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2 years ago

A rectangular box is 6 inches long, 5 inches wide and 7 inches tall. What is the approximate length of its longest diagonal?

Mathematics

2 answers:

xxTIMURxx [149]2 years ago

7 0

Answer:

10.5 inches

Step-by-step explanation:

The length of the longest diagonal is across two opposite points of the solid, namely

L = sqrt ( 6^2 + 5^2 + 7^2)

= sqrt (36+25+49)

= sqrt(110)

= 10.5"

V125BC [204]2 years ago

3 0

Answer:

im sorry i need points plz dont hate me for not answering and wasting you time

Step-by-step explanation:

truly sorry

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Which ratio is equivalent to 12 : 32? A. 48/128 B. 28/63 C. 7/15 D. 48/64

Sladkaya [172]

A because 12*4=48 and 32*4=128

4 0

3 years ago

The Council of American Beet Farmers estimate that 60% of Americans love beets.

harkovskaia [24]

Answer: 13% or 0.1314

Step-by-step explanation: Binomial PDF on the calculator or by hand its

22 nCr 15 (0.60)^15(1-0.6)^7 = 0.131378

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2 years ago

In the triangle pictured, let A, B, C be the angles at the three vertices, and let a,b,c be the sides opposite those angles. Acc

Troyanec [42]

Answer:

Step-by-step explanation:

(a)

Consider the following:

$A=\frac{\pi}{4}=45°\\\\B=\frac{\pi}{3}=60°$

Use sine rule,

$\frac{b}{a}=\frac{\sinB}{\sin A}
\\\\=\frac{\sin{\frac{\pi}{3}}
}{\sin{\frac{\pi}{4}}}\\\\=\frac{[\frac{\sqrt{3}}{2}]}{\frac{1}{\sqrt{2}}}\\\\=\frac{\sqrt{2}}{2}\times \frac{\sqrt{2}}{1}=\sqrt{\frac{3}{2}}$

Again consider,

$\frac{b}{a}=\frac{\sin{B}}{\sin{A}}
\\\\\sin{B}=\frac{b}{a}\times \sin{A}\\\\\sin{B}=\sqrt{\frac{3}{2}}\sin {A}\\\\B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{A}]$

Thus, the angle B is function of A is, $B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{A}]$

Now find $\frac{dB}{dA}$

Differentiate implicitly the function $\sin{B}=\sqrt{\frac{3}{2}}\sin{A}$ with respect to A to get,

$\cos {B}.\frac{dB}{dA}=\sqrt{\frac{3}{2}}\cos A\\\\\frac{dB}{dA}=\sqrt{\frac{3}{2}}.\frac{\cos A}{\cos B}$

When $A=\frac{\pi}{4},B=\frac{\pi}{3}$ , the value of $\frac{dB}{dA}$ is,

$\frac{dB}{dA}=\sqrt{\frac{3}{2}}.\frac{\cos {\frac{\pi}{4}}}{\cos {\frac{\pi}{3}}}\\\\=\sqrt{\frac{3}{2}}.\frac{\frac{1}{\sqrt{2}}}{\frac{1}{2}}\\\\=\sqrt{3}$

In general, the linear approximation at x= a is,

$f(x)=f'(x).(x-a)+f(a)$

Here the function $f(A)=B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{A}]$

At $A=\frac{\pi}{4}$

$f(\frac{\pi}{4})=B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{\frac{\pi}{4}}]\\\\=\sin^{-1}[\sqrt{\frac{3}{2}}.\frac{1}{\sqrt{2}}]\\\\\=\sin^{-1}(\frac{\sqrt{2}}{2})\\\\=\frac{\pi}{3}$

And,

$f'(A)=\frac{dB}{dA}=\sqrt{3}$ from part b

Therefore, the linear approximation at $A=\frac{\pi}{4}$ is,

$f(x)=f'(A).(x-A)+f(A)\\\\=f'(\frac{\pi}{4}).(x-\frac{\pi}{4})+f(\frac{\pi}{4})\\\\=\sqrt{3}.[x-\frac{\pi}{4}]+\frac{\pi}{3}$

Use part (c), when $A=46°$ , B is approximately,

$B=f(46°)=\sqrt{3}[46°-\frac{\pi}{4}]+\frac{\pi}{3}\\\\=\sqrt{3}(1°)+\frac{\pi}{3}\\\\=61.732°$

8 0

2 years ago

Distribute and combine like terms. Please show all of your work. -5(3x + 7) - 4(x - 4) + 11

Varvara68 [4.7K]

For this case we have the following expression:

$-5 (3x + 7) -4 (x-4) +11$

For simplicity we follow the steps:

We apply distributive property to the terms within the parenthesis, bearing in mind that:

$- * + = -\\- * - = +\\-15x-35-4x + 16 + 11 =$

We add similar terms taking into account that equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the major is placed.

$-15x-4x-35 + 16 + 11 =\\-19x-8$

ANswer:

$-19x-8$

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just olya [345]

I think it’s -4 but i’m not sure

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