{lw}=h\\\\\therefore h=\frac{V}{lw}

#Substitute to solve for height:

h=\frac{V}{lw}\\\\=\frac{72}{2\times 6}\\\\=6\ ft

Hence, the prism has a height of 6 ft.

6 0
3 years ago
Estimate 8978 x 38 by first rounding each number so that it has only 1 nonzero digit.​
Afina-wow [57]

Answer:

9,000 x 40 = 360,000

Step-by-step explanation:

9,000 x 40 = 360,000

A one nonzero digit is a number that has only one number that's not 0. For example, 300 has only one nonzero digit.

Hope this helps!

6 0
2 years ago
Given f(x) =3x+7 find f(5)
ra1l [238]

Answer:

22

Step-by-step explanation:

f (5)=3 (5)+7

f (5)=15+7

f (5)=22

8 0
3 years ago
Which area model can u use to fine * find 39 x73
sweet [91]
The area model you can use is D , cs 70 +3 & 30+9
3 0
3 years ago
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